A cancer and hepatitis co-infection model

Cancer and hepatitis are global infectious diseases claiming millions of lives every year. In this study, we develop and analyse a cancer and hepatitis co-infection model to examine the relationship between the two diseases. In addition, we derive and analyse the reproduction numbers of each and both diseases. We explore the sensitivity of the reproduction numbers of both diseases to parameters, and performed the numerical simulations of the model. Our analyses show that the cancer-hepatitis model has disease-free equilibrium whenever the reproduction number is less than unity, and has a unique endemic equilibrium if the reproduction number is greater than one. Also our analyses highlight the impact of hepatitis on cancer and vise versa. Furthermore, our numerical solutions indicate that the carrying capacity and progression rate from susceptible to hepatitis and cancer play crucial roles in determining the population dynamics of both diseases. Although, our results highlight the impact of hepatitis on cancer, an increase in the proportion of cells migrating from susceptible to hepatitis will have more impact on the hepatitis-infected than cancer-infected cells. Our results also suggest that more cells are recovered under a reduced carrying capacity.