Modeling of Hepatitis B Virus Transmission with Fractional Analysis

Hepatitis B is one of the infectious diseases among other contagious diseases. In this paper, we analyze and discuss the time dynamics of hepatitis B under the effect of various infectious periods. We propose a model keeping in view the role of acute and chronic infections stages and analyze the temporal dynamics. To do this, first we develop the model and use the concept of fractional theory to fractionalize. We also study the qualitative analysis of both the integer and fractional order models. For the fractionalizing purpose, the Caputo–Fabrizio (CF) operator is utilized. We prove also, the existence and uniqueness of the solution to the considered fractional-order model to show that the epidemic problem is feasible and well possessed. For this, we use the fixed point theory and its applications. Moreover, we prove that the considered model possesses a positive as well as bounded solution. We calculate the basic reproductive number to find the equilibria of the model to execute the stabilities and to investigate that the proposed fractional model is stable asymptotically. We support our analytical findings with the use of some graphical visualization.