Global asymptotic properties of virus dynamics models withdose-dependent parasite reproduction and virulence and non-linearincidence rate

摘要

We consider two models for the spread of an infection with a free-living infective stage, where parasitereproduction and virulence (parasite-induced mortality) depend on the parasite dose to which the host isexposed and are given by unspecified non-linear functions of the number of the free pathogen particles,and the incidence rate is non-linear. We study the impact of these non-linearities with the focus on theglobal properties of these models. We consider a very general form of the non-linearities: we assumethat the virulence and the parasite reproduction rates are given by unspecified non-linear functions of thenumber of the free pathogen particles and that the incidence rate is an unspecified function of the numberof susceptible hosts and free pathogen particles; all these functions are constrained by a few biologi-cally feasible conditions. We construct Lyapunov functions that enable us to find biologically realisticconditions which are sufficient to ensure existence and uniqueness of a globally asymptotically stableequilibrium state. Depending on the value of the basic reproduction number, this equilibrium state can beeither positive, where parasite endemically persists, or infection free.