On a stochastic disease model with vaccination
The authors study a stochastic SIS (susceptible-infective-susceptible) model with vaccination and temporary immunity viewed as a stochastic perturbation of the deterministic system that governs the spread of a disease into a population with vaccinated individuals. First, existence of a unique positive solution of the stochastic differential system is established and a sufficient condition for the eradication of the disease is derived. Then, by using Lyapunov functions, the stability of a disease-free equilibrium is proved. Numerical simulations based on the Euler-Maruyama scheme are performed to compare the behaviour of solutions of the deterministic and stochastically perturbed SIS systems.
scientific article; zbMATH DE number 5177396