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.
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.
This work aims to study a model of partial differential equations (PDE) for the population dynamics of the Aedes aegypti mosquito. We propose a numerical resolution using finite volumes. We evaluated the influence of temperature in modeling the parameters and the results for simulations at three different temperatures. The obtained results encourage a discussion about the importance of prevention during the rainy season and compare the cases of dengue during the first thirty epidemiological weeks of two thousand and nineteen.
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time quantum walk on arbitrary graphs by providing a recipe for finding the optimal running time and the success probability of the algorithm. The quantum walk is driven by a Hamiltonian that is obtained from the adjacency matrix of the graph modified by the presence of the marked vertices. The success of our framework depends on the knowledge of the eigenvalues and eigenvectors of the adjacency matrix. The spectrum of the modified Hamiltonian is then obtained from the roots of the determinant of a real symmetric matrix, whose dimension depends on the number of marked vertices. We show all steps of the framework by solving the spatial searching problem on the Johnson graphs with fixed diameter and with two marked vertices. Our calculations show that the optimal running time is O( √ N ) with asymptotic probability 1 + o(1), where N is the number of vertices.
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