These easy No Bake Pumpkin Cheesecake Bars have a cinnamon sugar crust that will make you swoon, and require just 15 minutes of work!
It's official! We are head first into fall!
The days are getting shorter, I've bought approximately 654267282 Halloween decoration things, and we have settled back into our weeknight routine. One thing that has yet to change though (at least over here in North Carolina), is the heat.
Which seems really unfair. I'm done with iced coffee; I want a hot triple latte to start my mornings. I want to bake muffins, wear jeans in the yard without melting, and dang do I ever want my flowers to stop dying from heat exhaustion.
So this week I set out to get my fall flavor fix without baking. The oven is still on hiatus for me.
I went all-in and made us a pumpkin spice cheesecake, and decided to get a little creative with the crust. Crushed cookies or sweetened cracker crust were forfeited for… cereal.
Cereal is one of my favorite surprise ingredients (like in these Peanut Butter Honey Cereal Bars and these Cereal Crunch Chocolate Peanut Butter Cookies).
For my No Bake Pumpkin Cheesecake Bars here I used Malt-O-Meal® Cinnamon Toasters AKA generic Cinnamon Toast Crunch. They gave the crust a snickerdoodle cinnamon sugar flavor without actually adding any additional cinnamon or sugar.
Also!! The bag is 24.4 ounces which means that even though I used 4 whole cups of cereal to make the cheesecake crust, there was still cereal left for my teenage boy monsters to eat in the morning.
I know you guys must be sick of my teen boy appetite complaints by now, but seriously. DO YOU EVEN KNOW HOW MUCH THEY EAT?!
Anyway. Buying cereal by the bag means it lasts more than one morning. Even when you are no-baking with it.
Place the cereal in a food processor and pulse until uniform crumbs form. If you do not have a food processor, you can place the cereal in a large Ziploc bag and then crush them inside the bag. Stir together the melted butter and the cereal crumbs together and then press into an ungreased 9 X 13 pan.
Beat together the cream cheese and sugars until fluffy. Spoon in the pumpkin, pumpkin pie spice, and vanilla, and beat until smooth.
Using a rubber spatula, gently fold in one container of the whipped topping until the batter is fluffy and smooth. Spread it over the crust and refrigerate for at least 3 hours or overnight.
After you have chilled the cheesecake, spread the remaining container of whipped topping over the top. Slice into 24 bars and serve.


text:
class InternalBillingObject < KFSDataObject

  include AccountingLinesMixin

  DOC_INFO = { label: 'Internal Billing', type_code: 'IB', transactional?: true, action_wait_time: 30 }

  attr_accessor :organization_document_number, :explanation

  def initialize(browser, opts={})
    @browser = browser

    defaults = { description: random_alphanums(40, 'AFT') }.merge!(default_accounting_lines)

    set_options(defaults.merge(get_aft_parameter_values_as_hash(ParameterConstants::DEFAULTS_FOR_INTERNAL_BILLING)).merge(opts))
  end

  def build
    visit(MainPage).internal_billing
    on InternalBillingPage do |page|
      page.expand_all
      page.description.focus
      page.alert.ok if page.alert.exists? # Because, y'know, sometimes it doesn't actually come up...
      fill_out page, :description, :organization_document_number, :explanation
    end
  end

end

redpajama_set_name: RedPajamaGithub


DHAKA: A five-day fair of the Real Estate and Housing Association of Bangladesh (REHAB) will begin at Bangabandhu International Conference Centre in the capital today.
Housing and Public Works Minister SM Rezaul Karim will formally inaugurate the fair while chairman of the National Board of Revenue Mosharraf Hossain Bhuiyan will be present.
"There will be a total of 202 stalls in the fair. About 20 building materials and 14 moneylender organisations will take part in fair," REHAB first Vice-President Liaquat Ali Bhuiyan told a press conference here yesterday.
On the first day, the visitors and buyers will be able to enter the fair from 2 pm. It will remain open from 10 am to 9 pm every day.
REHAB has been organising the fair for 18 years considering the customers facilities, which helps the buyers find out flats and plots of their own choice, Liaquat Ali said.
There will be arrangement for two types of ticket for entering the fairground, a single entry ticket at Taka 50 and multiple entries (up to five times) at Taka 100.
The fair will continue till February 10.


text:
Episode 55: A Labour of Love: International Wedding Cake-Maker Gillian Bell
Listen Here To talk to Gillian Bell about baking is to be swept along on a journey inspired by children's story book adventures and the true romances of the couples she bakes wedding cakes for. Like Mary Poppins herself, Gillian flies in to spread her special type of magic at weddings in far-flung destinations. Gillian doesn't know what she's going to bake for each occasion until she arrives and meets the happy couple; she says the recipe for a wedding cake that captures their unique and personal story appears to her as she gets to know them. Baking wedding cakes has taken Gillian from her home-base in Brisbane, Australia to such places as Sweden, France and Scotland, the US, Japan, China and more. Her cakes are breath-taking works of art but first and foremost, Gillian says, she wants them to be delicious. Most of her clients are well-travelled people who find her work through word of mouth, although there are certainly some Hollywood stars and landed gentry among her clients. In this episode of ExtraVirgin Podcast, we hear how her love of baking developed, and about her unique approach to creating a wedding cake, including why she starts baking at midnight on the eve of the wedding. She also shares tips for anyone who's a little nervous about baking but would like to give it a go. Her motto is "has whisk will travel" and there's a fair chance that listening to this episode will have you reaching for a whisk and a recipe too. Enjoy! Click here to listen. You may also be interested in checking out Gillian's own lovely podcast, Dispatch to a Friend, which she creates with her good friend Annabelle Hickson. The podcast is a heart-warming look into their lives through the letters they write each other while Gillian travels, whisk in hand, and writer Annabelle captures life on her pecan farm in north-western NSW. The podcast, like many things in Covid-effected 2020, is in hiatus but the back catalogue is worth dipping into while we wait for new episodes. Like Gillian's cakes, it's a tribute to travel, cooking, flowers and love. You can find Gillian at her website Gillian Bell Cake and on Instagram @gillianbell cake.

redpajama_set_name: RedPajamaCommonCrawl


text:
Compartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I,  or R, (Susceptible, Infectious, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again.

The origin of such models is the early 20th century, with important works being that of Ross in 1916, Ross and Hudson in 1917, Kermack and McKendrick in 1927 and Kendall in 1956. The Reed-Frost model was also a significant and widely-overlooked ancestor of modern epidemiological modelling approaches.

The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze.

Models try to predict things such as how a disease spreads, or the total number infected, or the duration of an epidemic, and to estimate various epidemiological parameters such as the reproductive number. Such models can show how different public health interventions may affect the outcome of the epidemic, e.g., what the most efficient technique is for issuing a limited number of vaccines in a given population.

The SIR model

The SIR model is one of the simplest compartmental models, and many models are derivatives of this basic form. The model consists of three compartments:
S: The number of susceptible individuals. When a susceptible and an infectious individual come into "infectious contact", the susceptible individual contracts the disease and transitions to the infectious compartment.
I: The number of infectious individuals. These are individuals who have been infected and are capable of infecting susceptible individuals.
R for the number of removed (and immune) or deceased individuals. These are individuals who have been infected and have either recovered from the disease and entered the removed compartment, or died. It is assumed that the number of deaths is negligible with respect to the total population. This compartment may also be called "recovered"  or "resistant".

This model is reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella.

These variables (S, I, and R) represent the number of people in each compartment at a particular time. To represent that the number of susceptible, infectious and removed individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control.

As implied by the variable function of t, the model is dynamic in that the numbers in each compartment may fluctuate over time. The importance of this dynamic aspect is most obvious in an endemic disease with a short infectious period, such as measles in the UK prior to the introduction of a vaccine in 1968. Such diseases tend to occur in cycles of outbreaks due to the variation in number of susceptibles (S(t)) over time. During an epidemic, the number of susceptible individuals falls rapidly as more of them are infected and thus enter the infectious and removed compartments. The disease cannot break out again until the number of susceptibles has built back up, e.g. as a result of offspring being born into the susceptible compartment.

Each member of the population typically progresses from susceptible to infectious to recovered. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.

Transition rates
For the full specification of the model, the arrows should be labeled with the transition rates between compartments. Between S and I, the transition rate is assumed to be d(S/N)/dt = -βSI/N2, where N is the total population, β is the average number of contacts per person per time, multiplied by the probability of disease transmission in a contact between a susceptible and an infectious subject, and SI/N2 is the fraction of those contacts between an infectious and susceptible individual which result in the susceptible person becoming infected. (This is mathematically similar to the law of mass action in chemistry in which random collisions between molecules result in a chemical reaction and the fractional rate is proportional to the concentration of the two reactants).

Between I and R, the transition rate is assumed to be proportional to the number of infectious individuals which is γI. This is equivalent to assuming that the probability of an infectious individual recovering in any time interval dt is simply γdt. If an individual is infectious for an average time period D, then γ = 1/D. This is also equivalent to the assumption that the length of time spent by an individual in the infectious state is a random variable with an exponential distribution. The "classical" SIR model may be modified by using more complex and realistic distributions for the I-R transition rate (e.g. the Erlang distribution).

For the special case in which there is no removal from the infectious compartment (γ=0), the SIR model reduces to a very simple SI model, which has a logistic solution, in which every individual eventually becomes infected.

The SIR model without birth and death

The dynamics of an epidemic, for example, the flu, are often much faster than the dynamics of birth and death, therefore, birth and death are often omitted in simple compartmental models.  The SIR system without so-called vital dynamics (birth and death, sometimes called demography) described above can be expressed by the following system of ordinary differential equations:

where  is the stock of susceptible population,  is the stock of infected,  is the stock of removed population (either by death or recovery), and  is the sum of these three.

This model was for the first time proposed by William Ogilvy Kermack and Anderson Gray McKendrick as a special case of what we now call Kermack–McKendrick theory, and followed work McKendrick had done with Ronald Ross.

This system is non-linear, however it is possible to derive its analytic solution in implicit form. Firstly note that from:

it follows that:

expressing in mathematical terms the constancy of population . Note that the above relationship implies that one need only study the equation for two of the three variables.

Secondly, we note that the dynamics of the infectious class depends on the following ratio:

the so-called basic reproduction number (also called basic reproduction ratio). This ratio is derived as the expected number of new infections (these new infections are sometimes called secondary infections) from a single infection in a population where all subjects are susceptible. This idea can probably be more readily seen if we say that the typical time between contacts is , and the typical time until removal is . From here it follows that, on average, the number of contacts by an infectious individual with others before the infectious has been removed is:

By dividing the first differential equation by the third, separating the variables and integrating we get

where  and  are the initial numbers of, respectively, susceptible and removed subjects.
Writing  for the initial proportion of susceptible individuals, and
 and
 for the proportion of susceptible and removed individuals respectively
in the limit  one has

(note that the infectious compartment empties in this limit).
This transcendental equation has a solution in terms of the Lambert  function, namely

This shows that at the end of an epidemic that conforms to the simple assumptions of the SIR model, unless , not all individuals of the population have been removed, so some must remain susceptible. A driving force leading to the end of an epidemic is a decline in the number of infectious individuals. The epidemic does not typically end because of a complete lack of susceptible individuals.

The role of both the basic reproduction number and the initial susceptibility are extremely important. In fact, upon rewriting the equation for infectious individuals as follows:

it yields that if:

then:

i.e., there will be a proper epidemic outbreak with an increase of the number of the  infectious (which can reach a considerable fraction of the population). On the contrary, if

then

i.e., independently from the initial size of the susceptible population the disease can never cause a proper epidemic outbreak. As a consequence, it is clear that both the basic reproduction number and the initial susceptibility are extremely important.

The force of infection

Note that in the above model the function:

models the transition rate from the compartment of susceptible individuals to the compartment of infectious individuals, so that it is called the force of infection. However, for large classes of communicable diseases it is more realistic to consider a force of infection that does not depend on the absolute number of infectious subjects, but on their fraction (with respect to the total constant population ):

Capasso and, afterwards, other authors have proposed nonlinear forces of infection to model more realistically the contagion process.

Exact analytical solutions to the SIR model
In 2014, Harko and coauthors derived an exact so-called analytical solution (involving an integral that can only be calculated numerically) to the SIR model. In the case  without vital dynamics setup, for , etc., it corresponds to the following time parametrization

for

with initial conditions

where  satisfies . By the transcendental equation for  above, it follows that , if  and .

An equivalent so-called analytical solution (involving an integral that can only be calculated numerically) found by Miller yields

Here  can be interpreted as the expected number of transmissions an individual has received by time .  The two solutions are related by .

Effectively the same result can be found in the original work by Kermack and McKendrick.

These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to . The equations may thus be divided through by , and the time rescaled so that the differential operator on the left-hand side becomes simply , where , i.e. . The differential equations are now all linear, and the third equation, of the form  const., shows that  and  (and  above) are simply linearly related.

A highly accurate analytic approximant of the SIR model as well as exact analytic expressions for the final values , , and  were provided by Kröger and Schlickeiser, so that there is no need to perform a numerical integration to solve the SIR model (a simplified example practice on COVID-19 numerical simulation using Microsoft Excel can be found here ), to obtain its parameters from existing data, or to predict the future dynamics of an epidemics modeled by the SIR model. The approximant involves the Lambert  function which is part of all basic data visualization software such as Microsoft Excel, MATLAB, and Mathematica.

While Kendall considered the so-called all-time SIR model where the initial conditions , , and  are coupled through the above relations, Kermack and McKendrick proposed to study the more general semi-time case, for which  and  are both arbitrary. This latter version, denoted as semi-time SIR model, makes predictions only for future times . An analytic approximant and exact expressions for the final values are available for the semi-time SIR model as well.

Numerical solutions to the SIR model with approximations
Numerical solutions to the SIR model can be found in the literature. An example is using the model to analyze COVID-19 spreading data.   Three reproduction numbers can be pulled out from the data analyzed with numerical approximation,
the basic reproduction number:

the real-time reproduction number:

and the real-time effective reproduction number:

 represents the speed of reproduction rate at the beginning of the spreading when all populations are assumed susceptible, e.g. if  and  meaning one infectious person on average infects 0.4 susceptible people per day and recovers in 1/0.2=5 days. Thus when this person recovered, there are two people still infectious directly got from this person and , i.e. the number of infectious people doubled in one cycle of 5 days. The data simulated by the model with  or real data fitted will yield a doubling of the number of infectious people faster than 5 days because the two infected people are infecting people. From the SIR model, we can tell that  is determined by the nature of the disease and also a function of the interactive frequency between the infectious person  with the susceptible people  and also the intensity/duration of the interaction like how close they interact for how long and whether or not they both wear masks, thus, it changes over time when the average behavior of the carriers and susceptible people changes. The model use  to represent these factors but it indeed is referenced to the initial stage when no action is taken to prevent the spread and all population is susceptible, thus all changes are absorbed by the change of .

 is usually more stable over time assuming when the infectious person shows symptoms, she/he will seek medical attention or be self-isolated. So if we find  changes, most probably the behaviors of people in the community have changed from their normal patterns before the outbreak, or the disease has mutated to a new form. Costive massive detection and isolation of susceptible close contacts have effects on reducing  but whose efficiencies are under debate. This debate is largely on the uncertainty of the number of days reduced from after infectious or detectable whichever comes first to before a symptom shows up for an infected susceptible person. If the person is infectious after symptoms show up, or detection only works for a person with symptoms, then these prevention methods are not necessary, and self-isolation and/or medical attention is the best way to cut the  values. The typical onset of the COVID-19 infectious period is in the order of one day from the symptoms showing up, making massive detection with typical frequency in a few days useless.

 does not tell us whether or not the spreading will speed up or slow down in the latter stages when the fraction of susceptible people in the community has dropped significantly after recovery or vaccination.  corrects this dilution effect by multiplying the fraction of the susceptible population over the total population. It corrects the effective/transmissible interaction between an infectious person and the rest of the community when many of the interaction is immune in the middle to late stages of the disease spreading. Thus, when , we will see an exponential-like outbreak; when , a steady state reached and no number of infectious people changes over time; and when , the disease decays and fades away over time.

Using the differential equations of the SIR model and converting them to numerical discrete forms, one can set up the recursive equations and calculate the S, I, and R populations with any given initial conditions but accumulate errors over a long calculation time from the reference point. Sometimes a convergence test is needed to estimate the errors. Given a set of initial conditions and the disease-spreading data, one can also fit the data with the SIR model and pull out the three reproduction numbers when the errors are usually negligible due to the short time step from the reference point. Any point of the time can be used as the initial condition to predict the future after it using this numerical model with assumption of time-evolved parameters such as population, , and . However, away from this reference point, errors will accumulate over time thus convergence test is needed to find an optimal time step for more accurate results.

Among these three reproduction numbers,  is very useful to judge the control pressure, e.g., a large value meaning the disease will spread very fast and is very difficult to control.  is most useful in predicting future trends, for example, if we know the social interactions have reduced 50% frequently from that before the outbreak and the interaction intensities among people are the same, then we can set . If social distancing and masks add another 50% cut in infection efficiency, we can set .  will perfectly correlate with the waves of the spreading and whenever , the spreading accelerates, and when , the spreading slows down thus useful to set a prediction on the short term trends. Also, it can be used to directly calculate the threshold population of vaccination/immunization for the herd immunity stage by setting .

The SIR model with vital dynamics and constant population

Consider a population characterized by a death rate  and birth rate , and where a communicable disease is spreading. The model with mass-action transmission is:

for which the disease-free equilibrium (DFE) is:

In this case, we can derive a basic reproduction number:

which has threshold properties. In fact, independently from biologically meaningful initial values, one can show that:

The point EE is called the Endemic Equilibrium (the disease is not totally eradicated and remains in the population). With heuristic arguments, one may show that  may be read as the average number of infections caused by a single infectious subject in a wholly susceptible population, the above relationship biologically means that if this number is less than or equal to one the disease goes extinct, whereas if this number is greater than one the disease will remain permanently endemic in the population.

The SIR model

In 1927, W. O. Kermack and A. G. McKendrick created a model in which they considered a fixed population with only three compartments: susceptible, ; infected, ; and recovered, . The compartments used for this model consist of three classes:
  is used to represent the individuals not yet infected with the disease at time t, or those susceptible to the disease of the population.
  denotes the individuals of the population who have been infected with the disease and are capable of spreading the disease to those in the susceptible category.
  is the compartment used for the individuals of the population who have been infected and then removed from the disease, either due to immunization or due to death. Those in this category are not able to be infected again or to transmit the infection to others.
The flow of this model may be considered as follows:

Using a fixed population,  in the three functions resolves that the value  should remain constant within the simulation, if a simulation is used to solve the SIR model. Alternatively, the analytic approximant can be used without performing a simulation. The model is started with values of ,  and . These are the number of people in the susceptible, infected and removed categories at time equals zero. If the SIR model is assumed to hold at all times, these initial conditions are not independent. Subsequently, the flow model updates the three variables for every time point with set values for  and . The simulation first updates the infected from the susceptible and then the removed category is updated from the infected category for the next time point (t=1). This describes the flow persons between the three categories. During an epidemic the susceptible category is not shifted with this model,  changes over the course of the epidemic and so does . These variables determine the length of the epidemic and would have to be updated with each cycle.

Several assumptions were made in the formulation of these equations: First, an individual in the population must be considered as having an equal probability as every other individual of contracting the disease with a rate of  and an equal fraction  of people that an individual makes contact with per unit time. Then, let  be the multiplication of  and . This is the transmission probability times the contact rate. Besides, an infected individual makes contact with  persons per unit time whereas only a fraction,  of them are susceptible. Thus, we have every infective can infect  susceptible persons, and therefore, the whole number of susceptibles infected by infectives per unit time is . For the second and third equations, consider the population leaving the susceptible class as equal to the number entering the infected class. However, a number equal to the fraction  (which represents the mean recovery/death rate, or  the mean infective period) of infectives are leaving this class per unit time to enter the removed class. These processes which occur simultaneously are referred to as the Law of Mass Action, a widely accepted idea that the rate of contact between two groups in a population is proportional to the size of each of the groups concerned. Finally, it is assumed that the rate of infection and recovery is much faster than the time scale of births and deaths and therefore, these factors are ignored in this model.

Steady-state solutions
The expected duration of susceptibility will be  where  reflects the time alive (life expectancy) and  reflects the time in the susceptible state before becoming infected, which can be simplified to:

such that the number of susceptible persons is the number entering the susceptible compartment  times the duration of susceptibility:

Analogously, the steady-state number of infected persons is the number entering the infected state from the susceptible state (number susceptible, times rate of infection)  times the duration of infectiousness :

Other compartmental models
There are many modifications of the SIR model, including those that include births and deaths, where upon recovery there is no immunity (SIS model), where immunity lasts only for a short period of time (SIRS), where there is a latent period of the disease where the person is not infectious (SEIS and SEIR), and where infants can be born with immunity (MSIR). Compartmental models can also be used to model multiple risk groups, and even the interaction of multiple pathogens.

Variations on the basic SIR model

The SIS model

Some infections, for example, those from the common cold and influenza, do not confer any long-lasting immunity. Such infections may give temporary resistance but do not give long-term immunity upon recovery from infection, and individuals become susceptible again.

We have the model:

Note that denoting with N the total population it holds that:

.

It follows that:

,

i.e. the dynamics of infectious is ruled by a logistic function, so that :

It is possible to find an analytical solution to this model (by making a transformation of variables:  and substituting this into the mean-field equations), such that the basic reproduction rate is greater than unity. The solution is given as

.

where  is the endemic infectious population, , and . As the system is assumed to be closed, the susceptible population is then .

Whenever the integer nature of the number of agents is evident (populations with fewer than tens of thousands of individuals), inherent fluctuations in the disease spreading process caused by discrete agents result in uncertainties. In this scenario, the evolution of the disease predicted by compartmental equations deviates significantly from the observed results. These uncertainties may even cause the epidemic to end earlier than predicted by the compartmental equations.

As a special case, one obtains the usual logistic function by assuming . This can be also considered in the SIR model with , i.e. no removal will take place. That is the SI model. The differential equation system using  thus reduces to:

In the long run, in the SI model, all individuals will become infected.

The SIRD model

The Susceptible-Infectious-Recovered-Deceased model differentiates between Recovered (meaning specifically individuals having survived the disease and now immune) and Deceased. This model uses the following system of differential equations:

where  are the rates of infection, recovery, and mortality, respectively.

The SIRV model
The Susceptible-Infectious-Recovered-Vaccinated model is an extended SIR model that accounts for vaccination of the susceptible population. This model uses the following system of differential equations:

where  are the rates of infection, recovery, and vaccination, respectively. For the semi-time initial conditions , ,  and constant ratios  and  the model had been solved approximately. The occurrence of a pandemic outburst requires  and there is a critical reduced vaccination rate  beyond which the steady-state size of the susceptible compartment remains relatively close to . Arbitrary initial conditions satisfying  can be mapped to the solved special case with .

The numerical solution of this model to calculate the real-time reproduction number  of COVID-19 can be practiced based on information from the different populations in a community. Numerical solution is a commonly used method to analyze complicated kinetic networks when the analytical solution is difficult to obtain or limited by requirements such as boundary conditions or special parameters. It uses recursive equations to calculate the next step by converting the numerical integration into Riemann sum of discrete time steps e.g., use yesterday's principal and interest rate to calculate today's interest which assumes the interest rate is fixed during the day. The calculation contains projected errors if the analytical corrections on the numerical step size are not included, e.g. when the interest rate of annual collection is simplified to 12 times the monthly rate, a projected error is introduced. Thus the calculated results will carry accumulative errors when the time step is far away from the reference point and a convergence test is needed to estimate the error. However, this error is usually acceptable for data fitting. When fitting a set of data with a close time step, the error is relatively small because the reference point is nearby compared to when predicting a long period of time after a reference point. Once the real-time  is pulled out, one can compare it to the basic reproduction number . Before the vaccination,  gives the policy maker and general public a measure of the efficiency of social mitigation activities such as social distancing and face masking simply by dividing . Under massive vaccination, the goal of disease control is to reduce the effective reproduction number , where  is the number of susceptible population at the time and  is the total population. When , the spreading decays and daily infected cases go down.

The MSIR model
For many infections, including measles, babies are not born into the susceptible compartment but are immune to the disease for the first few months of life due to protection from maternal antibodies (passed across the placenta and additionally through colostrum). This is called passive immunity. This added detail can be shown by including an M class (for maternally derived immunity) at the beginning of the model.

To indicate this mathematically, an additional compartment is added, M(t). This results in the following differential equations:

Carrier state

Some people who have had an infectious disease such as tuberculosis never completely recover and continue to carry the infection, whilst not suffering the disease themselves. They may then move back into the infectious compartment and suffer symptoms (as in tuberculosis) or they may continue to infect others in their carrier state, while not suffering symptoms. The most famous example of this is probably Mary Mallon, who infected 22 people with typhoid fever. The carrier compartment is labelled C.

The SEIR model

For many important infections, there is a significant latency period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed).

Assuming that the latency period is a random variable with exponential distribution with parameter  (i.e. the average latency period is ), and also assuming the presence of vital dynamics with birth rate  equal to death rate  (so that the total number  is constant), we have the model:

We have  but this is only constant because of the simplifying assumption that birth and death rates are equal; in general  is a variable.

For this model, the basic reproduction number is:

Similarly to the SIR model, also, in this case, we have a Disease-Free-Equilibrium (N,0,0,0) and an Endemic Equilibrium EE, and one can show that, independently from biologically meaningful initial conditions

it holds that:

In case of periodically varying contact rate  the condition for the global attractiveness of DFE is that the following linear system with periodic coefficients:

is stable (i.e. it has its Floquet's eigenvalues inside the unit circle in the complex plane).

The SEIS model
The SEIS model is like the SEIR model (above) except that no immunity is acquired at the end.

In this model an infection does not leave any immunity thus individuals that have recovered return to being susceptible, moving back into the S(t) compartment.  The following differential equations describe this model:

The MSEIR model
For the case of a disease, with the factors of passive immunity, and a latency period there is the MSEIR model.

The MSEIRS model
An MSEIRS model is similar to the MSEIR, but the immunity in the R class would be temporary, so that individuals would regain their susceptibility when the temporary immunity ended.

Variable contact rates
It is well known that the probability of getting a disease is not constant in time. As a pandemic progresses, reactions to the pandemic may change the contact rates which are assumed constant in the simpler models. Counter-measures such as masks, social distancing and lockdown will alter the contact rate in a way to reduce the speed of the pandemic.

In addition, Some diseases are seasonal, such as the common cold viruses, which are more prevalent during winter.  With childhood diseases, such as measles, mumps, and rubella, there is a strong correlation with the school calendar, so that during the school holidays the probability of getting such a disease dramatically decreases. As a consequence, for many classes of diseases, one should consider a force of infection with periodically ('seasonal') varying contact rate

with period T equal to one year.

Thus, our model becomes

(the dynamics of recovered easily follows from ), i.e. a nonlinear set of differential equations with periodically varying parameters. It is well known that this class of dynamical systems may undergo very interesting and complex phenomena of  nonlinear parametric resonance. It is easy to see that if:

whereas if the integral is greater than one the disease will not die out and there may be such resonances. For example, considering the periodically varying contact rate as the 'input' of the system one has that the output is a periodic function whose period is a multiple of the period of the input.
This allowed to give a contribution to explain the poly-annual (typically biennial) epidemic outbreaks of some infectious diseases as interplay between the period of the contact rate oscillations and the pseudo-period of the damped oscillations near the endemic equilibrium. Remarkably, in some cases, the behavior may also be quasi-periodic or even chaotic.

SIR model with diffusion
Spatiotemporal compartmental models describe not the total number, but the density of susceptible/infective/recovered persons. Consequently, they also allow to model the distribution of infected persons in space. In most cases, this is done by combining the SIR model with a diffusion equation

where ,  and  are diffusion constants. Thereby, one obtains a reaction-diffusion equation. (Note that, for dimensional reasons, the parameter  has to be changed compared to the simple SIR model.) Early models of this type have been used to model the spread of the black death in Europe. Extensions of this model have been used to incorporate, e.g., effects of nonpharmaceutical interventions such as social distancing.

Interacting Subpopulation SEIR Model

As social contacts, disease severity and lethality, as well as the efficacy of prophylactic measures may differ substantially between interacting subpopulations, e.g., the elderly versus the young, separate SEIR models for each subgroup may be used  that are mutually connected through interaction links. Such Interacting Subpopulation SEIR models have been used for modeling the COVID-19 pandemic at continent scale to develop personalized, accelerated, subpopulation-targeted vaccination strategies that promise a shortening of the pandemic and a reduction of case and death counts in the setting of limited access to vaccines during a wave of virus Variants of Concern.

SIR Model on Networks
The SIR model has been studied on networks of various kinds in order to model a more realistic form of connection than the homogeneous mixing condition which is usually required. A simple model for epidemics on networks in which an individual has a probability p of being infected by each of his infected neighbors in a given time step leads to results similar to giant component formation on Erdos Renyi random graphs.

SIRSS model - combination of SIR with modelling of social stress

Dynamics of epidemics depend on how people's behavior changes in time. For example, at the beginning of the epidemic, people are ignorant and careless, then, after the outbreak of epidemics and alarm, they begin to comply with the various restrictions and the spreading of epidemics may decline. Over time, some people get tired/frustrated by the restrictions and stop following them (exhaustion), especially if the number of new cases drops down. After resting for some time, they can follow the restrictions again. But during this pause the second wave can come and become even stronger than the first one. Social dynamics should be considered. The social physics models of social stress complement the classical epidemics models.

The simplest SIR-social stress (SIRSS) model is organised as follows. The susceptible individuals (S) can be split in three subgroups by the types of behavior: ignorant or unaware of the epidemic (Sign), rationally resistant (Sres), and exhausted (Sexh) that do not react on the external stimuli (this is a sort of refractory period). In other words: S(t) = Sign(t) + Sres(t) + Sexh(t). Symbolically, the social stress model can be presented by the "reaction scheme" (where I denotes the infected individuals):
  – mobilization reaction (the autocatalytic form here means that the transition rate is proportional to the square of the infected fraction I);
  – exhaustion process due to fatigue from anti-epidemic restrictions;
  – slow relaxation to the initial state (end of the refractory period).

The main SIR epidemic reaction

has different reaction rate constants  for Sign,  Sres, and Sexh. Presumably, for Sres,  is lower than for Sign and Sign.

The differences between countries are concentrated in two kinetic constants: the rate of mobilization and the rate of exhaustion calculated for COVID-19 epidemic in 13 countries. These constants for this epidemic in all countries can be extracted by the fitting of the SIRSS model to publicly available data

The KdV-SIR equation
Based on the classical SIR model, a Korteweg-de Vries (KdV)–SIR equation and its analytical solution have been proposed to illustrate the fundamental dynamics of an epidemic wave, the dependence of solutions on parameters, and the dependence of predictability horizons on various types of solutions. The KdV-SIR equation is written as follows:

.

Here,

,

,

and

.

 indicates the initial value of the state variable . Parameters (σ-naught) and  (R-naught) are the time-independent relative growth rate and basic reproduction number, respectively.  presents the maximum of the state variables  (for the number of infected persons). An analytical solution to the KdV-SIR equation is written as follows:

,

which represents a solitary wave solution.

Modelling vaccination
The SIR model can be modified to model vaccination. Typically these introduce an additional compartment to the SIR model, , for vaccinated individuals. Below are some examples.

Vaccinating newborns
In presence of a communicable diseases, one of the main tasks is that of eradicating it via  prevention measures and, if possible, via the establishment of a mass vaccination program. Consider a disease for which the newborn are vaccinated (with a vaccine giving lifelong immunity) at a rate :

where  is the class of vaccinated subjects. It is immediate to show that:

thus we shall deal with the long term behavior of  and , for which it holds that:

In other words, if

the vaccination program is not successful in eradicating the disease, on the contrary, it will remain endemic, although at lower levels than the case of absence of vaccinations. This means that the mathematical model suggests that for a disease whose basic reproduction number may be as high as 18 one should vaccinate at least 94.4% of newborns in order to eradicate the disease.

Vaccination and information
Modern societies are facing the challenge of "rational" exemption, i.e. the family's decision to not vaccinate children as a consequence of a "rational" comparison between the perceived risk from infection and that from getting damages from the vaccine. In order to assess whether this behavior is really rational, i.e. if it can equally lead to the eradication of the disease,  one may simply assume that the vaccination rate is an increasing function of the number of infectious subjects:

In such a case the eradication condition becomes:

i.e. the baseline vaccination rate should be greater than the "mandatory vaccination" threshold, which, in case of exemption, cannot hold. Thus, "rational" exemption might be myopic since it is based only on the current low incidence due to high vaccine coverage, instead taking into account future resurgence of infection due to coverage decline.

Vaccination of non-newborns
In case there also are vaccinations of non newborns at a rate ρ the equation for the susceptible and vaccinated subject has to be modified as follows:

leading to the following eradication condition:

Pulse vaccination strategy
This strategy repeatedly vaccinates a defined age-cohort (such as young children or the elderly) in a susceptible population over time. Using this strategy, the block of susceptible individuals is then immediately removed, making it possible to eliminate an infectious disease, (such as measles), from the entire population. Every T time units a constant fraction p of susceptible subjects is vaccinated in a relatively short (with respect to the dynamics of the disease) time. This leads to the following impulsive differential equations for the susceptible and vaccinated subjects:

It is easy to see that by setting  one obtains that the dynamics of the susceptible subjects is given by:

and that the eradication condition is:

The influence of age: age-structured models
Age has a deep influence on the disease spread rate in a population, especially the contact rate. This rate summarizes the effectiveness of contacts between susceptible and infectious subjects. Taking into account the ages of the epidemic classes  (to limit ourselves to the susceptible-infectious-removed scheme) such that:

(where  is the maximum admissible age) and their dynamics is not described, as one might think, by "simple" partial differential equations, but by integro-differential equations:

where:

is the force of infection, which, of course, will depend, though the contact kernel  on the interactions between the ages.

Complexity is added by the initial conditions for newborns (i.e. for a=0), that are straightforward for infectious and removed:

but that are nonlocal for the density of susceptible newborns:

where  are the fertilities of the adults.

Moreover, defining now the density of the total population   one obtains:

In the simplest case of equal fertilities in the three epidemic classes, we have that in order to have demographic equilibrium the following necessary and sufficient condition linking the fertility  with the mortality  must hold:

and the demographic equilibrium is

automatically ensuring the existence of the disease-free solution:

A basic reproduction number can be calculated as the spectral radius of an appropriate functional operator.

Other considerations within compartmental epidemic models

Vertical transmission
In the case of some diseases such as AIDS and Hepatitis B, it is possible for the offspring of infected parents to be born infected.  This transmission of the disease down from the mother is referred to as vertical transmission. The influx of additional members into the infected category can be considered within the model by including a fraction of the newborn members in the infected compartment.

Vector transmission
Diseases transmitted from human to human indirectly, i.e. malaria spread by way of mosquitoes, are transmitted through a vector.  In these cases, the infection transfers from human to insect and an epidemic model must include both species, generally requiring many more compartments than a model for direct transmission.

Others
Other occurrences which may need to be considered when modeling an epidemic include things such as the following:
Non-homogeneous mixing
Variable infectivity
Distributions that are spatially non-uniform
Diseases caused by macroparasites

Deterministic versus stochastic epidemic models
It is important to stress that the deterministic models presented here are valid only in case of sufficiently large populations, and as such should be used cautiously.

To be more precise, these models are only valid in the thermodynamic limit, where the population is effectively infinite. In stochastic models, the long-time endemic equilibrium derived above, does not hold, as there is a finite probability that the number of infected individuals drops below one in a system. In a true system then, the pathogen may not propagate, as no host will be infected. But, in deterministic mean-field models, the number of infected can take on real, namely, non-integer values of infected hosts, and the number of hosts in the model can be less than one, but more than zero, thereby allowing the pathogen in the model to propagate. The reliability of compartmental models is limited to compartmental applications.

One of the possible extensions of mean-field models considers the spreading of epidemics on a network based on percolation theory concepts. Stochastic epidemic models have been studied on different networks and more recently applied to the COVID-19 pandemic.

See also
Mathematical modelling in epidemiology
Flatten the curve
Modifiable areal unit problem
Next-generation matrix
Risk assessment
Attack rate
List of COVID-19 simulation models

References

Further reading

External links
 SIR model: Online experiments with JSXGraph

Epidemiology
Scientific models

redpajama_set_name: RedPajamaWikipedia


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Home / Categories / Advertising Essay / Paper On Production And Cost Analysis
Paper On Production And Cost Analysis
Pages: 5 Words: 1415 Downloads: 10 Date added: 2017/09/23
Production and Cost Analysis Please read this article and answer the questions keeping in mind the information we have covered in the textbook: Fundamentals of Managerial Economics by Mark Hirschey (at least a good paragraph for each question) Article #1: Supersizing Hits Freight World By JENNIFER LEVITZ AUGUST 15, 2010, The Wall Street Journal When Kraft Foods Inc. packs trucks with weighty items such as jars of Miracle Whip and pouches of Capri Sun juice, 40% of the rigs must leave the loading dock partly empty to avoid exceeding federal truck weight limits. Kraft says those rules force it and others to make extra trips and spend more on fuel. Now, the Illinois food giant is part of a coalition of 150 companies lobbying Congress to allow trucks that are 20% heavier on U. S. highways. Supporters of the idea say truckers could pay an extra fee to offset road repairs. Some 19 Western governors wants Congress to allow for more giant trailers, like this "triple" tractor trailer. There is an arms race of sorts in the shipping industry—and it is prompting a backlash. Efforts are under way to supersize trucks, trains, and cargo ships as freight haulers look to move more goods in fewer trips. Driving the trend are rising fuel costs, an emphasis on reducing carbon footprints and capacity constraints created during the recession as freight movers scaled down, said Paul Bingham, managing director of transportation markets for the research firm IHS Global Insights. Road-safety officials say rigs are big enough now. "It's insane," said Deputy Chris Rizzo, a truck inspector for Loudon County, Va. , of efforts to increase the weight limits set by Congress in 1974. "I can actually feel bridges bouncing up and down" when trucks go over them, he said. The heavier the truck, the more the bridge bounces. " Earlier this year, California safety regulators were alarmed when a record-setting, 3. 4-mile train—two to three times the length of a typical freight train—rolled through Southern California. Witnesses dubbed it "the monster train" and posted videos online. It turned out to be a test by Union Pacific Corp. , which increased the length of its intermodal trains 15% in the first quarter, and was experimenting with an even longer train. Richard Clark, director of safety for the California Public Utilities Commission, said there was no otice of the experimental train, and the agency didn't realize it would be that long. "We were surprised," he said. Longer trains raise concerns about blocked rail crossings, especially when emergency vehicles need to cross tracks, and about whether trains can safely make turns, he said. A Union Pacific spokesman said the company did make required federal notifications but "in hindsight, we probably should have made the courtesy call" to state agencies also. Union Pacific said the ultra-long train was a one-time test. But in an April earnings conference call, a company official said Union Pacific believes it can increase its average train length by another 10% to 15% in an effort to reduce fuel use and emissions as well as wear and tear on its tracks.
Juvenile vs. Adult Criminal System
Due to the advance of youth development age and impact of frequent acceptance of the violence culture. The violence behavior carried by the minor under age 18 gradually increased which not only affects the victims but also jeopardizes the community. Therefore, the issues and debate around the how to punish the juvenile was been bring [...]
Juvenile Justice Essay Pages: 2 Words: 627 Downloads: 4 Date added: 2019/07/08
Reclutamiento y selección de personal
INTRODUCCION En el desarrollo de nuestra investigación trataremos de analizar y determinar las Incidencias de Agencias de Recursos Humanos en los Procesos de Reclutamiento y Selección del Personal en Empresas de República Dominicana enfocándonos específicamente en el Caso Adecco Dominicana. En el Primer Capítulo, se presentarán los Aspectos Generales de los Recursos Humanos, para así [...]
Pages: 53 Words: 15886 Downloads: 5 Date added: 2017/06/26
The Most Famous Series Of Witch Trials
The Salem Witch trials were a series of immoral injustices among a small village known as Salem. In the trials, a few young girls convinced the entire population of the village that witches lived among them and, in turn, doomed dozens into a position of death or imprisonment with no evidence of their claims. They [...]
Salem Witch Trials Essay Pages: 3 Words: 780 Downloads: 9 Date added: 2019/05/28


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Chinese President Xi Jinping and his Zimbabwean counterpart Emmerson Mnangagwa on Tuesday agreed to establish a comprehensive strategic partnership of cooperation between their countries.
The two heads of state reached the agreement during their talks at the Great Hall of the People in Beijing.
Xi said the Zimbabwean people have started a new journey in building their country since Mnangagwa took office last November.
"As a good friend, partner and brother of Zimbabwe, we are glad to see that," Xi told Mnangagwa.
Hailing the long-term close relationship between the two countries, Xi said the development of China-Zimbabwe ties is facing new opportunities.
China stands ready to work with Zimbabwe to jointly lay out the new blueprint of bilateral cooperation to continue the relationship and better benefit the two peoples, Xi said.
Calling Mnangagwa "an old friend of the Chinese people who has been long committed to the cause of China-Zimbabwe friendship," Xi said that the visit by Mnangagwa, who chose China as the first non-African country to visit, demonstrates the high importance he attaches to bilateral ties.
China and Zimbabwe are "all-weather friends," said Xi, stressing that the two countries have always weathered hard times together, no matter how the international landscape changes. He added that the bilateral friendship will emerge even fresher and stronger.
He called on both sides to maintain the momentum of high-level exchanges and exchanges at all levels, carry out top-level planning in various areas of cooperation and continue to understand and support each other on issues regarding core interests and major concerns.
Xi also encouraged both sides to dovetail development strategies, enhance cooperation on the Belt and Road Initiative and within the framework of the Forum on China-Africa Cooperation (FOCAC), and continue to promote cooperation in infrastructure construction, agriculture, investment and financing.
China supports Zimbabwe in exploring a development path in line with its own national conditions, he said.
The two countries should also enhance people-to-people and cultural exchanges so as to consolidate the public opinion foundation of both sides, Xi said.
China is willing to strengthen coordination and cooperation in regional and international affairs, said Xi, calling on Western countries and organizations to improve relations with Zimbabwe at an early date.
Mnangagwa, who is on a state visit to China from April 2 to 6 at the invitation of Xi, congratulated Xi once again on his election as Chinese president.
Speaking highly of Xi's vision and foresight on state governance, Mnangagwa said Xi Jinping Thought on Socialism with Chinese Characteristics for a New Era greatly inspired Zimbabwe to take a development path with its own characteristics.
He said he remembered clearly his study in China in the 1960s, expressing admiration for the achievements the Communist Party of China (CPC) and the country have scored in past decades.
Noting that Zimbabwe-China friendship has endured the tests of time and change, Mnangagwa said his country and people will never forget China's long-term assistance and support for improving people's livelihood.
Zimbabwe will adhere to the one-China policy and promote the comprehensive strategic partnership of cooperation with China, enhance exchanges of views on state governance and expand cooperation in areas including trade, investment, technology, telecommunication, infrastructure and people-to-people exchanges, said Mnangagwa.
Zimbabwe stands committed to deepening Africa-China friendship, supports China's Belt and Road Initiative and cooperation under the FOCAC framework and encourages Africa to take an active part in Belt and Road construction, he said.
Calling China-Africa friendship the "precious wealth of both sides," Xi said that as stated at the 19th CPC National Congress, China will work with all countries to build a new type of international relations and a community with a shared future for humanity, and it will enhance unity and cooperation with developing countries, including African countries.
"No matter how the international situation changes and to what stage China develops, China will, as always, stand with all developing countries, including African countries, and be a sincere friend and a reliable partner of Africa," Xi said.
After the talks, the two presidents witnessed the signing of bilateral documents on economic and technology cooperation, agriculture, science and technology and human resources.


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The Cliffhanger, Jan. 25
Today's news includes a HUGE protest the media doesn't like to cover.
Ever since the language of the �??fiscal cliff�?� was appropriated to describe the political battle over a tax increase, it�??s become increasingly clear that every issue is a �??cliff�?� now. Here are today�??s snapshots from the edge�?�
** March for Life fills Washington, driving reporters from the streets: Today is the annual March for Life, in which half a million pro-life demonstrators will form up between 7th and 9th streets in Washington and march past the Supreme Court building, somehow managing to find every place a camera is not pointing along the way. Since this is the 40th anniversary of Roe vs. Wade, a healthy turnout can be expected. The "abortion cliff" is looking pretty steep these days.
"Please dispose of your trash properly," March for Life organizers instruct, at the very top of their website. "Use the receptacles on the mall. If you can't find a receptacle, or if the receptacles are full, please take your trash with you–do not leave it on top of, or on the ground next to, a full trash can. Do not leave trash anywhere on the mall where someone else will have to pick it up." Maybe that's why they get so much less coverage than the relatively tiny Occupy Wall Street demonstration that the media obsessed over for months.
** Second anniversary of Tahrir Square uprising observed: Not only is the 40th anniversary of Roe v. Wade upon us, but it's also the second anniversary of the Tahrir Square uprising. Not everyone is celebrating. At least one protester has been marching around the square with a sign calling U.S. President Barack Obama an "idiot" for helping the Muslim Brotherhood seize power, and now the Brotherhood is "killing Egyptians." He's probably just an agent of that Jewish media conspiracy that Egypt's Muslim Brotherhood president, Mohammed Morsi, was warning the United States Senate about the other day.
** More gun control legislation heading our way: Republican Senator Mark Kirk of Illinois, who recently returned to his seat after recovering from a stroke, is "working with two Democrats to draft bipartisan gun control legislation," according to the Daily Herald of Chicago. Ah, Chicago, that peaceful gun-free Shangri-La, where the mayor occasionally pleads with gang-bangers to aim more carefully, lest they hit young innocent bystanders in their zeal to pump each other full of lead! How can a legislator fail to be inspired to new heights of gun-control creativity, with such a muse perched upon his shoulder?
In Kirk's case, he's working with Democrat Senator Kirsten Gillibrand of New York to "crack down on gun trafficking," and also on background checks with the fabled Joe Manchin of West Virginia, a Democrat who loves guns so much that he once used a rifle (mercifully devoid of terrifying features like a flash suppressor or bayonet lug) to blow away cap-and-trade legislation in a political ad. He once said he was totally behind ObamaCare, but then he said he might bust a cap in that, too. Then he decided he wasn't really totally behind the Second Amendment, either. No matter what he works out with Kirk, his legislation-shooting days are probably behind him. Unless the legislation was taped to a duck, and Manchin proceeded to shot it in a responsible manner. Democrats are fine with that, because they love "responsible hunters" more than anybody in the whole wide world.
** The FBI looks into Senator Menendez: In foreign-prostitute-cliff news, the Daily Caller reports that the FBI has opened an inquiry into the adventures of Democrat Senator Bob Menendez of New Jersey, who was enjoying a visit with a big campaign contributor at his lavish Dominican Republican estate when a couple of Caribbean hookers fell on him. Funny, that never happens on Downton Abbey, but estates have changed a lot over the past hundred years.
Based on official emails revealed by an anonymous source, it appears Menendez might have skirted around Senate Ethics Committee rules requiring members to report gifts from contributors (no, not the hookers, he allegedly paid for that himself; it's contributor-provided travel to the Dominican Republic he should have reported.) This information was all made available to major media sources as far back as last May, but they tactfully avoided saying a single word about it until after the election, which is exactly how they would have handled the situation if Bob Menendez was a Republican.
** Medicare fraud gobbles up $120 million: The good news is that Medicare has been dispensing money with blinding speed. The bad news is that a lot of the people getting that money are illegal aliens, prison inmates, and other people ineligible to receive it. There goes $120 million over the last two years! But it's okay, because Politico says "Medicare lacks the tools to get the money back." Wait, that's not okay. Isn't all-powerful, all-knowing Big Government wonderful?
** Bobby Jindal thinks all-powerful, all-knowing Big Government is not wonderful: How's that for a segue? Louisiana's Republican governor, Bobby Jindal, delivered a major speech to the Republican National Committee on Thursday, in which he said it was essential for Republicans to make it clear they are "a populist party." Jindal declared, "If any rational human being were to create our government anew, today, from a blank piece of paper, we would have about one-fourth of the buildings we have in Washington, and about half the government workers." Something tells me the media will suddenly become interested in high unemployment again, if anyone takes a shot at reducing the federal workforce by fifty percent.
�??Washington has spent a generation trying to bribe our citizens and extort our states,�?� continued Governor Jindal, who just might be running for President in 2016. �??As Republicans, it�??s time to quit arguing around the edges of that corrupt system.�?� He had some tough advice for his party, including "compete for every single vote" and "stop insulting the intelligence of voters." Hey, the Democrats do that on a regular basis, and they seem to be getting along just fine.
** The government no longer thinks Dreamliners are just fine: Once upon the time, federal regulators insisted the Boeing Dreamliner was perfectly safe, even though it had a long history of battery problems during testing. But that was a long time ago. Fourteen days, to be exact. Now the entire Dreamliner fleet is grounded, as battery fires and overheating make it clear the thing is basically a huge Chevy Volt with wings. That's actually not far from the truth, because they both use lithium-ion battery technology. "We have yet to understand why this battery resulted in a fire when there were so many protections that were to be designed into the system," said National Transportation Safety Board chair Deborah Hersman. "Were to be?" The race to produce super-efficient batteries seems to have been moving a bit too swiftly.
** North Korea remains testy: Things have not gotten any calmer in Pyongyang since yesterday, because now North Korea is threatening to go to war with South Korea over U.N. sanctions, which the North views as an outrageous and unreasonable response to their entirely peaceful program for building long-range rockets. Each North Korean rocket comes packed with a delightful surprise toy, ranging from a crummy satellite that doesn't work to a nuclear bomb.
"If the puppet group of traitors takes a direct part in the U.N. 'sanctions,' the DPRK will take strong physical counter-measures against it," the North's Committee for the Peaceful Reunification of Korea declared, according to Reuters. Whoa… I sure hope they don't have a Committee for Non-Peaceful Reunification! Imagine how angry that committee would be right now!
Even China seems to be running out of patience with North Korea, grumbling through its state media (which is roughly as independent as Pyongyang's) that "it seems North Korea does not appreciate China's efforts."
But it's cool, because Beijing doesn't let such things keep it down in the dumps. "China hopes for a stable peninsula," the state media mused, "but it's not the end of the world if there's trouble there." The sun will come out tomorrow… bet your bottom yuan that there'll be sun… Oh, hell, that bright flash wasn't the Sun…
Eagle Eye Opener: European Markets Buoyed by Central Bank Report; Japan's Nikkei 225 Surges 2.9 Percent; Oil Tops $96 a Barrel
Broun hosts Capitol Hill gun rights briefing


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Vanessa bipunctata är en fjärilsart som beskrevs av Gussitsch 1917. Vanessa bipunctata ingår i släktet Vanessa och familjen praktfjärilar. Inga underarter finns listade i Catalogue of Life.

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Home/ What's happening / Stories of Australian Wine / November 2016 / Shiraz: The story of an Australian legend
The story of an Australian legend
Shiraz The story of an Australian legend
01 Nov 2016 in Styles with 1 comments
tagged with Revolution , Evolution , History , shiraz , McLaren Vale , Barossa Valley
When it comes to Australian wine no other grape is more synonymous than Shiraz. Almost universally planted, capable of everything from affordable, quaffable BBQ reds to magnificent, age-worthy classics that are truly world-class, Shiraz has it all.
Shiraz is Australia's stable red grape variety, makes the most popular red wine and is at the core of the country's incredible export success. The most widely planted wine grape in the country, Shiraz continues to dominate the Australian wine scene with its bold, ripe flavours and easy-drinking nature. A dedicated band of winemakers are ensuring that Shiraz is known for quality rather than quantity by bringing back traditional, hands-on winemaking that is creating Shiraz with distinctive character and personality. By virtue of its capabilities, army of winemaking advocates and consumer adoration, Shiraz is something special.
Shiraz: French in origin, Australian by nature
With its modern winemaking origins in southeast France, Shiraz, or Syrah as it's commonly known there, is a late budding and late ripening red grape that is the foundation of leading wines including Hermitage, Côte Rôtie and St-Joseph, as well as being a major component of wines from Châteauneuf-du-Pape, the Languedoc-Roussillon and many a Vin De Pays.
The first Shiraz vines made their way to Australia in James Busby's 1832 collection. Recognised as the father of Australian wine, Busby travelled through Spain and France collecting vine cuttings that were the foundation of the Australian wine industry. The first wines to come from these cuttings were labelled 'Hermitage', or rather more curiously, 'Claret' or 'Burgundy', by bin numbers or with other generic, non-varietal descriptors. Australia adopted the name Shiraz in the mid 19th century and soon popularised it as an internationally accepted term for the variety.
Shiraz finds its place in the sun
To ripen fully Shiraz needs a warm growing season, however, the most aromatic, elegant styles are grown in regions with cool nights and high diurnal temperature ranges - such as the Canberra District, Adelaide Hills, Mornington Peninsula and the Yarra Valley. In warm to hot regions, Shiraz shows greater jammy, blackberry and plum fruit characters and less of the delicate aromas that are the hallmark of the premium styles.
With popularity has come competition and Old World Shiraz (Syrah) challengers come from nations as diverse as France (wines which often Australia the greatest compliment by labelling their wines as Shiraz), Italy, Spain, South Africa, Chile, Argentina and the United States. But the brand identity and recognition that Australian Shiraz has built up over the years plays a large part in the ongoing worldwide success of this quintessential Australian red wine.
The world's oldest Shiraz vines
Australia is home to the world's oldest continuously productive Shiraz vines with vineyards believed to date back to 1843 (Langmeil), 1847 (Turkey Flat) and 1860 (Tahbilk). These ungrafted, pre-phylloxera vines produce tiny crops of intensely concentrated grapes.
As with most red wine grapes grown in the early 19th century, Shiraz was historically used for blending, often with Grenache, Cabernet Sauvignon or Mataro (Mourvedre), rather than to make single-varietal wines. Shiraz quickly became a significant part of the output from the Hunter Valley, parts of Victoria (Geelong, Bendigo, Rutherglen, Ballarat, Glenrowan, Yarra Valley) and South Australia (Barossa, Clare Valley, McLaren Vale, Adelaide Hills and Coonawarra). Led by pioneer winemakers such as George Wyndham, Henry Lindeman, William Angove, Joseph Seppelt and Thomas Hardy, wines made with a high proportion of Shiraz found their way onto tables in Australia, Britain and Europe, to widespread acceptance and critical acclaim. Australia's export industry waxed and waned in the following decades, eventually experiencing a decisive resurgence in the 1980s and '90s.
Shiraz – Just what the Doctor ordered
Many of Australia's early wine promoters were doctors, among them Dr Christopher Rawson Penfold who arrived in Adelaide in 1844 establishing Magill Estate. He called his property the Grange, a name that would become synonymous with Australian fine wine. Penfold's first wines were available on prescription, thought to be of benefit to anaemic patients – lucky them!
With the immigration of Silesian settlers in the mid 1800s, the Barossa Valley became home to generations of winemakers that would take Shiraz production to new levels of quality and output. Renowned Shiraz producers such as Orlando, Jacob's Creek, Seppelt, Henschke, and Yalumba all have links to those original settlers. English immigrant Samuel Smith founded Yalumba in 1849, with his vineyard planted mainly to Shiraz.
The trajectory of Shiraz from its early days as a blend component to standalone star can, in part, be attributed to the consistent nature of the wines – full-bodied with bold, upfront dark blackberry and plum fruit, most often made with oak – toasted American oak for vanilla characters or French oak for subtler cedar notes.
Shiraz: Nation domination achieved
Shiraz is now Australia's number-one wine grape overall. The 2016 harvest yielded a crush of more than 430,000 tonnes, followed by Chardonnay at 406,000 tonnes, then Cabernet Sauvignon at a mere 255,000 tones. The popularity of Shiraz is due to the ease of production for large-scale commercial wines across all price points. But at the boutique end of the market, Shiraz takes centre stage, making some of Australia's most revered, collected and expensive wines.
The history of Australia's Shiraz success is linked directly to the efforts of a visionary winemaker, Max Schubert. In 1951, inspired by a visit to Bordeaux, Schubert set out to make the 'great Australian red'; a wine that would be capable of cellaring for at least 20 years. Schubert developed a revolutionary technique and matured his Shiraz in new American oak casks. When he presented the wines to management seven years later, he was ordered to cease production immediately. But Schubert continued his work in secret, hidden out of sight in the cellars of Magill Estate. In 1960, a new wine, Penfolds Grange Bin 1, hit the market to great critical acclaim and instant commercial success. With renewed confidence, Penfolds head office ordered Max to resume production of this groundbreaking wine. It was then they discovered he hadn't missed a vintage and Penfolds subsequently released the 1952 vintage to the public. Penfolds Grange has become one of the world's most iconic, collected and revered wines, and proudly wears the mantle of 'Australia's greatest red'. Penfolds Grange is still predominantly Shiraz, with some vintages including a small portion of Cabernet Sauvignon.
The Shiraz export boom
Through the 1980s and 1990s, the great Australian export boom saw the popularity of Australian Shiraz soar overseas. The style found favour with its approachability, full-flavoured fruit and irreverent approach. In a market dominated by Old World producers with arcane labelling and stratospheric prices, Australia's fresh new wines hit the market with a bang. Sometimes called 'critter wines' after the quirky, colourful labels depicting Australian animals, Australia's low-cost, commercially produced Shiraz became a huge export success.
In the United States, consumers looked to critics for guidance, closely following one of the world's most influential wine voices, Robert Parker Jr. of 'The Wine Advocate'. Parker found favour in the intensely bold flavours and characters of Australian Shiraz, awarding 100-point scores to wines like Penfolds Grange, Torbreck The Laird, Chris Ringland (Three Rivers) and Greenock Creek. The popularity and commercial success of a such ratings saw many Australian winemakers chase high scores, picking fruit riper, making wines with deeper colour, higher alcohol levels, maturation in toasted new oak. At first the market lapped up these wines, but consumers soon realised that too much of a good thing was, indeed, too much. With such high alcohol levels and intensely powerful flavours, the wines didn't offer much subtlety or the complexity, aroma and texture of lighter-bodied, restrained examples. Buyers were also finding that the wines didn't age as well as anticipated. In response, the market shifted slightly, encouraging winemakers back to a more moderate approach to Shiraz. Today, while blockbuster Shiraz is still being made, with inky depth and syrupy richness, tastes are largely now aimed at a more moderate, easy-to-enjoy style.
Cool-climate Shiraz takes centre stage
In the cool Yarra Valley, Luke Lambert lets wild yeast kick off the fermentation of his Syrah, which is partly whole-bunch pressed then matured in large old oak casks and bottled without fining or filtration. This rustic approach creates a wine with layers of aromatics and savoury dark fruits knitted together with firm tannins.
As happy surfing the world's best surf breaks as he is in a winery, Taras Ochota brings a casual, laid-back approach to wine, letting the fruit and terroir do the talking. Ochota Barrels' 'I am the Owl' Syrah (McLaren Vale) and 'Shellac' Shiraz (Barossa Valley) are textural wines reflecting delicate spice and smoke characters with a beguiling balance of power and elegance.
Ray Nadeson of boutique producer in Geelong says his Shiraz is 'out on a limb'. Grown on red clay over limestone and ironstone, it's savoury, tannic and brooding, 'like a double-bass quintet' enthused a taster at a recent wine show.
In the Clare Valley, Col MacBryde and Jen Gardner apply organic principles to grow 100-year-old Shiraz, using old-fashioned winemaking techniques and fermenting in concrete tanks to create Adelina Shiraz.
Biodynamic winery Yangarra Estate focuses on grape varieties of the southern Rhône. Peter Fraser, Australian Winemaker of the Year 2016 (Australian Wine Companion, James Halliday) handcrafts wines that reflect the nature of the land and climate in McLaren Vale. His 'PF' Shiraz, made with wild yeast and cold-soaked with no additives or fining, shows fragrant floral characters.
Although Abel Gibson grew up in the Barossa surrounded by wine, he didn't find inspiration to make wine himself until 2002, when he gained experience at Rockford followed by a vintage in Spain and work at Spinifex. Inspired by the hands-on, low-tech approach, Gibson established Ruggabellus to craft red wines with a touch of lightness that belies the traditional Barossa style.
Australia's benchmark cool-climate Shiraz is crafted by Tim Kirk at Clonakilla in Murrumbateman, in the heart of the Canberra District. Co-fermented with Viognier, the wine reflects a vast aromatic spectrum of white pepper and spice over a palate that's elegant yet powerful.
Australian Shiraz: The future
The status of Shiraz as Australia's number-one wine grape looks set to continue well into the future as consumers continue to lap up the easy-drinking, rich, full-bodied styles made by the major commercial brands. But it's the smaller, boutique producers who are really getting the best out of the style, creating Shiraz with a beguiling balance of aromatics, flavour, tannins and personality. It's these wines that we'll continue to watch with interest in the years to come, and who knows, perhaps in another decade we'll be adding yet another chapter to the story of Shiraz.
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Barossa Valley Shiraz
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