Stability and Hopf Bifurcation of a Mathematical Model of HIV-1 with Two Saturation Responses

Authors

  • Vahid Roomi Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; Insurance Reserach Center, Tehran, Iran
  • Tohid Kasbi Department of Mathematics and Statistics, Imam Hossein University, Tehran, Iran
  • Zeynab Hemmatzadeh Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; Insurance Reserach Center, Tehran, Iran Corresponding Author

Keywords:

HIV-1 infection, stability, hopf bifurcation, dynamical systems, ODE

Abstract

In this manuscript, the dynamical behavior of an HIV-1 infection model with logistic target cell growth and two major transmissions will be studied.  Functional response and saturation response are nonlinear in the model. The positivity and boundedness of the solutions will be proven. The reproduction number will be computed as the sum of reproduction numbers determined by any method of disease transmission. It will be shown that the infection-free equilibrium is globally asymptotically stable if the reproduction number is less than one and if it is more than one, then the infection-free equilibrium is unstable. We find that within certain conditions, positive equilibrium is locally asymptotically stable and the Hopf bifurcation can occur.

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Published

2023-10-19

Issue

1 (2023) No. 3

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Articles

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