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Global dynamics of a diffusive viral infection model with spatial heterogeneity. (English) Zbl 1517.35124

Summary: To explore the joint impact of cell-free infection and cytokine-enhanced viral infection, we propose a PDE model with spatial heterogeneity by taking into account a general cell reproduction function, free-virus infection function and cytokine-enhanced viral infection function. Mathematical challenges lie in the facts that (i) the solution map of the model system loses its compactness; and (ii) the definition of the basic reproduction number and the global asymptotic stability of the infection-free steady state become challenging since the linear system at the infection-free steady state is constituted by three equations. We define the basic reproduction number \(R_0\) as the spectral radius of the sum of two linear operators corresponding to cell-free infection and cytokine-enhanced viral infection, and prove its threshold role: if \(R_0 < 1\), the infection-free steady state is globally asymptotically stable; if \(R_0 = 1\), the infection-free steady state is locally asymptotically stable; and if \(R_0 > 1\), the model system is uniformly persistent. A special case is given to show the global attractiveness of the infection steady state.

MSC:

35K57 Reaction-diffusion equations
35K51 Initial-boundary value problems for second-order parabolic systems
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Full Text: DOI

References:

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