Constructing Lyapunov functionals for a delayed viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate

Volume 9, Issue 2, pp 524--536 http://dx.doi.org/10.22436/jnsa.009.02.18

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Authors

Jinliang Wang - School of Mathematical Science, Heilongjiang University, Harbin 150080, China. Jiying Lang - School of Mathematical Science, Heilongjiang University, Harbin 150080, China. Feng Li - School of Science, Linyi University, Linyi 276000, Shandong, China.

Abstract

For a viral infection model with multitarget cells, nonlinear incidence rate, state-dependent removal rate and distributed delays, we analyze the global asymptotic behavior of its solutions. In this model, the rate of contact between viruses and uninfected target cells and state-dependent removal rate of infected cells depend on general nonlinear functions. The basic reproduction number for the model is discussed. Under certain assumptions, it is shown that if \(\Re_0\leq 1\), then the infection-free equilibrium \(P_0\) is globally stable and the viruses are cleared; If \(\Re_0 > 1\), then there is a unique infection equilibrium, which is globally stable implying the infection becomes chronic. The global stability results are achieved by appealing to the direct Lyapunov method.

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Keywords

• Viral infection model
• nonlinear incidence rates
• state-dependent removal rate
• Lyapunov functionals
• global stability.

MSC

•  34D23
•  34K20
•  92D30

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