About Stability of SAIRP Epidemic Model Under Stochastic Perturbations of the Type of Poisson's Jumps

Asymptotic properties of the known SAIRP epidemic model are studied under stochastic perturbations, given by a combination of the white noise and Poisson's jumps. It is assumed that these stochastic perturbations are proportional to the deviation of a current state of the system under consideration from one of the system equilibria. Sufficient conditions of stability in probability for two different equilibria of the considered system are formulated via a simple linear matrix inequality (LMI) and are studied via MATLAB. Two demonstrative examples illustrate the obtained results via numerical simulation of solutions of the considered system of five nonlinear stochastic differential equations. The research method used here can be applied to many other more complex nonlinear models in various applications.