Spatio-temporal dynamics of an SIS model with nonlinear incidence and nonlocal disease transmission

Das, Dhiraj Kumar; Ghorai, S.; Banerjee, Malay

doi:10.1007/s11071-023-08633-1

Cited by 1 publication

(2 citation statements)

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“…This clearly explains the delayed model of HIV. Figure (6) and Figure (7) show the effect of therapy on the target cells and the viral population. As therapy efficacy is increasing, the target cell population increases and the viral population decreases drastically.…”

Section: Existence Of Hopf Bifurcationmentioning

confidence: 99%

“…The stability and bifurcation of an optimally controlled HIV model with delays were investigated in [31]. The authors discussed the spatio-temporal dynamics of an SIS model that incorporates Turing and Turing-Hopf pattern bifurcations by introducing SIR model dynamics [6,15,22]. In [30], bifurcation analysis of an HIV-1 infection model involving cell-to-cell transmission and immune response latency was investigated.…”

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confidence: 99%

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Threshold dynamics of time-delay in HIV infection model with immune impairment

Murugan,

Mani

2024

DCDS-S

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This study focuses on investigating the dynamical properties of a differential model for the human immunodeficiency virus (HIV) involving the effect of antiretroviral therapy (ART). The model is composed of four cell populations: target cells, infected cells, free virions, and effector cells involving viral production delay. Further, the parameters in the model are estimated with the help of clinical data. The activation of the immune response against a foreign agent potentially in impairment is discussed. This study explores the effects of time delay under ART through stability properties. The basic reproduction number is derived to ensure community spread. Also, this paper performs stability analysis for disease-free, immune-free, and infection-steady states. In addition, bifurcation analyses are performed by choosing viral production time-delay as a bifurcation parameter. Further, the existence of Hopf bifurcation with respect to time delay is confirmed, and the corresponding threshold value for delay is derived and validated. This paper formulates the optimal control problem by choosing the ART therapy coefficient as a control parameter and investigating it through the Hamiltonian-Lagrangian method and Pontryagin's maximum principle. Moreover, numerical simulations are performed to validate the proposed stability and bifurcation conditions with estimated and referred parameter values.

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Section: Existence Of Hopf Bifurcationmentioning

confidence: 99%

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confidence: 99%