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 = t f 0 I(t)dt 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 vaccine available V .

In this paper, we aim to determine an optimal insurance premium rate for health-care in deterministic and stochastic SEIR models. The studied models consider two standard SEIR centres characterised by migration fluxes and vaccination of population. The premium is calculated using the basic equivalence principle. Even in this simple set-up, there are non-intuitive results that illustrate how the premium depends on migration rates, the severity of a disease and the initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program affects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.