Local stochastic stability of SIRS models without Lyapunov functions

Abstract

[EN]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.