  Quarantine of those individuals who are suspected of being infected is one of
the intervention measures to contain the spread of an infectious disease. We
propose an age structured SEQIR (S-Susceptible, E-Exposed, Q-Quarantine,
I-Infected, R-Recovered) model with vaccination of susceptible and exposed
individuals. Firstly without vaccination, basic reproduction number is derived
by using the appearance of endemic steady state. With an appropriate Liapunov
function, stability of disease free equilibrium point is checked. Vaccinating a
population with reduction in number of infected individuals at minimal cost is
considered as an optimization problem. We show that the vaccination strategy is
concentrated on atmost three age classes.

Analysis of PDEs