| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Mathematical immunology
|
|
|---|---|---|
| Article Number | 16 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/mmnp/2019038 | |
| Published online | 12 March 2020 | |
Hopf bifurcation of an HIV-1 virus model with two delays and logistic growth*
School of Mathematics and Computer Science, Shanxi Normal University,
Linfen 041004,
Shanxi, PR China.
** Corresponding author: Jiajw.2008@163.com
Received:
28
December
2018
Accepted:
8
September
2019
The paper establish and investigate an HIV-1 virus model with logistic growth, which also has intracellular delay and humoral immunity delay. The local stability of feasible equilibria are established by analyzing the characteristic equations. The globally stability of infection-free equilibrium and immunity-inactivated equilibrium are studied using the Lyapunov functional and LaSalles invariance principle. Besides, we prove that Hopf bifurcation will occur when the humoral immune delay pass through the critical value. And the stability of the positive equilibrium and Hopf bifurcations are investigated by using the normal form theory and the center manifold theorem. Finally, we confirm the theoretical results by numerical simulations.
Mathematics Subject Classification: D25 / 34C23 / 37B25 / 34D23
Key words: HIV-1 virus model / delay / stability / Hopf bifurcation / logistic growth
© EDP Sciences, 2020
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