Mathematical modelling for the transmission of dengue: Symmetry and travelling wave analysis

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. 2010 AMS Mathematics Classification numbers: 34D20, 35B35, 76M60, 92Bxx

Symmetry analysis for a Fisher equation with exponential diffusion

“…19 Recently, symmetries are becoming a common tool studying biological phenomena. [20][21][22] The paper is organized as follows. In Section 2, by using the infinitesimal method, we obtain the equivalence transformations.…”

The first integrals and closed‐form solutions of a Susceptible‐Exposed‐Infectious epidemic model

“…Anderson 2 developed a model for the human immunodeficiency virus (HIV) to analyze the HIV transmission dynamics in San Francisco. The transmission dynamics of tuberculosis was studied by Song et al 3 A variety of models have been developed to analyze the transmission and control of the novel coronavirus (COVID- 19), which include SIR model, 4 Susceptible-Asymptotic-Infectious-Recovered (SAIR), 5 Susceptible-Exposed-Infectious-Recovered (SEIR), 6 and extensions of these models.…”

“…A separate strand of literature analyzed the dispersal dynamics of models for vectors of some epidemic diseases. [19][20][21] To the best of our knowledge, the first integrals and closed-form solutions for the SEI disease model studied by Guihua and Zhen 22 have not yet been considered in the literature and are the subject of this work. The different techniques to construct first integrals/conservation laws are presented in previous works.…”

“…Naz and Al‐Raeei 18 investigated the transmission dynamics of COVID‐19 via closed‐form solutions of Susceptible‐Infectious‐Quarantined‐Diseased (SIQD) model by utilizing the classical methods of solving ODEs. A separate strand of literature analyzed the dispersal dynamics of models for vectors of some epidemic diseases 19–21 …”

Group classification and analytical solutions of a radially symmetric avascular cancer model

“…26, where language models were studied; Ref. [27][28][29], where symmetries were used to explore problems related to dengue; Refs. 30,31, where the authors considered and examined generalizations of the Fisher equation; Ref.…”