Optimal vaccine allocation during the mumps outbreak in two SIR centers

The aim of this work is to investigate the optimal vaccine sharing between two SIR centers in the presence of migration fluxes of susceptibles and infected individuals during the mumps outbreak. Optimality of the vaccine allocation means the minimization of the total number of lost working days during the whole period of epidemic outbreak $[0,t_f]$, which can be described by the functional $Q={\int }_0^{t_f}I(t)\mathrm{d}t$ where $I(t)$ stands for the number of infectives at time $t$. We explain the behavior of the optimal allocation, which depends on the model parameters and the amount of available vaccine.