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The causes of viral rebound leading to disease relapse in some chronic hepatitis C virus-infected patients at the end of treatment with direct-acting antiviral drugs are still unclear, which poses a challenge to further improve the permanent cure rate of HCV-infected patients. In this paper, a stochastic within-host HCV model is studied in detail to gain insights into the phenomena of unexpected relapse and recovery in HCV-infected patients. Theoretically, the existence of an ergodic stationary distribution, which also reflects the long-term coexistence of uninfected hepatocytes and free viruses, is proved by constructing suitable stochastic Lyapunov functions at a threshold condition related to the basic reproduction number of the corresponding deterministic model. In addition, the sufficient conditions for the extinction of free viruses is also given, which implies that the viral load eventually drops to zero and HCV-infected patients are cured. In the numerical simulations, the phenomenon of unexpected relapse and recovery in HCV-infected patients is demonstrated by a few simple examples. By Monte Carlo method, under certain conditions, it is observed that the increase in noise intensities makes the phenomena of unexpected relapse and recovery in HCV-infected patients increase as well. [ABSTRACT FROM AUTHOR]

This paper proposes a delayed periodic Microcystins degradation model with nonlinear functional responses. By using the continuation theorem in the coincidence degree, we obtain two classes of explicit sufficient conditions for the existence of positive periodic solutions of the model. [ABSTRACT FROM AUTHOR]

This paper considers global dynamics of a nonautonomous Kawasaki disease model with two time delays. We establish two important parameters R p and R e. It is shown that, (i) if R p > 1 , the model is permanent, and some explicit analytic expressions of ultimate lower bounds of any positive solution of the model are given; (ii) if R e < 1 , the model is globally attractive, and inflammatory factors will be eventually cleared. Our results extend and improve related works in the existing literature. [ABSTRACT FROM AUTHOR]