Stochastic stability and instability of rumor model

Abstract

In this study, we present a stochastic rumor model. The stability of the disease-free equilibrium state and instability of the free equilibrium E0{E}_{0} of stochastic epidemics model are considered with the help of Lyapunov functions. Sufficient conditions of persistence and extinction of rumor are given. Numerical simulations verify the analytical results.

Keywords

• itô’s formula
• stochastic rumor model
• stability
• instability
• lyapunov functions
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