Mathematical Modeling of Hepatitis B Virus Transmission with control Strategies in Ethiopia

Abstract

Hepatitis B virus (HBV) infection remains a major public health challenge in high-endemic countries such as Ethiopia, where chronic carriers play a critical role in sustaining long-term transmission. In this study, a deterministic compartmental SEICR model is developed to describe the transmission dynamics of HBV, incorporating vaccination of susceptible individuals and treatment of chronic carriers as control strategies. The model is formulated under biologically meaningful assumptions and is shown to be mathematically well-posed through positivity and boundedness analysis. The basic reproduction number, denoted by R0, is derived using the next-generation matrix method and decomposed into contributions from acute and chronic infectious classes. Local stability analysis of the disease-free equilibrium is carried out, and conditions for disease elimination are established in terms of R0. Numerical simulations are performed to investigate the impact of vaccination and treatment strategies under baseline parameter values relevant to the Ethiopian context. Sensitivity analysis is conducted to identify the most influential parameters governing HBV transmission. The results indicate that reducing R0 below unity requires vaccination coverage exceeding a critical threshold. Under baseline parameter assumptions, the model predicts that vaccination coverage must reach approximately 70% in order to ensure R0 < 1 and achieve disease elimination. These findings highlight the importance of sustained immunization programs combined with effective treatment of chronic carriers. The proposed modeling framework provides quantitative insight into HBV transmission dynamics and offers a useful tool for evaluating control strategies in high-endemic, resource-limited settings such as Ethiopia.