Monotonicity properties arising in a simple model of invasion for wild mosquito populations.

In this paper, we propose a simplified bidimensional infestation model in a population of mosquitoes, preserving the main features associated with the biology of this species that can be found in higher-dimensional models. Namely, our model represents the maternal transmission of the symbiont, expresses the reproductive phenotype of cytoplasmic incompatibility, accounts for different fecundities and mortalities of infected and wild insects, and exhibits the bistable nature leading to the so-called . Using tools borrowed from monotone dynamical system theory, in the proposed model, we prove the existence of an invariant threshold manifold that allows us to provide practical recommendations for performing single and periodic releases of -carrying mosquitoes, seeking the eventual elimination of wild insects that are capable of transmitting infections to humans. We illustrate these findings with numerical simulations using parameter values corresponding to the strain of that is considered the best virus blocker but induces fitness loss in its carriers. In these tests, we considered multiple scenarios contrasting a periodic release strategy against a strategy with a single inundative release, comparing their effectiveness. Our study is presented as an expository and mathematically accessible tool to study the use of Wolbachia-based biocontrol versus more complex models.