Abstract
Due to recent advances in genetic manipulation, transgenic mosquitoes may be a viable alternative to reduce some diseases. Feasibility conditions are obtained by simulating and analyzing mathematical models that describe the behavior of wild and transgenic populations living in the same geographic area. In this paper, we present a reaction–diffusion model in which the reaction term is a nonlinear function that describes the interaction between wild and transgenic mosquitoes, considering the zygosity, and the diffusive term that represents a nonuniform spatial spreading characterized by a random diffusion parameter. The resulting nonlinear system of partial differential equations is numerically solved using the sequential operator splitting technique, combining the finite element method and Runge-Kutta method. This scheme is numerically implemented considering uncertainty in the diffusion parameters of the model. Several scenarios simulating spatial release strategies of transgenic mosquitoes are analyzed, demonstrating an intrinsic association between the transgene frequency in the total population and the strategy adopted.
Highlights
Vector-borne diseases have always been of great concern to populations and government authorities in countries with a tropical climate, especially those with a low human development
We propose a new mathematical model that describes the dynamics of the interaction by the mating between transgenic and wild-type mosquitoes, as well as the spreading of the transgene that determines the interruption of an epidemiological process
We assume that there is no flow of mosquito populations on the boundary
Summary
Vector-borne diseases have always been of great concern to populations and government authorities in countries with a tropical climate, especially those with a low human development. The combination of favorable climate and precarious sanitation provides ideal environmental conditions for the proliferation of many vectors causing various types of diseases that affect the populations of these regions, leading to considerable economic and social disruption. Intensive farming, dams, irrigation, deforestation, population movements, rapid unplanned urbanization, and increases in international travel and trade [1], the incidence of tropical diseases has been extended to regions beyond the tropics, making such diseases a worldwide focus.
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