Mathematical Modelling and Numerical Analysis of Hepatitis B Virus Transmission Dynamics with Vaccination and Treatment Control Strategies
B. G. Urekar *
Late Babasaheb Deshmukh Gorthekar Mahavidyalaya, Umri Dist- Nanded (MH) -431807, India.
S. B. Chavhan
Digambarrao Bindu Mahavidyalaya, Bhokar Dist- Nanded (MH)- 431801, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper presents a mathematical model for studying the transmission dynamics of the Hepatitis B Virus (HBV), incorporating vaccination and treatment strategies. The proposed model is analyzed to establish important mathematical properties, including positivity, boundedness, and the feasible region, ensuring the biological validity of the system. The disease-free equilibrium (DFE) and endemic equilibrium (EE) points are derived, and their local as well as global stability. conditions are investigated through the basic reproduction number R0. The analysis indicates that the disease can be effectively controlled when R0 < 1, whereas HBV persists within the population when R0 > 1. Furthermore, the findings highlight the crucial impact of vaccination and treatment interventions in reducing HBV transmission. The study provides valuable theoretical insights that may support the development of effective public health policies and disease management strategies for controlling Hepatitis B infection.
Keywords: Hepatitis B, mathematical model, stability, basic reproduction number, disease-free equilibrium state, endemic equilibrium state