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Global analysis of virus dynamics model with logistic mitosis, cure rate and delay in virus production
Author(s) -
VargasDeLeón Cruz,
Chí Noé Chan,
Vales Eric Ávila
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3096
Subject(s) - mathematics , hopf bifurcation , stability theory , quadratic equation , thermodynamic equilibrium , stability (learning theory) , bifurcation , nonlinear system , computer science , physics , thermodynamics , geometry , quantum mechanics , machine learning
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 R 0 , the basic reproductive number, satisfies R 0 ≤ 1, then the infection‐free equilibrium state is globally asymptotically stable. Our system is persistent if R 0 > 1. On the other hand, if R 0 > 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 R 0 > 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.