Modeling and simulation of the spatial population dynamics of the Aedes aegypti mosquito with an insecticide application

Abstract

Background The Aedes aegypti mosquito is the primary vector for several diseases. Its control requires a better understanding of the mosquitoes’ live cycle, including the spatial dynamics. Several models address this issue. However, they rely on many hard to measure parameters. This work presents a model describing the spatial population dynamics of Aedes aegypti mosquitoes using partial differential equations (PDEs) relying on a few parameters. Methods We show how to estimate model parameter values from the experimental data found in the literature using concepts from dynamical systems, genetic algorithm optimization and partial differential equations. We show that our model reproduces some analytical formulas relating the carrying capacity coefficient to experimentally measurable quantities as the maximum number of mobile female mosquitoes, the maximum number of eggs, or the maximum number of larvae. As an application of the presented methodology, we replicate one field experiment numerically and investigate the effect of different frequencies in the insecticide application in the urban environment. Results The numerical results suggest that the insecticide application has a limited impact on the mosquitoes population and that the optimal application frequency is close to one week. Conclusions Models based on partial differential equations provide an efficient tool for simulating mosquitoes’ spatial population dynamics. The reduced model can reproduce such dynamics on a sufficiently large scale.

Modeling the Transmission of Wolbachia in Mosquitoes for Controlling Mosquito-Borne Diseases

“…Diffusion coefficient for F w (m 2 /day) 1.25×10 4 [21,23] condition for a sustained Wolbachia infection. Qu and Hyman [16] provided a detailed description of the reduction process and the comparison among different reduced models, and we summarize the key findings below.…”

Modeling the impact of genetically modified male mosquitoes in the spatial population dynamics of Aedes aegypti

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“…In the present work, we extend the base model for the spatial mosquito population dynamics 24 to include wild male mosquitoes and genetically modified male mosquitoes. Thus, five populations will be considered: the aquatic mosquito population, including larvae and pupae, the egg mosquito population, the reproductive female mosquito population, the wild male mosquito population, and the genetically modified male population.…”

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