Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis

Abstract

Liver cirrhosis is the liver scarring in human body which causes the liver organ failure to function its regular activities effectively and normally. In this paper, we proposed and analyzed the combined effect of hepatitis B virus (HBV) infection and heavy alcohol consumption on the progression dynamics of liver cirrhosis. In order to study the progression dynamics of cirrhosis and to describe the effect of alcohol intake variation on a chronic hepatitis B patients a deterministic model and a logistic function are considered, respectively. The detailed proof of the positivity, boundedness, and biological feasibility of the proposed model is presented. The disease endemic equilibrium point and the existence of bifurcation were investigated in detail. We established and proved the existence theorems for forward and backward bifurcations, respectively. Finally, we performed large scale numerical simulations to verify the analytic work and the result of the numerical simulations reveal that heavy alcohol consumption significantly accelerates the progression of liver cirrhosis in chronic hepatitis B infected individuals.