Exploring the effectiveness of control measures and long-term behavior in Hepatitis B: An analysis of an endemic model with horizontal and vertical transmission

Abstract

This study presents an optimal control and stability analysis of a mathematical model for the spread of Hepatitis B with a harmonic mean type incidence rate, providing insights into the effectiveness of control measures and the long-term behavior of the disease dynamics. The hepatitis B virus causes hepatitis B infection. It is one of the most serious viral infections out there, as well as a global health issue. Various stages, such as chronic and acute carrier stages, serve an essential role in the transition of hepatitis B infection. Chronic disease is characterized by the presence of individuals who do not show any symptoms but are nevertheless able to spread the illness. In this study, we focused on the infectiousness of hepatitis B at different stages of illness and created an endemic model by means of a nonlinear occurrence rate. To accomplish so, we start by dividing the infectious group into two further sub-classes: i.e., acute infected and chronic carriers, both of which can transmit horizontally and vertically. The suggested model’s basic characteristics are provided. The method of the next-generation matrix is utilized to compute the basic reproduction number. The biological significance of the threshold state is thoroughly researched and addressed. We also discover the criteria for investigating all of the model’s potential equilibria in terms of the fundamental reproduction number. Finally, to supplement our analytical work, we do the numerical estimation.

Keywords

• Sensitivity analysis
• Epidemic model
• Hepatitis B infection
• Stability analysis
• Numerical simulations