Monotonicity properties arising in a simple model of <i>Wolbachia</i> invasion for wild mosquito populations
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Published:2022
Issue:1
Volume:20
Page:1148-1175
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ISSN:1551-0018
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Container-title:Mathematical Biosciences and Engineering
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language:
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Short-container-title:MBE
Author:
Vicencio Diego1, Vasilieva Olga2, Gajardo Pedro1
Affiliation:
1. Departmento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, 2390123, Chile 2. Departmento de Matemáticas, Universidad del Valle, Cl. 13,100-00, Cali, Valle del Cauca 760032, Colombia
Abstract
<abstract><p>In this paper, we propose a simplified bidimensional <italic>Wolbachia</italic> infestation model in a population of <italic>Aedes aegypti</italic> 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 <italic>Wolbachia</italic> 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 <italic>principle of competitive exclusion</italic>. 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 <italic>Wolbachia</italic>-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 <italic>wMelPop</italic> strain of <italic>Wolbachia</italic> 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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine
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