A note on the global properties of an age-structured viral dynamic model with multiple target cell populations

Shaoli Wang; Jianhong Wu; Libin Rong

doi:10.3934/mbe.2017044

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2017, Volume 14, Issue 3: 805-820. Doi: 10.3934/mbe.2017044

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A note on the global properties of an age-structured viral dynamic model with multiple target cell populations

1.
School of Mathematics and Statistics, Henan University, Kaifeng 475001, Henan, China
2.
Centre for Disease Modelling, York University, Toronto, Ontario, M3J 1P3, Canada
3.
Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA

Received: January 24, 2016

Accepted: October 29, 2016

Published: September 2017

This work was finished when S. Wang visited York University. Wang is supported by NSFC (No.11326200), Foundation of He’nan Educational Committee (No.15A110015, No.15A110018), and The Grant of China Scholarship Council (No.201408410018). L. Rong is partially supported by the NSF grant DMS-1349939.

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Abstract

Some viruses can infect different classes of cells. The age of infection can affect the dynamics of infected cells and viral production. Here we develop a viral dynamic model with the age of infection and multiple target cell populations. Using the methods of semigroup and Lyapunov function, we study the global asymptotic property of the steady states of the model. The results show that when the basic reproductive number falls below 1, the infection is predicted to die out. When the basic reproductive number exceeds 1, there exists a unique infected steady state which is globally asymptotically stable. The model can be extended to study virus dynamics with multiple compartments or coinfection by multiple types of viruses. We also show that under some scenarios the age-structured model can be reduced to an ordinary differential equation system with or without time delays.

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Mathematics Subject Classification: Primary: 37B25, 92D25; Secondary: 35A24, 35M30.

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