Global analysis of virus dynamics model with logistic mitosis, cure rate and delay in virus production
| Autor: | Cruz Vargas-De-León, Noé Chan Chí, Eric J. Avila Vales |
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| Rok vydání: | 2014 |
| Předmět: |
Hopf bifurcation
Thermodynamic equilibrium General Mathematics Dynamics (mechanics) Mathematical analysis General Engineering Quadratic function Stability (probability) symbols.namesake Stability theory symbols Quantitative Biology::Populations and Evolution Linear combination Basic reproduction number Mathematics |
| Zdroj: | Mathematical Methods in the Applied Sciences. 38:646-664 |
| ISSN: | 0170-4214 |
| Popis: | In this paper, we study a virus dynamics model with logistic mitosis, cure rate, and intracellular delay. By means of construction of a suitable Lyapunov functionals, obtained by linear combinations of Volterra—type functions, composite quadratic functions and Volterra—type functionals, we provide the global stability for this model. If R0, the basic reproductive number, satisfies R0 ≤ 1, then the infection-free equilibrium state is globally asymptotically stable. Our system is persistent if R0 > 1. On the other hand, if R0 > 1, then infection-free equilibrium becomes unstable and a unique infected equilibrium exists. The local stability analysis is carried out for the infected equilibrium, and it is shown that, if the parameters satisfy a condition, the infected equilibrium can be unstable and a Hopf bifurcation can occur. We also have that if R0 > 1, then the infected equilibrium state is globally asymptotically stable if a sufficient condition is satisfied. We illustrate our findings with some numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd. |
| Databáze: | OpenAIRE |
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