The Transmission Dynamics of Hepatitis B Virus via the Fractional‐Order Epidemiological Model
Tahir Khan, Zi-Shan Qian, Roman Ullah, Basem Al Alwan, Gul Zaman, Qasem M. Al‐Mdallal, Youssef El‐Khatib, Khaled Kheder
Abstract
We investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform the steady‐state analysis and to show that the fractional‐order epidemiological model is locally and globally asymptotically stable under certain conditions. For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat’s lemma, respectively. Finally, we perform some numerical findings to support the analytical work with the help of graphical representations.