Abstract
Due to recent advances in genetic manipulation, transgenic mosquitoes can be a viable alternative to reduce some diseases. Viability conditions are obtained by the simulation and analysis of mathematical models that describe the behavior of wild and transgenic mosquitoes population living in the same geographic area. In this work, we present a reaction-diffusion model, where the term reaction is a nonlinear function that describes the interaction between wild and transgenic mosquitoes taking into account their zygosity and the diffusive term representing a uniform spatial spread characterized by a fixed diffusion parameter. The system of partial differential equations obtained is solved numerically by combining the implicit Runge-Kutta method and the finite element method through the sequential operator splitting technique. Several scenarios are analyzed simulating the spatial release of transgenic mosquitoes, demonstrating an intrinsic relationship between the transgenic and wild varieties for different initial conditions.
Highlights
Vector-borne diseases have always been a big preoccupation for populations and government authorities in tropical countries, especially in those with low human development rates
The proposed mathematical model is based on strategies aimed at genetically modified mosquitoes that are designed to have a reduced transmission capacity of a given infectious agent
The mathematical model presented is based on the Fisher-KPP equation [4, 11], assuming that the populations have the same fitness, according to studies on A. stephensi [17], which ensures to the mosquitoes the reproductive success and adaptations to the environment wild, with competitive ability
Summary
Vector-borne diseases have always been a big preoccupation for populations and government authorities in tropical countries, especially in those with low human development rates. The scientists developed two different types of Anopheles stephensi using the CP (carboxypeptidase) promoter: one of them expressing peptide SM1 (salivary gland and midgut binding peptide 1) [10] and the other expressing the enzyme PLA2 (phospholipase A2), present in bee venom [16] These new insects must interact with wild mosquitoes by mating and spreading the gene that determines the interruption of the transmission process. The proposed mathematical model is based on strategies aimed at genetically modified mosquitoes that are designed to have a reduced transmission capacity of a given infectious agent They are fertile and able to propagate and perpetuate their hereditary trait in the wild mosquito population.
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