Global Dynamics of a Delayed Fractional-Order Viral Infection Model With Latently Infected Cells

In this paper, we propose a fractional-order viral infection model, which includes latent infection, a Holling type II response function, and a time-delay representing viral production. Based on the characteristic equations for the model, certain sufficient conditions guarantee local asymptotic stability of infection-free and interior steady states. Whenever the time-delay crosses its critical value (threshold parameter), a Hopf bifurcation occurs. Furthermore, we use LaSalle’s invariance principle and Lyapunov functions to examine global stability for infection-free and interior steady states. Our results are illustrated by numerical simulations.

Global Dynamics of a Stochastic Viral Infection Model with Latently Infected Cells

In this paper, we study the global dynamics of a stochastic viral infection model with humoral immunity and Holling type II response functions. The existence and uniqueness of non-negative global solutions are derived. Stationary ergodic distribution of positive solutions is investigated. The solution fluctuates around the equilibrium of the deterministic case, resulting in the disease persisting stochastically. The extinction conditions are also determined. To verify the accuracy of the results, numerical simulations were carried out using the Euler–Maruyama scheme. White noise’s intensity plays a key role in treating viral infectious diseases. The small intensity of white noises can maintain the existence of a stationary distribution, while the large intensity of white noises is beneficial to the extinction of the virus.

A delayed reaction–diffusion viral infection model with nonlinear incidences and cell-to-cell transmission

In this paper, we propose a reaction–diffusion viral infection model with nonlinear incidences, cell-to-cell transmission, and a time delay. We impose the homogeneous Neumann boundary condition. For the case where the domain is bounded, we first study the well-posedness. Then we analyze the local stability of homogeneous steady states. We establish a threshold dynamics which is completely characterized by the basic reproduction number. For the case where the domain is the whole Euclidean space, we consider the existence of traveling wave solutions by using the cross-iteration method and Schauder’s fixed point theorem. Finally, we study how the speed of spread in space affects the spread of cells and viruses. We obtain the existence of the wave speed, which is dependent on the diffusion coefficient.