Stability of Stochastic Model for Hepatitis C Transmission with an Isolation Stage

Abstract

In this paper we construct and investigate
stability features of two stochastic hepatitis C models with an
isolation stage which are obtained by an introduction of stochastic perturbations on the deterministic model for hepatitis C with an
isolation stage. One of the stochastic models has only disease--free
equilibrium and the other endemic equilibrium state.
Aforementioned equilibriums belong, normally, to the equilibriums of
corresponding deterministic system. For both of models, first of
all, we prove the existence and uniqueness of global positive stochastic solution.
Thereafter, by using suitable Lyapunov functions, we investigate stability properties of both models. We close the paper with numerical simulation with reliable data of hepatitis C transmission to illustrate our theoretical results.