Structured and unstructured continuous models for Wolbachia infections

TL;DR

This paper develops and analyzes continuous models, including age-structured variants, to understand Wolbachia infection dynamics in host populations, highlighting how different factors influence infection invasion and stability.

Contribution

It introduces a series of continuous and age-structured models for Wolbachia infections, exploring their dynamics and invasion criteria with minimal parameters.

Findings

Age-structured model shows different equilibrium stability compared to unstructured models.

Models predict conditions for Wolbachia strain invasion.

Dynamics depend on transmission, incompatibility, and fitness costs.

Abstract

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont \textit{Wolbachia}. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.