High host density favors greater virulence: a model of parasite-host dynamics based on multi-type branching processes

TL;DR

This paper introduces a multitype branching process model incorporating lethality and transmissibility to study how host density influences parasite virulence and prevalence, highlighting the role of population size and cross-population transmission.

Contribution

It develops a novel multitype branching process model that captures the interplay of virulence traits and host density, extending to multiple populations with parasite transmission.

Findings

Higher host density favors more virulent parasite types.

Enclosure size affects encounter rates and pathogen dominance.

Model extension includes multiple populations and cross-transmission.

Abstract

We use a multitype continuous time Markov branching process model to describe the dynamics of the spread of parasites of two types that can mutate into each other in a common host population. Instead of using a single virulence characteristic which is typical of most mathematical models for infectious diseases, our model uses a combination of two characteristics: lethality and transmissibility. This makes the model capable of reproducing the empirically observed fact that the increase in the host density can lead to the prevalence of the more virulent pathogen type. We provide some numerical illustrations and discuss the effects of the size of the enclosure containing the host population on the encounter rate in our model that plays the key role in determining what pathogen type will eventually prevail. We also present a multistage extension of the model to situations where there are several populations and parasites can be transmitted from one of them to another.