Global threshold analysis on a diffusive host–pathogen model with hyperinfectivity and nonlinear incidence functions.

In this paper, we are concerned with the mathematical analysis of a host–pathogen model with diffusion, hyperinfectivity and nonlinear incidence. We define the basic reproduction number ℜ 0 by the spectral radius of the next generation operator, and study the relation between ℜ 0 and the principal eigenvalue of the problem linearized at the disease-free steady state (DFSS). Under some assumptions, we show the threshold property of ℜ 0 : if ℜ 0 < 1 , then the DFSS is globally asymptotically stable (GAS), whereas if ℜ 0 > 1 , then the system is uniformly persistent and a positive steady state (PSS) exists. Moreover, for the special case where all parameters are constants, we show that the PSS is GAS for ℜ 0 > 1. Numerical simulation suggests that the spatial heterogeneity could enhance the intensity of epidemic, whereas the diffusion effect could reduce it. [ABSTRACT FROM AUTHOR]