Local stochastic stability of SIRS models without Lyapunov functions

Abstract

Most of stability analysis for stochastic epidemiological models involve Lyapunov functions. This work shows how sufficient conditions for the local stochastic asymptotic stability of a nonlinear system can be derived from the stability analysis of an ordinary linear system. In the particular stochastic SIR/SIRS models proposed here to illustrate the technique, the stability study of the obtained ordinary systems reduces to calculate the spectrum of the governing matrix.