Abstract
We propose and study a viral infection model with two nonlocal effects and a general incidence rate. First, the semigroup theory and the classical renewal process are adopted to compute the basic reproduction number R0 as the spectral radius of the next-generation operator. It is shown that R0 equals the principal eigenvalue of a linear operator associated with a positive eigenfunction. Then we obtain the existence of endemic steady states by Shauder fixed point theorem. A threshold dynamics is established by the approach of Lyapunov functionals. Roughly speaking, if R0<1, then the virus-free steady state is globally asymptotically stable; if R0>1, then the endemic steady state is globally attractive under some additional conditions on the incidence rate. Finally, the theoretical results are illustrated by numerical simulations based on a backward Euler method.
Highlights
We still assume that there are three compartments involved in the viral infection for uninfected target cells, infected cells, and free virions
We firstly proposed a within-host viral infection model with nonlocal diffusion and nonlocal transmission
The model can be considered as a spatial generalization of that proposed by Nowark and Bangham [43], a continuous spatial model of Funk et al [9]
Summary
In a typical compartmental viral infection model, there are three compartments for uninfected target cells (T), infected cells (I), and free virions (V). Motivated by the aforementioned works, we propose a nonlocal diffusive viral infection model with a general incidence rate. We still assume that there are three compartments involved in the viral infection for uninfected target cells, infected cells, and free virions. Their densities at time t and position x ∈ Ω are denoted by T(t, x), I(t, x), and V(t, x), respectively.
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