Vertical Transmission of HIV-HBV Co-infection with Liquor Habit and Vaccination

In this paper, the transmission of HIV-HBV co-infection is carried out. The individuals who are infected with both diseases HIV and HBV simultaneously, are said to be HIV-HBV co-infected. These infected individuals have high risk of liver failure. It is the main cause for serious liver complications like cirrhosis and liver cancer at younger age. A deterministic model is considered with liquor habit in men and vaccination to new-borns and carrier mother. Carrier class results in the vertical transmission. In this paper, the transmission dynamics of the model is analyzed. The total population is divided in to twenty eight class viz. Susceptible, HBV Vaccinated, HBV-infected female, HBV-carrier female, HBV infected alcoholic male, HBV carrier alcoholic male, HBV infected non-alcoholic male, HBV carrier non-alcoholic male, HBV recovered class, pre-AIDS female, AIDS female, pre-AIDS-HBV co-infected female, AIDS-HBV co-infected female, pre-AIDS-HBV carrier female, AIDS-HBV carrier female, pre-AIDS alcoholic male, AIDS alcoholic male, pre-AIDS non-alcoholic male, AIDS non-alcoholic male, pre-AIDS-HBV co-infected alcoholic male, pre-AIDS-HBV co-infected non-alcoholic male, pre-AIDS-HBV carrier alcoholic male, pre-AIDS-HBV carrier non-alcoholic male, AIDS-HBV co-infected alcoholic male, AIDS-HBV co-infected non-alcoholic male, AIDS-HBV carrier non-alcoholic male, HIV infected-HBV recovered classes. The basic reproduction numbers for HIV, for HBV and for HIV-HBV are found using next generation matrix. Local and global stability of HIV-HBV disease free equilibrium is worked out. Model is validated with the numerical simulation.