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

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.