Global Stability for a Virus Dynamics Model with Nonlinear Incidence of Infection and Removal

Abstract

Global dynamics of a compartmental model which describes virus propagation in vivo is studied using the direct Lyapunov method, where the incidence rate of the infection and the removal rate of the virus are assumed to be nonlinear. In the case where the functional quotient between the force of infection and the removal rate of the virus is a nonincreasing function of the virus concentration, the existence of a threshold parameter, i.e., the basic reproduction number or basic reproductive ratio, is established and the global stability of the equilibria is discussed. Moreover, in the absence of the above-mentioned monotonicity property, estimations for the sizes of the domains of attraction are given. Biological significance of the results and possible extensions of the model are also discussed.

Global stability of the endemic equilibrium in infinite dimension: Lyapunov functions and positive operators

“…Threshold operator is an operational name for what is often called the next generation operator [11]. We prefer it in this context because the interpretation as next generation operator is less compelling than in other contexts because we include non-bilinear incidence [14,[28][29][30][31]35,36,49,51]. Other transmission terms than the bilinear κ S I have some history in mathematical biology (see [7,Chapter 3] and [28] for surveys); as for epidemiological evidence see [6,16,47,60] and the references therein.…”

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

“…In particular, the Lyapunov functions from [9] are available also for the study of the asymptotic behaviour of the basic model of virus dynamics, see also [2], [4]. Thus there arises the natural question whether it is possible to generalize this approach to the case of models taking into account immune response, cf.…”

Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages

“…This function, which has its origin in ecology, was extended to the models of epidemiology by Korobeinikov and Wake (2002) and Korobeinikov (2004a), and then effectively applied to a variety of compartment models, including the models with multiple progressive stages (Guo and Li, 2006;Korobeinikov, 2004b), and models with nonlinear incidence rates of different forms (Georgescu and Hsieh, 2006;Korobeinikov, 2006Korobeinikov, , 2007Korobeinikov, , 2008Maini, 2004, 2005;Korobeinikov and Petrovskii, 2008).…”