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- Title
Global analysis of virus dynamics model with logistic mitosis, cure rate and delay in virus production.
- Authors
Vargas‐De‐León, Cruz; Chí, Noé Chan; Vales, Eric Ávila
- Abstract
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.
- Subjects
MITOSIS regulation; MITOSIS; LYAPUNOV functions; NUMERICAL solutions to differential equations; NUMERICAL analysis; FUNGI
- Publication
Mathematical Methods in the Applied Sciences, 2015, Vol 38, Issue 4, p646
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.3096