Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations

Abstract

This article introduces a kind of stochastic SEIR models containing virus mutation and logistic growth of susceptible populations, whose deterministic versions have a positively invariant set and globally asymptotically stable equilibrium points. For these stochastic SEIR epidemic models, we prove they have a unique global positive solution, and also obtain sufficient conditions respectively for survival and extinction of the infectious disease. Eventually, we validate our theoretical findings using numerical simulations.