as of july 2010 , who has reported 501 confirmed human cases of avian influenza a/(h5n1 ) which resulted in 287 deaths worldwide . at the same time , the statistics for the h1n1 2009 outbreak has so far included 214 countries with a total reported number of infections and deaths of 419,289 and 18,239 , respectively .
today , an ominous expectation exists that the next pandemic will be triggered by a highly pathogenic virus , to which there is little or no pre - existing immunity in humans .
the nation 's ability to mitigate a pandemic influenza depends on the available emergency response resources and infrastructure , and , at present , challenges abound .
predicting the exact virus subtype remains a difficult task , and even when identified , reaching an adequate vaccine supply can currently take up to nine months [ 4 , 5 ] .
even if the existing vaccines prove to be potent , their availability will be limited by high production and inventory costs [ 6 , 7 ] and also will be constrained by the supply of antiviral drugs , healthcare providers , hospital beds , medical supplies , and logistics .
hence , pandemic mitigation will have to be done amidst limited availability of resources and supporting infrastructure .
this challenge has been acknowledged by who   and echoed by the hhs and cdc [ 8 , 9 ] .
the existing models on pandemic influenza ( pi ) containment and mitigation aims to address various complex aspects of the pandemic evolution process including : ( i ) the mechanism of disease progression , from the initial contact and infection transmission to the asymptomatic phase , manifestation of symptoms , and the final health outcome [ 1012 ] , ( ii ) the population dynamics , including individual susceptibility [ 13 , 14 ] and transmissibility [ 10 , 1517 ] , and behavioral factors affecting infection generation and effectiveness of interventions [ 1820 ] , ( iii ) the impact of pharmaceutical and nonpharmaceutical measures , including vaccination [ 2123 ] , antiviral therapy [ 2426 ] , social distancing [ 2731 ] and travel restrictions , and the use of low - cost measures , such as face masks and hand washing [ 26 , 3234 ] .
recently , the modeling efforts have focused on combining pharmaceutical and nonpharmaceutical interventions in search for synergistic strategies , aimed at better resource utilization .
most of such approaches attempt implementing a form of social distancing followed by application of pharmaceutical measures . for
one of the most notable among these efforts is a 2006 - 07 initiative by midas , which cross - examined independent simulation models of pi spread in rural areas of asia [ 43 , 44 ] , usa and uk [ 45 , 46 ] , and the city of chicago , respectively .
midas cross - validated the models by simulating the city of chicago , with 8.6 m inhabitants and implementing a targeted layered containment [ 48 , 49 ] .
the research findings of midas and some other groups [ 12 , 33 ] were used in a recent  modeling community containment for pandemic influenza 
these findings were also used in a pandemic preparedness guidance developed by cdc . at the same time
, the iom report   points out several limitations of the midas models , observing that  because of the significant constraints placed on the models  the scope of models should be expanded . 
the iom recommends  to adapt or develop decision - aid models that can  provide real - time feedback  and include the costs and benefits of intervention strategies . 
our literature review yields a similar observation that most existing approaches focus on assessment of a priori defined strategies , and virtually none of the models are capable of  learning ,  that is , adapting to changes in the pandemic progress , or even predicting them , to generate dynamic strategies .
such a strategy has the advantage of being developed dynamically , as the pandemic spreads , by selecting a mix of available mitigation options at each decision epoch , based on both the present state of the pandemic and its predicted evolution . in an attempt to address the iom recommendations , we present a simulation optimization model for developing predictive resource distribution over a network of regional outbreaks . the underlying simulation model mimics the disease and population dynamics of each of the affected regions ( sections 2.1 and 2.2 ) .
as the pandemic spreads from region to region , the optimization model distributes mitigation resources , including stockpiles of vaccines and antiviral and administration capacities ( section 2.3 ) .
the model seeks to minimize the impact of ongoing outbreaks and the expected impact of potential outbreaks , using measures of morbidity , mortality , and social distancing , translated into the cost of lost productivity and medical expenses .
the methodology is calibrated and implemented on a sample outbreak in fla , usa with over 4 m inhabitants ( section 3 ) .
the strategy is compared to the reactive myopic policy , which allocates resources from one actual outbreak region to the next , each time trying to cover the entire regional population at risk , regardless of the resource availability .
the comparison is done at different levels of vaccine and antiviral availability and administration capacity .
we also present a sensitivity analysis for assessing the impact of variability of some critical factors , including : ( i ) antiviral efficacy , ( ii ) social distancing conformance , and ( iii ) cdc response delay .
the objective of our methodology is to generate a progressive allocation of the total resource availability over a network of regional outbreaks .
the methodology incorporates ( i ) a cross - regional simulation model , ( ii ) a set of single - region simulation models , and ( iii ) an embedded optimization model .
we consider a network of regions with each of which classified as either unaffected , ongoing outbreak , or contained outbreak ( figure 1 ) .
the single - region simulation models mimic the population and disease dynamics of each ongoing region , impacted by intervention measures .
the pandemic can spread from ongoing to unaffected regions by infectious travelers who pass through regional border control . at every new regional outbreak epoch
, the optimization model allocates available resources to the new outbreak region ( actual distribution ) and unaffected regions ( virtual distribution ) .
daily statistics is collected for each ongoing region , including the number of infected , deceased , and quarantined cases , for different age groups . as a regional outbreak
a testbed illustration and a comparison of our strategy to the myopic policy is given in section 3 .
the model is initialized by creating population entities and mixing groups , for each region .
the details of the resulting regional contact dynamics and infection transmission are given in section 2.2 .
as the infected cases start seeking medical help , a new regional outbreak is detected .
the outbreak can spread to unaffected regions as some infectious travelers pass undetected through the border control . by tracing these travelers , the model determines which of the unaffected regions , if any , become new outbreaks .
the single - region model subsumes the following components ( see figure 3 ) : ( i ) population dynamics ( mixing groups and schedules ) , ( ii ) contact and infection process , ( iii ) disease natural history , and ( iv ) mitigation strategies , including social distancing , vaccination , and antiviral application .
the model collects detailed statistics , including number of infected , recovered , deceased , and quarantined cases , for different age groups . for a contained outbreak ,
the societal cost includes the cost of lost lifetime productivity of the deceased ; the economic cost includes the cost of medical expenses of the recovered and deceased and the cost of lost productivity of the quarantined .
each region is modeled as a set of population centers formed by mixing groups or places where individuals come into contact with each other during the course of their social interaction .
examples of mixing groups include households , offices , schools , universities , shopping centers , entertainment centers , and so forth , .
each individual is assigned a set of attributes such as age , gender , parenthood , workplace , infection susceptibility , and probability of travel , among others .
each person is also assigned t time - discrete ( e.g. , t = 1 hour ) weekday and weekend schedules , which depend on : ( i ) person 's age , parenthood , and employment status , ( ii ) disease status , ( iii ) travel status , and ( iv ) person 's compliance to social distancing decrees . as their schedules advance , the individuals circulate throughout the mixing groups and come into contact with each other ( see section 2.2.2 ) .
it is assumed that at any point of time , an individual belongs to one of the following compartments ( see figure 4 ) : susceptible , contacted ( by an infectious individual ) , infected ( asymptomatic or symptomatic ) , and recovered / deceased . in what follows ,
we present the infection transmission and disease natural history model , which delineates the transitions between the above compartments .
infection transmission occurs during contact events between susceptible and infectious cases , which take place in the mixing groups . at the beginning of every t period ( e.g. , one hour ) , for each mixing group g , the simulation tracks the total number of infectious cases , ng , present in the group .
it is assumed that each infectious case generates rg per t unit of time new contacts , chosen randomly ( uniformly ) from the pool of susceptibles present in the group .
we also assume the following : ( i ) during t period , a susceptible may come into contact with at most one infectious case and ( ii ) each contact exposure lasts t units of time .
once a susceptible has started her contact exposure at time t , she will develop infection at time t + t with a certain probability that is calculated as shown below .
let li(t ) be a nonnegative continuous random variable that represents the duration of contact exposure , starting at time t , required for susceptible i to become infected .
we assume that li(t ) is distributed exponentially with mean 1/i(t ) , where i(t ) represents the instantaneous force of infection applied to susceptible i at time t [ 5557 ] .
the probability that susceptible i , whose contact exposure has started at time t , will develop infection at time t + t is then given as 
 ( 1)p{li(t)t}=1ei(t)t . 
 
a schematic of the disease natural history is shown in figure 5 . during the incubation phase
, the infected case stays asymptomatic . at the end of the latency phase , she enters the infectious phase [ 44 , 46 , 48 ] .
she becomes symptomatic at the end of the incubation period . at the end of the infectious phase
, she enters the period leading to a health outcome , which culminates in her recovery or death .
mortality for influenza - like diseases is a complex process affected by many factors and variables , most of which have limited accurate data support available from past pandemics .
furthermore , the time of death can sometimes be weeks following the disease episode ( which is often attributable to pneumonia - related complications ) .
because of the uncertainty underlying the mortality process , we adopted an age - based form of the mortality probability of infected i , as follows : 
 ( 2)mi=i(1i ) , 
 where i is the age - dependent base mortality probability of infected i , i is her status of antiviral therapy ( 0 or 1 ) , and  is the antiviral efficacy measured as the relative decrease in the base probability .
we assume that a recovered case develops full immunity but continues circulating in the region .
mitigation is initiated upon detection of a critical number of confirmed infected cases , which triggers resource distribution and deployment .
vaccination is constrained by the allocated stockpile and administration capacity , measured in terms of the immunizer - hours .
we assume that as some symptomatic cases seek medical help [ 62 , 63 ] , those at risk of them will receive an antiviral .
the process is constrained by the allocated stockpile and administration capacity , measured in terms of the number of certified providers .
both vaccination and antiviral application are affected by a number of sociobehavioral factors , including conformance of the target population , degree of risk perception , and compliance of healthcare personnel [ 6466 ] .
the conformance level of the population at risk can be affected , among other factors , by the demographics and income level [ 6771 ] as well as by the quality of public information available .
the degree of risk perception can be influenced by the negative experience developed during previous pharmaceutical campaigns [ 72 , 73 ] , as well as by public fear and rumors [ 74 , 75 ] . 

we adopted a cdc guidance , which establishes five categories of pandemic severity and recommends quarantine and closure options according to the category .
the categories are determined based on the value of the case fatality ratio ( cfr ) , the proportion of fatalities in the total infected population . for cfr values
lower than 0.1% ( category 1 ) , voluntary at - home isolation of infected cases is implemented . for cfr values between 0.1% and 1.0% ( categories 2 and 3 ) , in addition to at - home isolation , the following measures are recommended : ( i ) voluntary quarantine of household members of infected cases and ( ii ) child and adult social distancing . for cfr values exceeding 1.0% ( categories 4 and 5 ) ,
is affected by some of the behavioral factors listed above , we assume a certain social distancing conformance level .
travel restrictions considered in the model included regional air and land border control for infected travelers .
as presented in figure 2 , the optimization model is invoked at the beginning of every nth new regional outbreak epoch ( n = 1,2 ,  ) , starting from the initial outbreak region ( n = 1 ) .
the objective of the model is to allocate some of the available mitigation resources to the new outbreak region ( actual distribution ) while reserving the rest of the quantities for potential outbreak regions ( virtual distribution ) . by doing so
, the model seeks to progressively minimize the impact of ongoing outbreaks and the expected impact of potential outbreaks , spreading from the ongoing locations .
mitigation resources can include stockpiles of vaccines and antivirals , administration capacity , hospital beds , medical supplies , and social distancing enforcement resources , among others .
the predictive mechanism of the optimization model is based on a set of regression equations obtained using single - region simulation models . in what follows ,
we present the construction of the optimization model and explain the solution algorithm for the overall simulation - based optimization methodology .
we introduce the following general terminology and notation : : set of all network regions : set of regions in which pandemic is contained at the nth outbreak epoch ( n = 1,2 ,  ) : set of ongoing regions at the nth outbreak epoch : set of unaffected regions at the nth outbreak epoch : set of available types of mitigation resources ( r = { 1,2 ,  ,
r } ) : amount of resource i allocated to region k : available amount of resource i  r at the nth outbreak epoch : set of age groups .  

the optimization criterion ( objective function ) of the model incorporates measures of expected societal and economic costs of the pandemic : the societal cost includes the cost of lost lifetime productivity of the deceased ; the economic cost includes the cost of medical expenses of the recovered and deceased and the cost of lost productivity of the quarantined . to compute these costs ,
the following impact measures of morbidity , mortality , and quarantine are used , for each region k : : total number of infected cases in age group h who seek medical assistance : total number of infected cases in age group h who do not seek medical assistance : total number of deceased cases in age group h : total number of person - days of cases in age group h who comply with quarantine .  

to estimate these measures , we use the following regression models obtained using a single - region simulation of each region k : 
 ( 3)xhk=hk0+irhkiqik+i , mr ,  imhkimqikqmk , 
 where  denotes the regression coefficient associated with resource i and  is the regression coefficient for the interaction between resources i and m. similar models are used for yhk , dhk , and vhk .
the above relationships between the impact measures and the resource distributions ought to be determined a priori of implementing a cross - regional scenario ( see section 3 ) . here
we assume , however , that as the pandemic evolves , the disease infectivity will naturally subside .
hence , the regression equations need to be re - estimated at every new outbreak epoch , for each region k  c , using the single - region simulation models , where each simulation must be initialized to the current outbreak status in region k in the cross - regional simulation . as an alternative to using a computationally burdensome approach of re - estimating the regression equations , a modeler may choose to use a certain decay factor    to adjust the estimates of the regional impact measures at every nth outbreak epoch , in the following way : 
 ( 4)xhjn=nxhj ,  yhjn=nyhj , dhjn=ndhj ,  vhjn=nvhj . 
 
in addition , we use the following regression model to estimate the probability of pandemic spread from affected region l to unaffected region k , as a function of resources allocated to region l , which , in turn , impact the number of outgoing infectious travelers from the region : 
 ( 5)plk=lk0+irlkiqil+i , mrimlkimqilqml , 
 where  denotes the regression coefficient associated with resource i ,  is the regression coefficient associated with interaction between resources i and m , and  represents the intercept . consequently , the total outbreak probability for unaffected region k can be found as pk = lbplk . as in the case of the impact measures ,
the estimates of the regional outbreak probabilities need to be progressively re - estimated or adjusted using a scheme similar to ( 4 ) , as follows : finally , we calculate the total cost of an outbreak in region k at the nth decision epoch as follows : 
 ( 7)tckn=h(mh+wh)xhkn+hwhyhkn+hw^hdhkn  + hwhvhkn , 
 where mh is total medical cost of an infected case in age group h over his / her disease period ,  wh is total cost of lost wages of an infected case in age group h over his / her disease period , w^h is cost of lost lifetime wages of a deceased case in age group h , and wh is daily cost of lost wages of a non - infected case in age group h who complies with quarantine .  
 the model the optimization model has the following form . 
 ( 8)minimize  tcjn(q1j , q2j, 
,qrj )  + scntcsn(q1s , q2s,  ,qrs)psnsubject to  qij+scnqispsnqin  ir ,  qij , qis0  ir . 

the first term of the objective function represents the total cost of the new outbreak j , estimated at the nth outbreak epoch , based on the actual resource distribution { q1j , q2j , 
the second term represents the total expected cost of outbreaks in currently unaffected regions , based on the virtual distributions { q1s , q2s ,  , qrs } ( 7 ) and the regional outbreak probabilities ps ( 6 ) .
the set of constraints assures that for each resource i , the total quantity allocated ( current and virtual , both nonnegative ) does not exceed the total resource availability at the nth decision epoch .
note that both the objective function and the availability constraints are nonlinear in the decision variables . 
  
,qrj )  + scntcsn(q1s , q2s,  ,qrs)psnsubject to  qij+scnqispsnqin  ir ,  qij , qis0  ir . 

the first term of the objective function represents the total cost of the new outbreak j , estimated at the nth outbreak epoch , based on the actual resource distribution { q1j , q2j ,  , qrj } ( see ( 7 ) ) .
the second term represents the total expected cost of outbreaks in currently unaffected regions , based on the virtual distributions { q1s , q2s ,  , qrs } ( 7 ) and the regional outbreak probabilities ps ( 6 ) . the set of constraints assures that for each resource i , the total quantity allocated ( current and virtual , both nonnegative ) does not exceed the total resource availability at the nth decision epoch .
note that both the objective function and the availability constraints are nonlinear in the decision variables .
the solution algorithm for our dynamic predictive simulation optimization ( dpo ) model is given below .  
initialize the sets of regions : a =  , b =  , c = s.    select randomly the initial outbreak region j. set n = 1 .   
c{j}.    solve the resource distribution model for region j. update the total resource availabilities .    if b   , do step 8 .
else , do step 10 . 
  for each ongoing region , implement a next day run of its single - region simulation .  
based on the outbreak probability values , determine if there is a new outbreak region(s ) j.   if there is no new outbreak(s ) , go to step 7 .
otherwise , go to step 9 . 
   for each ongoing region , implement a next day run of its single - region simulation .   
update sets a and b , if needed .    for each unaffected region , calculate its outbreak probability .   
based on the outbreak probability values , determine if there is a new outbreak region(s ) j.    if there is no new outbreak(s ) , go to step 7 .
otherwise , go to step 9 .    for each new outbreak region j ,  
 
update sets b  b  { j } and c  c{j}.   re - estimate regression equations for each region k  b  c using the single - region simulations , where each simulation is initialized to the current outbreak status in the region ( alternatively , use ( 4 ) and ( 6 ) ) .  
solve the resource distribution model for region j.   update the total resource availabilities . 
  
c{j}.    re - estimate regression equations for each region k  b  c using the single - region simulations , where each simulation is initialized to the current outbreak status in the region ( alternatively , use ( 4 ) and ( 6 ) ) .    solve the resource distribution model for region j.    update the total resource availabilities .   
to illustrate the use of our methodology , we present a sample h5n1 outbreak scenario including four counties in fla , usa : hillsborough , miami dade , duval , and leon , with populations of 1.0 , 2.2 , 0.8 , and 0.25 million people , respectively .
a basic unit of time for population and disease dynamics models was taken to be t = 1 hour .
regional simulations were run for a period ( up to 180 days ) until the daily infection rate approached near zero ( see section 3.3 ) .
below , we present the details on selecting model parameter values . most of the testbed data can be found in the supplement .
each infected person was assigned a daily travel probability of 0.24% , of which 7% was by air and 93% by land .
the probabilities of travel among the four regions were calculated using traffic volume data [ 8083 ] , see table 1 .
infection detection probabilities for border control for symptomatic cases were assumed to be 95% and 90% , for air and land , respectively .
the instantaneous force of infection applied to contact i at time t ( ( 1 ) , ) was modeled as 
 ( 9)i(t)=ln(1pi(t ) ) ,  where  pi(t)=ii(t ) , 
 where i is the age - dependent base instantaneous infection probability of contact i , i(t ) is her status of vaccination at time t ( 0 or 1 ) , and  is the vaccine efficacy , measured as the reduction in the base instantaneous infection probability ( achieved after 10 days ) .
the values of age - dependent base instantaneous infection probabilities were adopted from   ( see table 2 ) .
the disease natural history included a latent period of 29 hours ( 1.21 days ) , an incubation period of 46 hours ( 1.92 days ) , an infectiousness period from 29 to 127 hours ( 1.21 to 5.29 days ) , and a period leading to health outcome from 127 to 240 hours ( 5.29 to 10 days ) .  
base mortality probabilities ( i in ( 2 ) ) were found using the statistics recommended by the working group on pandemic preparedness and influenza response .
this data shows the percentage of mortality for age - based high - risk cases ( hrc ) ( table 3 , columns 13 ) .
mortality probabilities ( column 4 ) were estimated under the assumption that high - risk cases are expected to account for 85% of the total number of fatalities , for each age group .
single - region simulation models were calibrated using two common measures of pandemic severity [ 35 , 45 , 46 ] : the basic reproduction number ( r0 ) and the infection attack rate ( iar ) .
r0 is defined as the average number of secondary infections produced by a typical infected case in a totally susceptible population .
iar is defined as the ratio of the total number of infections over the pandemic period to the size of the initial susceptible population . to determine r0 , all infected cases inside the simulation were classified by generation of infection , as in [ 33 , 43 ] .
the value of r0 was calculated as the average reproduction number of a typical generation in the early stage of the pandemic , with no interventions implemented ( the baseline scenario ) . historically , r0 values for pi ranged between 1.4 and 3.9 [ 37 , 43 ] . to attain similar values , we calibrated the hourly contact rates of mixing groups   ( original rates were adopted from ) .
for the four regions , the average baseline value of r0 was 2.54 , which represented a high transmissibility scenario .
mitigation resources included stockpiles of vaccines and antiviral and administration capacities ( section 3.4 ) .
phi the vaccination risk group included healthcare providers , and individuals younger than 5 years ( excluding younger than 12 months old ) and older than 65 years .
the risk group for antiviral included symptomatic individuals below 15 years and above 55 years [ 60 , 86 ] . the efficacy levels for the vaccine (  in ( 9 ) ) and antiviral (  in ( 2 ) )
we did not consider the use of antiviral for a mass prophylactic reduction of infection susceptibility due to the limited antiviral availability   and the risk of emergence of antiviral resistant transmissible virus strains .
the vaccination risk group included healthcare providers , and individuals younger than 5 years ( excluding younger than 12 months old ) and older than 65 years .
the risk group for antiviral included symptomatic individuals below 15 years and above 55 years [ 60 , 86 ] .
the efficacy levels for the vaccine (  in ( 9 ) ) and antiviral (  in ( 2 ) ) were assumed to be 40% [ 44 , 87 ] and 70% , respectively .
we did not consider the use of antiviral for a mass prophylactic reduction of infection susceptibility due to the limited antiviral availability   and the risk of emergence of antiviral resistant transmissible virus strains .
npi a version of the cdc guidance for quarantine and isolation for category 5 was implemented ( section 2.2.4 , ) .
once the reported cfr value had reached 1.0% , the following policy was declared and remained in effect for 14 days : ( i ) individuals below a certain age  ( 22 years ) stayed at home during the entire policy duration , ( ii ) of the remaining population , a certain proportion    stayed at home and was allowed a one - hour leave , every three days , to buy essential supplies , and ( iii ) the remaining ( 1   ) noncompliant proportion followed a regular schedule .
a version of the cdc guidance for quarantine and isolation for category 5 was implemented ( section 2.2.4 , ) . once the reported cfr value had reached 1.0% , the following policy was declared and remained in effect for 14 days : ( i ) individuals below a certain age  ( 22 years ) stayed at home during the entire policy duration , ( ii ) of the remaining population , a certain proportion    stayed at home and
was allowed a one - hour leave , every three days , to buy essential supplies , and ( iii ) the remaining ( 1   ) noncompliant proportion followed a regular schedule .
an outbreak was considered contained , if the daily infection rate did not exceed five cases , for seven consecutive days . once contained , a region was simulated for an additional 10 days for accurate estimation of the pandemic statistics .
a 2 statistical design of experiment   was used to estimate the regression coefficient values of the significant decision factors and their interactions ( see section 2.3 ; the values of adjusted r ranged from 96.36% to 99.97% ) .
the running time for a cross - regional simulation replicate involving over four million inhabitants was between 17 and 26 minutes ( depending on the initial outbreak region , with a total of 150 replicates ) on a pentium 3.40  ghz with 4.0  gb of ram .
the performance of the dpo and myopic policies is compared at different levels of resource availability . 

table 4 summarizes the total vaccine and antiviral requirements for each region , based on the composition of the regional risk groups ( see section 3.3 ) .  
table 5 shows the per capita costs of lost productivity and medical expenses , which were adopted from   and adjusted for inflation for the year of 2010 .  
comparison of the two strategies is done at the levels of 20% , 50% , and 80% of the total resource requirement shown in table 4 .
figures 6(a ) and 6(b ) show the policy comparison in the form of the 95% confidence intervals ( ci ) for the average number of infected and deceased , respectively .  

figure 7 also shows the policy comparison using the 95% ci for the average total pandemic cost , calculated using the pandemic statistics , and the per capita costs from table 5 .
for illustrative purposes , we also show the average number of regional outbreaks , for each policy , at different levels of resource availability , in the testbed scenario involving four regions , with the hillsborough as the initial outbreak region ( table 6 ) .
it can be observed that the values of all impact measures exhibit a downward trend , for both dpo and myopic policies , as the total resource availability increases from 20% to 80% .  
an increased total resource availability not only helps alleviating the pandemic impact inside the ongoing regions but also reduces the probability of spread to the unaffected regions .
for both policies , as the total resource availability approaches the total resource requirement ( starting from approximately 60% ) , the impact numbers show a converging behavior , whereby the marginal utility of additional resource availability diminishes .
this behavior can be explained by noting that the total resource requirements were determined assuming the worst case scenario when all ( four ) regions would be affected and ought to provided with enough resources to cover their respective regional populations at risk .
it can also be seen that on average , the dpo policy outperforms the myopic approach at all levels , which can attest to a more efficient resource utilization achieved by the dpo policy ( see also table 6 ) .
the difference in the policy performance is particularly noticeable at the lower levels of resource availability , and it gradually diminishes , as the resource availability increases and becomes closer to be sufficient to cover the entire populations at risk in all regions . it can also be noted that the variability in the performance of the dpo strategy is generally smaller than that of the myopic policy . in general , for both strategies , the performance variability decreases with higher availability of resources . in this section , we assess the marginal impact of variability of some of the critical factors .
the impact was measured separately by the change in the total pandemic cost and the number of deaths ( averaged over multiple replicates ) , resulting from a unit change in a decision factor value , one factor at a time .
factors under consideration included : ( i ) antiviral efficacy , ( ii ) social distancing conformance , and ( iii ) cdc response delay .
we have used all four regions , separately , as initial outbreak regions for each type of sensitivity analysis .
due to limited space , we have opted to show the results for only one initial region , chosen arbitrarily , for each of the three types of sensitivity studies . while duval county was selected as the initial outbreak region to show the sensitivity results on antiviral efficacy , hillsborough and miami dade were used as the initial regions to show the results on , respectively , social distancing conformance and cdc response delay .  

figure 8 depicts the sensitivity of the average total cost and average total deaths to antiviral efficacy values between 0% and 80% . as expected , for both policies , the curves for the average number of deaths exhibit a decreasing trend which is almost linear for the values of  between 0% and 40% .
as the value of  approaches 70% , the curves start exhibit a converging behavior . the curves for the average total pandemic cost exhibit a similar pattern for both policies .
it can be noted that the performance of both policies is somewhat identical for low antiviral efficacy ( between 0% and 30% ) .
however , the performance of the dpo policy improves consistently as  increases which can be attributed to a more discretionary allocation of the antiviral stockpile by the dpo policy .
reduction of the contact intensity through quarantine and social distancing has proven to be one of the most effective containment measures , especially in the early stages of the pandemic [ 27 , 30 , 31 , 41 ] . 

figure 9 shows the sensitivity of the average total cost and average total deaths to the social distancing conformance ranging between 60% and 80% .
we observed that for both impact measures , the dpo policy demonstrated a better performance with the difference ranging from $ 3b to $ 26b in the total cost and from 1,400 to 20,000 in the number of fatalities . the biggest difference in performance
was achieved at the lower - to - medium levels of conformance ( between 65% and 72% ) . as the conformance level approached 80% , the dominating impact of social distancing masked the effect of better utilization of vaccines and antivirals achieved by the dpo strategy .
the cdc response delay corresponds to the interval of time from the moment an outbreak is detected to a complete deployment of mitigation resources .
depending on the disease infectivity , cdc response delay may represent one of the most critical factors in the mitigation process . 

figure 10 shows how the performance of both policies was significantly impacted by this factor .
the dpo policy showed a uniformly better performance with the difference ranging between $ 3b to $ 4b in the average total cost , and between 800 to 1,800 in the average number of mortalities , over the range ( 2472 hours ) of the response delay that we examined .
for both policies , there was no significant difference when the delay was between 24 and 48 hours .
however , for the delay values exceeding 48 hours , the average number of deaths and total cost increased at a high rate .
as recently pointed by the iom , the existing models for pi mitigation fall short of providing dynamic decision support which would incorporate  the costs and benefits of intervention  . in this paper , we present a large - scale simulation optimization model which is attempted at filling this gap .
the model supports dynamic predictive resource distribution over a network of regions exposed to the pandemic .
the model aims to balance both the ongoing and potential outbreak impact , which is measured in terms of morbidity , mortality , and social distancing , translated into the cost of lost productivity and medical expenses .
the model was calibrated using historic pandemic data and compared to the myopic strategy , using a sample outbreak in fla , usa , with over 4 million inhabitants . 

, the marginal utility of additional resource availability was found to be diminishing , as the total resource availability approached the total requirement . in the testbed scenario ,
the dpo strategy on average outperformed the myopic policy . as opposed to the dpo strategy , the myopic policy is reactive , rather than predictive , as it allocates resources regardless of the remaining availability and the overall cross - regional pandemic status .
in contrast , the dpo model distributes resources trying to balance the impact of actual outbreaks and the expected impact of potential outbreaks .
it does so by exploiting region - specific effectiveness of mitigation resources and dynamic reassessment of pandemic spread probabilities , using a set of regression submodels .
hence , we believe that in scenarios involving regions with a more heterogeneous demographics , the dpo policy will likely to perform even better and with less variability than the myopic strategy
. we also note that the difference in the model performance was particularly noticeable at lower levels of resource availability , which is in accordance with a higher marginal utility of additional availability at that levels .
we thus believe that the dpo model can be particularly useful in scenarios with very limited resources . 

the simulation optimization methodology presented in this paper is one of the first attempts to offer dynamic predictive decision support for pandemic mitigation , which incorporates measures of societal and economic costs .
our comparison study of the dpo versus myopic cross - regional resource distribution is also novel .
additionally , our simulation model represents one of the first of its kind in considering a broader range of social behavioral aspects , including vaccination and antiviral treatment conformance .
the simulation features a flexible design which can be particularized to a broader range of phi and npi and even more granular mixing groups .
we also developed a decision - aid simulator which is made available to the general public through our web site at http://imse.eng.usf.edu/pandemics.aspx .
the tool is intended to assist public health decision makers in implementing what - if analysis for assessment of mitigation options and development of policy guidelines .
examples of such guidelines include vaccine and antiviral risk groups , social distancing policies ( e.g. , thresholds for declaration / lifting and closure options ) , and travel restrictions
lack of reliable data prevented us from considering geo - spatial aspects of mixing group formation .
we also did not consider the impact of public education and the use of personal protective measures ( e.g. , face masks ) on transmission , again due to a lack of effectiveness data .
we did not study the marginal effectiveness of individual resources due to a considerable uncertainty about the transmissibility of an emerging pandemic virus and efficacy of vaccine and antiviral .
for the same reason , the vaccine and antiviral risk groups considered in the testbed can be adjusted , as different prioritization schemes have been suggested .
the form of social distancing implemented in the testbed can also be modified as a variety of schemes can be found in the literature , including those based on geographical and social targeting .
effectiveness of these approaches is substantially influenced by the compliance factor , for which limited accurate data support exists .
it will thus be vital to gather the most detailed data on the epidemiology of a new virus and the population dynamics early in the evolution of a pandemic , and expeditiously analyze the data to adjust the interventions accordingly .
 as recently pointed out by the institute of medicine , the existing pandemic mitigation models lack the dynamic decision support capability . 
 we develop a large - scale simulation - driven optimization model for generating dynamic predictive distribution of vaccines and antivirals over a network of regional pandemic outbreaks . 
 the model incorporates measures of morbidity , mortality , and social distancing , translated into the cost of lost productivity and medical expenses . 
 the performance of the strategy is compared to that of the reactive myopic policy , using a sample outbreak in fla , usa , with an affected population of over four millions . 
 the comparison is implemented at different levels of vaccine and antiviral availability and administration capacity . 
 sensitivity analysis is performed to assess the impact of variability of some critical factors on policy performance . 
 the model is intended to support public health policy making for effective distribution of limited mitigation resources . 
1. Introduction
2. Methodology
3. Testbed Illustration
4. Conclusions