"On Stability of One Mathematical Model of the Epidemic Spread Under Stochastic Perturbations"

Abstract

This paper continues the study of the asymptotic properties of the known SAIRP epidemic model under stochastic perturbations. The SAIRP epidemic model is described by a system of five nonlinear differential equations. It is assumed that the system is influenced by stochastic perturbations that are of the type of white noise and are proportional to the deviation of the current system state from one of the system equilibriums. It is shown that sufficient conditions of stability in probability for two different equilibria of the considered system are formulated via a simple linear matrix inequality (LMI), that can be easily studied via MATLAB. Two demonstrative examples illustrate the obtained results via numerical simulation of solutions of the considered system of five nonlinear Ito's stochastic differential equations. The research method used here can be applied to a lot of other more complicated models in different applications.