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

TL;DR

This paper develops reaction-diffusion models for dengue transmission, analyzing symmetry, stability, and wave speeds to understand disease spread and mosquito invasion dynamics.

Contribution

It introduces mathematical models incorporating symmetry analysis and wave speed calculations for dengue transmission, extending previous work with new stability insights.

Findings

Identified Lie symmetries of the models

Determined stability regions based on reproduction numbers

Calculated wave speeds for mosquito invasion and dengue spread

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.