Mathematical modelling of the transmission dynamics of Hepatitis B incorporating vertical and horizontal transmission with vaccination and treatment as control strategies

Abstract

In this study, we formulated a mathematical model of the transmission dynamics of hepatitis B considering both vertical and horizontal transmission and the impact of treatment and vaccination as control measures. The basic reproduction number R^B₀ was calculated to represent the persistence and eradication conditions of the disease. The following results of the analysis indicate that the disease free equilibrium is locally stable for R^B₀ <1 , globally stable forR^B₀ <1  and a stable endemic equilibrium is reached for R^B₀ >1. The parameters whose values had a positive sensitivity index increased the transmission of hepatitis B, such as contact and transmission rate, while the parameters whose values had a negative sensitivity index reduced the transmission of hepatitis B, such as the treatment and vaccination rate, etc. Numerical simulations also revealed that if the treatment and vaccination rate is increased, the burden of hepatitis B to the population is greatly reduced. This underscores the need for treatment interventions to break and potentially prevent the transmission of hepatitis B in humans. Thus, it is recommended to improve vaccination and treatment programmes, including interventions to prevent mother-to-child transmission, to effectively reduce and control the transmission of hepatitis B to the population.