On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids
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On an Age-Structured Hepatitis B Virus Infection Model with HBV DNA-Containing Capsids Sanhong Liu1 · Ran Zhang2 Received: 8 October 2019 / Revised: 17 June 2020 / Accepted: 28 August 2020 © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2020
Abstract In this paper, we study an age-structured hepatitis B virus model with DNA-containing capsids. We obtain the well-posedness of the model by reformulate the model as an abstract Cauchy problem, and we find a threshold number 0 for the existence of the steady states. The local stability of each steady states is established by linearizing the system and analyze the corresponding characteristic equation. Furthermore, we investigate the uniform persistence of the system and constructing Lyapunov functionals to show the global stability of each steady states. We observe that the virus-free steady state is globally asymptotically stable when 0 < 1, while the infection steady state is globally asymptotically stable when 0 > 1. Numerical simulations are also presented to support the analytical results. Keywords HBV DNA-containing capsids · Age structure · Lyapunov functional · Stability · Hepatitis B virus Mathematics Subject Classification 92D30 · 35B35 · 34K20
Communicated by Syakila Ahmad.
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Ran Zhang [email protected] Sanhong Liu [email protected]
1
School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China
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Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
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S. Liu, R. Zhang
1 Introduction Viral hepatitis causes a life-threatening liver infection. World Health Organization estimated that there were about 325 millions people who living with chronic hepatitis infection or carriers and about 1.34 million deaths in 2015, where hepatitis B accounted for 80% of all hepatitis infection and 66% of all hepatitis mortality, respectively [44]. HBV infection can be acute or chronic in nature. Acute infection could last for several weeks and the acute patients eventually recover with immunity. However, chronic infection which lasts for several decades can potentially cause severe symptoms such as liver cirrhosis and hepatocellular carcinoma [36]. Therefore, HBV infection is a major concern for public health in the world. Over the past two decades, many researchers have used mathematical models to describe the within-host viral infection of HBV. In 1996, Nowak et al. [33] proposed a simple ODE model to analyze the dynamical property of HBV. Their basic model consists of uninfected hepatocytes, infected hepatocytes and HBV. Uninfected hepatocytes are assumed to be produced at a constant rate and die at a constant rate. Infection between uninfected hepatocytes and free virus is assumed to satisfy the mass-action principle and infected hepatocytes die at a constant rate. To better understanding the viral dynamics of HBV infection, many authors have generalized the basic model of Nowark et al. by taking into account of some factors such as t
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