A mathematical model analysis of the human melioidosis transmission dynamics with an asymptomatic case

Habtamu Ayalew Engida; David Mwangi Theuri; Duncan Gathungu; John Gachohi; Haileyesus Tessema Alemneh

doi:10.1016/j.heliyon.2022.e11720

A mathematical model analysis of the human melioidosis transmission dynamics with an asymptomatic case

Heliyon. 2022 Nov 15;8(11):e11720. doi: 10.1016/j.heliyon.2022.e11720. eCollection 2022 Nov.

Authors

Habtamu Ayalew Engida¹, David Mwangi Theuri², Duncan Gathungu², John Gachohi³, Haileyesus Tessema Alemneh⁴

Affiliations

¹ Pan African University for Basic Science, Technology and Invocation (PAUSTI)/JKUAT, Nairobi, Kenya.
² Department of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.
³ School of Public Health, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.
⁴ Department of Applied Mathematics, University of Gondar, Ethiopia.

Abstract

In this paper, we develop and examine a mathematical model of human melioidosis transmission with asymptomatic cases to describe the dynamics of the epidemic. The basic reproduction number $(R_{0})$ of the model is obtained. Disease-free equilibrium of the model is proven to be globally asymptotically stable when $R_{0}$ is less than the unity, while the endemic equilibrium of the model is shown to be locally asymptotically stable if $R_{0}$ is greater than unity. Sensitivity analysis is performed to illustrate the effect of the model parameters influencing on the disease dynamics. Furthermore, numerical experiments of the model are conducted to validate the theoretical findings.

Keywords: Asymptomatic; Basic reproduction number; Burkholderia pseudomallei; Equilibria and stability; Melioidosis; Numerical simulation; Sensitivity analysis.