Global dynamics of an epidemiological model with acute and chronic HCV infections. (May 2020)

• Record Type: Journal Article
• Authors: Cui, Jing-An; Zhao, Shifang; Guo, Songbai; Bai, Yuzhen; Wang, Xiaojing; Chen, Tianmu
• Is Part Of: Applied mathematics letters. Volume 103(2020)
• Publication Date: 2020-05
• Subjects: Hepatitis C -- Acute infection -- Chronic infection -- Lyapunov function; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.106203
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, an epidemiological model of hepatitis C with acute and chronic infections is proposed, and then the global dynamics of this model is studied. It emphasizes that acute hepatitis C patients can eliminate the virus by themselves and step into the recovered class, while chronic hepatitis C patients can-not automatically eliminate the virus to enter into the recovered class, so a significant number of those patients eventually develop cirrhosis or hepatocellular carcinoma (HCC). By constructing appropriate Lyapunov functions, it shows that if the basic reproductive number R 0 < 1, the disease-free equilibrium of the model is globally asymptotically stable; if R 0 > 1, the disease-free equilibrium is unstable, and the endemic equilibrium of the model is globally asymptotically stable.