New virus dynamics in the presence of multiple infection

Abstract

While most aspects of virus dynamics are well understood in standard models, the phenomenon of multiple infection (or coinfection) can change the properties of the dynamics, and this has so far not been fully explored. An important parameter in determining the properties of the model is the virus output from multiply infected cells compared to that from singly infected cells. If the amount of virus produced by infected cells during their life-span is independent of the infection multiplicity, then multiple infection does not change the dynamics. If, however, multiply infected cells produce more virus during their life-span than singly infected cells, then the properties of the dynamics can change fundamentally. This paper presents a detailed mathematical analysis of this scenario. We demonstrate that under some realistic conditions, the equilibrium structure of the solutions acquires novel properties. In particular, infection can persist even for values of the basic reproductive number, R0, smaller than unity. In this regime, we observe the phenomenon of bistability, when two stable equilibria are present simultaneously, and the outcome is determined by the initial conditions. The two possible solutions are the virus-free equilibrium, which is exactly the same as the one observed in the absence of multiple infection, and a novel infection equilibrium. In the presence of this outcome, it is clear that the meaning of the parameter R0 changes, as it no longer simply indicates the possibility of successful infection. This adds to our understanding and interpretation of R0 in virus dynamics models, and also provides further insights about conditions that can lead to virus extinction rather than persistence. It turns out that conditions for bistability depend (in a fully specified way) on the model structure, particularly on the way the infection term is formulated. We provide a general condition that informs us whether or not bistability occurs, and define what needs to be measured when examining the dynamics of multiple infection in specific biological systems.