Chickenpox Childhood Disease: An insight from Mathematical Modelling

Abstract

Chickenpox is an infectious disease that causes an itchy, blister-like rash on the skin and can spread through bodily fluids and body contact. This study presents a mathematical model for the transmission dynamics of chickenpox among children by considering the impact of vaccination and treatment. The qualitative analysis of the model reveals that the model has two equilibrium points, namely: the chickenpox-free and endemic equilibrium points. The disease-free equilibrium point is globally asymptotically stable whenever the basic reproduction number is less than unity (R0<1) and the endemic equilibrium point is globally stable whenever the reproduction number is greater than unity (R0>1). The normalized forward sensitivity index is also used to obtain the critical factors responsible for the transmission of chickenpox in the population. Furthermore, it reveals that parameters with negative indices will reduce the transmission of chickenpox when increased. The qualitative analysis of the model is supported by numerical simulation