Mathematical Analysis of a Transformed ODE from a PDE Multiscale Model of Hepatitis C Virus Infection

• Published in: Bulletin of mathematical biology Vol. 81; no. 5; pp. 1427 - 1441
• Main Authors: Kitagawa, Kosaku, Kuniya, Toshikazu, Nakaoka, Shinji, Asai, Yusuke, Watashi, Koichi, Iwami, Shingo
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2019; Springer Nature B.V
• Subjects: Age; Basic Reproduction Number - statistics & numerical data; Cell Biology; Data analysis; Data processing; Hepacivirus - pathogenicity; Hepacivirus - physiology; Hepatitis C; Hepatitis C - transmission; Hepatitis C - virology; Humans; Life Sciences; Mathematical analysis; Mathematical and Computational Biology; Mathematical Concepts; Mathematical models; Mathematics; Mathematics and Statistics; Models, Biological; Ordinary differential equations; Partial differential equations; RNA, Viral - metabolism; Viral infections; Virus Replication; Viruses; PDE; Viral dynamics; Multiscale model; HCV; Mathematical model
• ISSN: 0092-8240; 1522-9602; 1522-9602
• DOI: 10.1007/s11538-018-00564-y

Mathematical modeling has revealed the quantitative dynamics during the process of viral infection and evolved into an important tool in modern virology. Coupled with analyses of clinical and experimental data, the widely used basic model of viral dynamics described by ordinary differential equations (ODEs) has been well parameterized. In recent years, age-structured models, called “multiscale model,” formulated by partial differential equations (PDEs) have also been developed and become useful tools for more detailed data analysis. However, in general, PDE models are considerably more difficult to subject to mathematical and numerical analyses. In our recently reported study, we successfully derived a mathematically identical ODE model from a PDE model, which helps to overcome the limitations of the PDE model with regard to clinical data analysis. Here, we derive the basic reproduction number from the identical ODE model and provide insight into the global stability of all possible steady states of the ODE model.