Control of Transmission of Hepatitis B Disease with Vaccination, Campaign, and Treatment

Abstract

Hepatitis B disease is an inflammatory liver disease caused by the hepatitis B virus and can cause liver cirrhosis, cancer, and liver failure. This study discusses the optimal control mathematical model of the dynamics of the spread of hepatitis B. This model consists of six population compartments, namely susceptible to infection with hepatitis B or  Susceptible, Exposed,  infected with acute hepatitis B or Acute Infected , infected with chronic hepatitis B or Chronic Infected, suffering from liver cirrhosis or Liver Cirrhotic, and infected who are recovering or Removed. The system is solved by using Pontryagin's minimum principle and numerically by the forward-backward sweep method. Numerical simulation of the optimal control  shows that with vaccination , campaign on hepatitis B, and treatment, the spread of hepatitis B can be eradicated more quickly. The implementation large amounts of vaccination, campaign on hepatitis B, and treatment  need to be carried out from the start and the proportion can be reduced until a certain time is no longer necessary. The use of controls in the form of vaccinations, campaigns on hepatitis B, and treatment  needs to be carried out for a longer time to prevent the spread of hepatitis B infection.