Modeling the spreading and interaction between wild and transgenic mosquitoes with a random dispersal

• Published in: PloS one Vol. 13; no. 10; p. e0205879
• Main Authors: Wyse, Ana Paula, Santos, Antonio José Boness Dos, Azevedo, Juarez Dos Santos, Lima, Josenildo Silva de, Faria, Jairo Rocha de
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 31.10.2018; Public Library of Science (PLoS)
• Subjects: Aquatic insects; Arthropods; Biology and Life Sciences; Climate change; Computer and Information Sciences; Computer simulation; Culicidae; Differential equations; Diffusion; Diffusion parameters; Disease; Dispersal; Feasibility studies; Finite element method; Genetic engineering; Malaria; Mathematical models; Medicine and Health Sciences; Mosquitoes; Nonlinear systems; Operators (mathematics); Parameter uncertainty; Partial differential equations; Pathogens; Peptides; Physical sciences; Population; Research and analysis methods; Runge-Kutta method; Spreading; Tropical diseases; Vectors (Biology); Zygosity; Brazil
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0205879

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.