Modelling Evolution of Virulence in Populations with a Distributed Parasite Load

Citation

Sandhu SK, Morozov AY & Farkas JZ (2020) Modelling Evolution of Virulence in Populations with a Distributed Parasite Load. Journal of Mathematical Biology, 80 (1-2), p. 111–141. https://doi.org/10.1007/s00285-019-01351-6

Abstract
Modelling evolution of virulence in host-parasite systems is an actively developing area of research with ever-growing literature. However, most of the existing studies overlook the fact that individuals within an infected population may have a variable infection load, i.e. infected populations are naturally structured with respect to the parasite burden. Empirical data suggests that the mortality and infectiousness of individuals can strongly depend on their infection load; moreover, the shape of distribution of infection load may vary on ecological and evolutionary time scales. Here we show that distributed infection load may have important consequences for the eventual evolution of virulence as compared to a similar model without structuring. Mathematically, we consider an SI model, where the dynamics of the infected subpopulation is described by a von Förster-type model, in which the infection load plays the role of age. We implement the adaptive dynamics framework to predict evolutionary outcomes in this model. We demonstrate that for simple trade-off functions between virulence, disease transmission and parasite growth rates, multiple evolutionary attractors are possible. Interestingly, unlike in the case of unstructured models, achieving an evolutionary stable strategy becomes possible even for a variation of a single ecological parameter (the parasite growth rate) and keeping the other parameters constant. We conclude that evolution in disease-structured populations is strongly mediated by alterations in the overall shape of the parasite load distribution.

Keywords
Structured populations; Infection load; Evolutionary attractor; Pairwise invasibility plot (PIP); Singular points; Trade-off; Stability

Journal
Journal of Mathematical Biology: Volume 80, Issue 1-2