A mathematical analysis of the dynamics of chikungunya virus transmission

Authors

  • Saiful Islam Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
  • Chandra Nath Podder Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh

DOI:

https://doi.org/10.3329/ganit.v41i1.55025

Keywords:

Chikungunya; Epidemiological Model; Stability and numerical results; Treatment; Sensitivity Analysis

Abstract

In this paper, a deterministic model for the dynamics of chikungunya virus transmission is formulated and analyzed. It is shown that the model has a disease free equilibrium (DFE) and by using the basic reprodution number (R0) local stability of DFE is proved when  R0 < 1. Also, the global stability of DFE is investigated by Lyapunov function and LaSalle Invariance Principle. We show that there exists a unique endemic equilibrium (EE) of the model which is locally asymptotically stable whenever R0 > 1 and establish the global stability of the EE when R0 > 1, by using Lyapunov function and LaSalle Invariance Principle for a special case. Numerical simulations and sensitivity analysis show that the destruction of breeding sites and reduction of average life spans of vector would be effective prevention to control the outbreak. Controlling of effective contact rates and reducing transmissions probabilities may reduce the disease prevalence.

GANITJ. Bangladesh Math. Soc.41.1 (2021) 41-61

Downloads

Download data is not yet available.
Abstract
72
PDF
73

Downloads

Published

2021-10-05

How to Cite

Islam, S. ., & Podder, C. N. . (2021). A mathematical analysis of the dynamics of chikungunya virus transmission. GANIT: Journal of Bangladesh Mathematical Society, 41(1), 41–61. https://doi.org/10.3329/ganit.v41i1.55025

Issue

Section

Articles