Stability Of Infection-free Steady State Research Articles

Global dynamics of a periodic viral infection model incorporating diffusion and antiretroviral therapy

A new viral infection model with cell-to-cell infection and periodic antiretroviral therapy was proposed and analyzed. With the help of defined basic reproduction number [Formula: see text], we proved that if [Formula: see text], then the infection-free steady state is globally attractive. If [Formula: see text], then the infection is uniformly persistent. Furthermore, the globally asymptotical stability of infection-free steady state has been established for the critical case of [Formula: see text]. Also, the global asymptotic stability of the infection steady state for a special case of the model has been established by applying the method of Lyapunov. Numerical simulations show that increasing the drug efficacy for blocking virus-to-cell infection, cell-to-cell infection and producing non-infectious virus contributes to weakening the severity of viral infection.

A viral co-infection model with general infection rate in deterministic and stochastic environments

In this paper, we present a model of infection in which a virus can simultaneously infect two types of target cells. The model has a general form of infection rates in deterministic and stochastic settings, incorporating bilinear infection rates, saturated incidences and half-saturated incidences. In the deterministic case, we investigate the existence and stability of infection-free steady state and infection steady state, respectively. Considering that the infection rate coefficient is affected by random noise, we built the corresponding stochastic model using the Ornstein–Uhlenbeck process. In the stochastic case, by constructing suitable Lyapunov functions, we established sufficient conditions for the stationary distribution and extinction of the model, respectively. In addition, the covariance matrix in the probability density function of the model near the infection steady state is determined. Finally, we consider the three most common forms of virus infection and perform comprehensive numerical simulations to support our theoretical results.

Viral diffusion and cell-to-cell transmission: Mathematical analysis and simulation study

We propose a general model to investigate the joint impact of viral diffusion and cell-to-cell transmission on viral dynamics. The mathematical challenge lies in the fact that the model system is partially degenerate and the solution map is not compact. While the simpler cases with only indirect transmission mode or weak cell-to-cell transmission mode have been extensively studied in the literature, it remains an open problem to understand the local and global dynamics of fully coupled viral infection model with partial degeneracy. In this paper, we identify the basic reproduction number as the spectral radius of the sum of two linear operators corresponding to direct and indirect transmission modes. It is well-known that viral mobility may induce infection in low-risk regions. However, as diffusion coefficient increases, we prove that the basic reproduction number actually decreases, which indicates that faster viral movements may result in a lower level of viral infection. By an innovative construction of Lyapunov functionals, we further demonstrate that the basic reproduction number is the threshold parameter which determines global picture of viral dynamics. In addition to the traditional dichonomy results of extinction and persistence as obtained in earlier works for many simpler models, we are able to prove global asymptotic stability of infection-free steady state and global attractiveness (as well as uniqueness) of chronic-infection steady state, depending on whether the basic reproduction number is smaller or greater than one. Numerical simulation supports our theoretical results and suggests an interesting phenomenon: boundary layer and internal layer may occur when the diffusion parameter tends to zero.

Global dynamics of a virus infection model with repulsive effect

This paper is devoted to investigate a virus infection model with a spatially heterogeneous structure and nonlinear diffusion. First we establish the properties of the basic reproduction number \begin{document}$ R_0 $\end{document} for infected cells and free virus particles. Then we prove that the comparison principle can be applied to an auxiliary system with quasilinear diffusion under appropriate conditions. Then the sufficient conditions for the globally asymptotical stability of infection-free steady state are obtained, which indicates that \begin{document}$ R_0 is necessary for infected cells and free virus particles to be extinct. Next we prove the existence of positive non-constant steady states and the persistence of infected cells and free virion where \begin{document}$ R_0>1 $\end{document} is required. Finally, it is shown that, for the spatially homogeneous case when the infected cells rate of change of the repulsive effect is small enough, \begin{document}$ R_0 $\end{document} is the only determinant of the global dynamics of the underlying virus infection system. The obtained results give an insight into the optimal control of the virion.