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

The mosquito Aedes aegypti is the primary vector of diseases such as dengue, Zika, chikungunya, and yellow fever. Improving control techniques requires a better understanding of the mosquito's life cycle, including spatial population dynamics in endemic regions. One of the most promising techniques consists of introducing genetically modified male mosquitoes. Several models proposed to describe this technique present mathematical issues or rely on numerous parameters, making their application challenging to real-world situations. We propose a model describing the spatial population dynamics of the Aedes aegypti in the presence of genetically modified males. This model presents some mathematical improvements compared to the literature allowing deeper mathematical analysis. Moreover, this model relies on few parameters, which we show how to obtain or estimate from the literature. Through numerical simulations, we investigate the impacts of environmental heterogeneity, the periodicity of genetically modified male releases, and released genetically modified males quantity on the population dynamics of Aedes aegypti. The main results point to that the successful application of this vector control technique relies on releasing more than a critical amount of modified males with a frequency exceeding a specific critical value.

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.