Modeling and qualitative analysis of a hepatitis B epidemic model.

We develop an epidemic mathematical model for hepatitis B contagious disease, which is one of the major causes of death among various infectious diseases. We prove the existence, positivity, and biological feasibility of the model. We find the threshold quantity of the model and analyze the sensitivity analysis to show the effect of various parameters on the spread of hepatitis B virus. Exploiting the linear stability approach, we find stability conditions to perform the stability analysis. We use the central manifold theory to discuss the existence of backward bifurcation of the proposed model. Finally, we present numerical simulations to verify the analytical calculations and to analyze the sensitivity of parameters.