A fractal-fractional order Atangana-Baleanu model for Hepatitis B virus with asymptomatic class

Abstract

Hepatitis B is still a major issue in most countries of the world. Due to many death and infection cases, the disease becoming a life-threatening issue and needs proper attention for its eradication. The main aim of this study is to design a new mathematical model with an asymptomatic class based on clinical investigations to study its dynamics. The asymptomatic carriers class do not possess symptoms but infect other healthy people. This new idea has been utilized for the first time in the present analysis with fractal-fractional operators. We formulate the model basically in integer-order and then apply the fractal-fractional derivative in Atangana-Baleanu type. For the fractional model, we study the related results and their numerical solution. Further, we apply the fractal operator together with fractional derivative which is known as fractal-fractional derivative in the Atangana-Baleanu case, and present the model. For the numerical solution, we provide a scheme based on the Adams-Bashforth method and obtained the results graphically. With various choices of the fractal and fractional orders, we present various graphical solutions. The model parameters that can reduce the infection of Hepatitis B are shown graphically. The disease in the population can be minimized well by taking into consideration the model important parameters. The important parameters and their effect have been shown graphically.