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In this paper, we propose a simplified bidimensional Wolbachia infestationmodel in a population of Aedes aegypti mosquitoes, preserving the main featuresassociated with the biology of this species that can be found inhigher-dimensional models. Namely, our model represents the maternaltransmission of the Wolbachia symbiont, expresses the reproductive phenotype ofcytoplasmic incompatibility, accounts for different fecundities and mortalitiesof infected and wild insects, and exhibits the bistable nature leading to theso-called principle of competitive exclusion. Since Wolbachia-based biocontrolis now accepted as an ecologically friendly and potentially cost-effectivemethod for prevention and control of dengue and other arboviral infections, itis essential to have reduced models with the main biological characteristics ofAedes aegypti in the presence of Wolbachia-carriers because such models help tosimplify the mathematical analysis for determining appropriate biocontrolstrategies. Using tools borrowed from monotone dynamical system theory, in theproposed model, we prove the existence of an invariant threshold manifold thatallows us to provide practical recommendations for performing single andperiodic releases of Wolbachia-carrying mosquitoes, seeking the eventualelimination of wild insects that are capable of transmitting infections tohumans. We illustrate these findings with numerical simulations using parametervalues corresponding to the wMelPop strain of Wolbachia that is considered thebest virus blocker but induces fitness loss in its carriers.

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