Optimal control of hepatitis B virus-induced liver cirrhosis model

Liver cirrhosis is a disease in which the liver is damaged and can cause death. One of the reasons that can lead to cirrhosis is the hepatitis B virus. Reducing liver cirrhosis infection requires a strategy for controlling hepatitis B infection. This study demonstrates control optimal strategies on a mathematical model for hepatitis B virus-induced cirrhosis. The control strategies are education/media campaign, vaccination, and treatment. The optimal controls aim to minimize the number of acute, chronic, and liver-cirrhosis individuals as well as control-associated costs. The optimal control problem is solved analytically using Pontryagin's minimum principle, and then an optimal system is obtained. Furthermore, the optimal control problem is solved numerically by the forward-backward sweep method. The numerical simulation results show that the combination of education/media campaign, vaccination, and treatment controls is the most effective strategy relative to the combination of two controls.