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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 into 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 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.

In this paper we study a stochastic model for tumor-immune interaction with delay. More precisely, we extend the deterministic delay tumor-immune interaction model by introducing random perturbations and obtain stochastic model. For this model, we first prove existence and uniqueness of the global positive solution, and then, by using suitable Lyapunov functionals, we obtain stability conditions for the equilibrium state when tumor cells and resting cells approach their carrying capacities. We also carry numerical simulation with reliable data to illustrate our theoretical findings.