Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays

M.L. Mann Manyombe, J. Mbang and G. Chendjou

Chaos, Solitons & Fractals, 2021, vol. 144, issue C

Abstract: In this paper, we assess the viral dynamics of a HIV-1 mathematical model that incorporates virus-to-cell and cell-to-cell transmissions, CTL response immune and three delays describing intracellular delays and immune response delay. The model includes a constant production rate of CTLs export from thymus. Our focus is on the effect of three delays on the infection dynamics. The basic reproduction number, R0, which depends on the intracellular delay, is shown to determine stability conditions of the model steady states. Employing a suitable Lyapunov function, we show that the infection-free equilibrium is globally asymptotically stable including the three time delays when the basic reproduction number is a smaller amount than one. Additionally, for the special case where there is no immune delay in the model, the global stability of the unique endemic equilibrium is also established (using suitable Lyapunov functions) whenever R0 is larger than one. Furthermore, we study the local and hopf bifurcation of the endemic equilibrium in general case with all delays being positive. When the three delays are positive, we determine some conditions for stability switches of the endemic equilibrium by using the immune delay as a bifurcation parameter. Numerical simulations indicate that an increase of the immune delay can stabilize and/or destabilize the endemic equilibrium.

Keywords: Within-host dynamics; Time delay; Hopf bifurcation; Stability; CTL immune response (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000485

DOI: 10.1016/j.chaos.2021.110695

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