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.
Highlights
Hepatitis B virus causes inflammation of the liver. It results from a noncytopathic virus which is called the hepatitis B virus (HBV)
Characteristic of HBV is its high tissue and species specificity, as well as a unique genomic organization and replication mechanism. e infection of HBV has multiple phases: acute and chronic. e acute one refers to the first six months whenever there is an exposure of some one to the virus. In this period, the immune system has the capability to vanish the infection, while for some severe cases, it may lead to the serious stage and so results in the lifelong illness. is is known as the chronic stage
In case of the chronic stage, often, the individual has no history of the acute stage. is infection may lead to the scarring of the liver, become liver failure, and produce liver cancer [1]
Summary
Hepatitis B virus causes inflammation of the liver. It results from a noncytopathic virus which is called the hepatitis B virus (HBV). Khan et al [24, 25] and Nana-Kyere et al [26] formulated some epidemiological models to study different parameters’ influences on the disease transmission and to suggest some control measures for the elimination of the infection. It could be noted that the increased development of fractional calculus and fractional-order epidemiological models are more suitable than the classical order epidemic models and complex dynamics of hepatitis B; we investigate a hepatitis B virus transmission epidemic model with various infection phases and multiple routes of transmission. Once we formulate the model, we study the existence analysis as well as uniqueness to prove the well-posedness and biological feasibility of the problem under consideration. Some numerical simulations will be performed to support the analytical work and show the difference between the classical and fractional order
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