An Algebraic Discussion of Bisexual Populations with Wolbachia Infection I: Discrete Dynamical System Approach

TL;DR

This paper models Wolbachia-infected bisexual populations using discrete dynamical systems, analyzing how initial infection frequencies and cytoplasmic incompatibility influence population dynamics, supported by experimental data comparisons.

Contribution

It introduces a novel discrete dynamical system framework for studying Wolbachia infection dynamics in bisexual populations, incorporating empirical data.

Findings

Model accurately predicts infection spread and stability.

Initial infection frequencies significantly affect population outcomes.

Comparison with real data validates the model's applicability.

Abstract

This is the first paper in the sequel studying the Wolbachia-infection in bisexual populations. This paper considers the behavior of the population as a discrete dynamical system. The recurrence relation is obtained as a function of the initial infected male/female frequencies and the cytoplasmic incompatibility of the population. The experimental data from Wolbachia-infected terrestrial isopod populations and the model proposed in Wolbachia-infected mosquitoes from literature is compared with the discrete dynamical system achieved.