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arXiv · 1708.01277

Mathematical modelling for the transmission of dengue: symmetry and traveling wave analysis

Felipo Bacani·Stylianos Dimas·Igor Leite Freire·Norberto Anibal Maidana·Mariano Torrisi
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Abstract

In this paper we propose some mathematical models for the transmission of dengue using a system of reaction-diffusion equations. The mosquitoes are divided into infected, uninfected and aquatic subpopulations, while the humans, which are divided into susceptible, infected and recovered, are considered homogeneously distributed in space and with a constant total population. We find Lie point symmetries of the models and we study theirs temporal dynamics, which provides us the regions of stability and instability, depending on the values of the basic offspring and the basic reproduction numbers. Also, we calculate the possible values of the wave speed for the mosquitoes invasion and dengue spread and compare them with those found in the literature.

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Felipo Bacani, Stylianos Dimas, Igor Leite Freire, Norberto Anibal Maidana, Mariano Torrisi. 2017-08-03. Mathematical modelling for the transmission of dengue: symmetry and traveling wave analysis. https://doi.org/10.1016/j.nonrwa.2017.10.013

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