Journal of Applied Mathematics

Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells

Shuo Liu, Lina Ma, Jianquan Li, and Qingbo Zhao

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Abstract

By introducing the probability function describing latency of infected cells, we unify some models of viral infection with latent stage. For the case that the probability function is a step function, which implies that the latency period of the infected cells is constant, the corresponding model is a delay differential system. The model with delay of latency and two types of target cells is investigated, and the obtained results show that when the basic reproduction number is less than or equal to unity, the infection-free equilibrium is globally stable, that is, the in-host free virus will be cleared out finally; when the basic reproduction number is greater than unity, the infection equilibrium is globally stable, that is, the viral infection will be chronic and persist in-host. And by comparing the basic reproduction numbers of ordinary differential system and the associated delayed differential system, we think that it is necessary to elect an appropriate type of probability function for predicting the final outcome of viral infection in-host.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 632381, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808151

Digital Object Identifier
doi:10.1155/2013/632381

Mathematical Reviews number (MathSciNet)
MR3108950

Zentralblatt MATH identifier
06950792

Citation

Liu, Shuo; Ma, Lina; Li, Jianquan; Zhao, Qingbo. Global Analysis of a Model of Viral Infection with Latent Stage and Two Types of Target Cells. J. Appl. Math. 2013 (2013), Article ID 632381, 7 pages. doi:10.1155/2013/632381. https://projecteuclid.org/euclid.jam/1394808151


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