Abstract
This contribution concerns a stochastic model for the spread of an infection. This model is a natural version of the Kermack-McKendrick model with vaccination and it is given by the stochastic differential equation.
Expected value of a solution to the equation and a solution to the deterministic model are compared, behavior of a solution to the equation depending on the size of population is discussed and finally, a solution of the optimizing of linear vaccination obtained by simulations is presented.