Analisis Dinamik Model SIRC pada Transmisi Hepatitis B dengan Sirosis Hati

Hepatitis B is an infection of the liver that can cause liver cirrhosis. Liver cirrhosis can occur due to the formation of scar tissue in individuals who have prolonged hepatitis B. Transmission of hepatitis B can occur in two ways, namely horizontal and vertical. In this research, this problem is modeled in a mathematical model using the SIRC model, where the population is grouped into four sub-populations, namely susceptible (S), infected (I), cured or immune due to vaccination (R) and cirrhosis. liver (C). From the analysis, two equilibrium points were obtained, namely the disease-free equilibrium point the endemic equilibrium point  The basic reproduction number   is obtained using the Next Generation Matrix. The analysis results show that if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if  , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , this means that hepatitis B transmission in liver cirrhosis is influenced by contact between susceptible and infectious individuals. To support the results of the analytical analysis, numerical simulations are provided to describe the behavior of the SIRC model.