A Mathematical Modelling of Lassa Fever Dynamics with Non-drug Compliance Rate

T.S. Faniran

doi:https://doi.org/10.14445/22315373/IJMTT-V47P542

International Journal of Mathematics Trends and Technology

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Volume 47 | Number 5 | Year 2017 | Article Id. IJMTT-V47P542 | DOI : https://doi.org/10.14445/22315373/IJMTT-V47P542

A Mathematical Modelling of Lassa Fever Dynamics with Non-drug Compliance Rate

T.S. Faniran

Abstract

This paper presents a mathematical model that tracks the transmission dynamics of Lassa fever in a two-interacting human host and rodent vector populations. The model incorporates a non-drug compliance rate in the parameters for the human population. Non-drug compliance rate is the rate at which infectious humans, who are given medication by their doctors, do not comply with drug. The basic reproduction number is derived and the stability of the disease-free and endemic equilibrium points is analysed. A locally asymptotically stable disease-free equilibrium at the basic reproduction number less than unity is derived through the analysis of characteristic equation. It was established that the disease-free equilibrium point is globally asymptotically stable when the reproduction number, Ro < 1 and the disease always dies out. For R0 > 1, the disease-free equilibrium point becomes unstable and the endemic equilibrium point is globally asymptotically stable.

Keywords

Lassa fever, non-drug compliance, basic reproduction number, compound matrices, stability.

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Citation :

T.S. Faniran, "A Mathematical Modelling of Lassa Fever Dynamics with Non-drug Compliance Rate," International Journal of Mathematics Trends and Technology (IJMTT), vol. 47, no. 5, pp. 305-318, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V47P542