Advances in Epidemiological Modeling and Control of Viruses: Chapter 2 - Hepatitis B virus transmission via epidemic model

We formulate an epidemiological mathematical model that demonstrates the transmission of the hepatitis B virus. The novelty of the model lies in studying the transmission dynamics of the disease under the effect of generalized incidence and treatment functions. This describes the transfer mechanism, i.e., preventive vaccination of susceptible population, and various treatment mechanisms for control depending on the size of the infected population in which the control measure treatment can find whether there is an epidemic outbreak or not, and also the number of endemic equilibria during endemic outbreaks. We also find the basic reproduction number R0 to show the local asymptotic stability at disease-free and endemic equilibria. In the end we present numerical simulations to illustrate the analytical findings graphically.