MODELING THE COINFECTION OF HEPATITIS B AND HIV: A CASE STUDY IN THE USA

Hepatitis B and HIV infections form a long-term chronic combination. Based on a hepatitis B epidemic model with vertical infection and vaccination, we develop an epidemic model of hepatitis B-HIV coinfection. There is always a unique disease-free equilibrium of our coinfection epidemic model, and it is stable when both basic reproduction numbers of hepatitis B and HIV are less than 1. If basic reproduction number of hepatitis B (HIV) is larger than 1, there is a unique boundary equilibrium of hepatitis B (HIV). The boundary equilibrium of hepatitis B (HIV) is locally stable if the invasion reproductive number of HIV (hepatitis B) is less than 1. Coexistence equilibrium of our model exists if all basic reproduction numbers and invasion reproductive numbers are greater than 1. Using data of hepatitis B cases and HIV cases from the US, we estimated that both basic reproduction numbers of hepatitis B and HIV are significantly less than 1, and the disease-free equilibrium is stable. Note that there is a competition between these two diseases. Increasing the recovery rate of chronic hepatitis B carrier (or increasing the vaccination rate) will result in enhanced HIV transmission when both basic reproduction numbers are larger than 1. Modeling and theoretical results derived here would be useful for modeling other multi-disease coinfection with vaccination and vertical infection.