Mathematical Analysis of an Immune-structured Chikungunya Transmission Model

Authors

  • Kambire Famane Nuniversity Joseph Ki Zerbo
  • Gouba Elisée University Joseph Ki Zerbo
  • Tao Sadou University Joseph Ki Zerbo
  • Blaise Some

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3532

Keywords:

Chikungunya, Differential equations, Asymptotic stability, Basic reproduction number, Modeling and numerical simulation

Abstract

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, it appears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the disease
free equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

Author Biographies

  • Kambire Famane, Nuniversity Joseph Ki Zerbo
    UFR/SEA Department of Mathematics
  • Gouba Elisée, University Joseph Ki Zerbo
    UFR/SEA, Department of Mathematics
  • Tao Sadou, University Joseph Ki Zerbo
    UFR/SEA, Department of Mathematics

Downloads

Published

2019-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Mathematical Analysis of an Immune-structured Chikungunya Transmission Model. (2019). European Journal of Pure and Applied Mathematics, 12(4), 1533-1552. https://doi.org/10.29020/nybg.ejpam.v12i4.3532