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.

Numerical modeling of mosquito population dynamics of Aedes aegypti.

BACKGROUND: The global incidences of dengue virus have increased the interest in studying and understanding the mosquito population dynamics. It is predominantly spread by Aedes aegypti in the tropical and sub-tropical countries in the world. Understanding these dynamics is important for public health in countries where climatic and environmental conditions are favorable for the propagation of these diseases. For this reason, a new model has been proposed to investigate the population dynamics of mosquitoes in a city. METHODS: The present paper discusses the numerical modeling of population dynamics of Ae. aegypti mosquitoes in an urban neighborhood of a city using the finite volume method. The model describes how populations spread through the city assisted by the wind. This model allows incorporating external factors (wind and chemical insecticides) and topography data (streets, building blocks, parks, forests and beach). The proposed model has been successfully tested in examples involving two Brazilian cities (City center, Juiz de Fora and Copacabana Beach, Rio de Janeiro). RESULTS: Invasion phenomena of Ae. aegypti mosquitoes have been observed in each of the simulations. It was observed that, inside the blocks, the growth of the population for both winged and aquatic phase causes an infestation of Ae. aegypti in a short time. Within the blocks the mosquito population was concentrated and diffused slowly. In the streets, there was a long-distance spread, which was influenced by wind and diffusion with a low concentration of mosquito population. The model was also tested taking into account chemical insecticides spread in two different configurations. It has been observed that the insecticides have a significant effect on the mosquito population for both winged and aquatic phases when the chemical insecticides spread more uniformly along all the streets in a neighborhood of a city. CONCLUSIONS: The presented methodology can be employed to evaluate and to understand the epidemic risks in a specific region of the city. Moreover the model allows an increase in efficiency of the existing mosquito population control techniques and to theoretically test new methods before involving the human population.