On a mathematical model and the efficacy of control measures on the transmission dynamics of chickenpox

Year 2025, Volume: 3 Issue: 1, 37 - 61, 30.04.2025

Charles Nkeki , I.a. Mbarie

https://doi.org/10.59292/bulletinbiomath.1707079

Abstract

In this paper, a mathematical model and stability analysis of the transmission dynamics of chickenpox in the presence of treatment, quarantine, precaution, and vaccination as control measures are presented. These control measures and vaccine efficacy on the spread of chickenpox are studied to see their role in influencing the basic reproduction number. The model's equilibrium points are studied, and the global asymptotic stability of the disease-free equilibrium and the local asymptotic stability of the endemic equilibrium are established. Numerical simulation is carried out to determine the significance and efficacy of the control measures in the control and management of the spread of chickenpox in the population. It is found that adopting the four control measures plays a prominent role in reducing the chance of contracting and the spread of chickenpox in the mentioned population. It is also found that compartmental treatment drastically reduces the spread of the disease.

Keywords

Mathematical modelling, chickenpox, control measures, endemic equilibrium, stability analysis, basic reproduction number

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