Modeling the Symbiotic Interactions Between Wolbachia and Insect Species

A sex-structured mathematical model is proposed to address the interactions among Wolbachia and Aedes mosquitoes. Several features associated with the infection that impacts mosquito phenotype like the cytoplasmic incompatibility, sex ratio biased to females, and maternal inheritance are considered. The analysis of the model shows the presence of three equilibria: the infection-free point, which is attainable only for a narrow range of initial conditions, the point where all individuals are infected, which however arises only in a very particular situation, namely the full vertical transmission of the bacterium, and the endemic equilibrium. Thresholds for the stability of the coexistence equilibrium are obtained, and they involve a relation among parameters and the initial prevalence of the infected mosquito in the population. As expected, increasing the sex ratio biased to females promotes the fixation of the infection on the population at high values.