Mathematical modeling of the HIV/AIDS epidemic in Cuba

Mastroberardino, Antonio; Cheng, Yumin; Abdelrazec, Ahmed; Líu, Hao

doi:10.1142/s1793524515500473

Cited by 20 publications

(14 citation statements)

References 8 publications

(6 reference statements)

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“…Ida et al [ 7 ] investigated nonlinear dynamical analysis of the deterministic model of HIV infection. Mastroberardino et al [ 8 ] studied the dynamics of the virus in Cuba. Attaullah et al [ 9 ] designed numerical schemes to study the dynamics of HIV infection in the human population.…”

Section: Literature Surveymentioning

confidence: 99%

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

et al. 2020

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In this manuscript, we investigate a nonlinear delayed model to study the dynamics of human-immunodeficiency-virus in the population. For analysis, we find the equilibria of a susceptible–infectious–immune system with a delay term. The well-established tools such as the Routh–Hurwitz criterion, Volterra–Lyapunov function, and Lasalle invariance principle are presented to investigate the stability of the model. The reproduction number and sensitivity of parameters are investigated. If the delay tactics are decreased, then the disease is endemic. On the other hand, if the delay tactics are increased then the disease is controlled in the population. The effect of the delay tactics with subpopulations is investigated. More precisely, all parameters are dependent on delay terms. In the end, to give the strength to a theoretical analysis of the model, a computer simulation is presented.

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Section: Literature Surveymentioning

confidence: 99%

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

et al. 2020

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“…Over the years mathematical modeling has been used in analyzing different dynamics of diseases, like Malaria, Tuberculosis and HIV/AIDS, it also plays a very important role in understanding the epidemiological patterns of the diseases control, because it can provides short and long term prediction of the incidence of the diseases [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] .…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a fractional order model for the COVID – 19 pandemic

Baba

Bilgehan

2021

Chaos, Solitons & Fractals

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“…The research on the spread of HIV infection can be tracked back to the early models proposed in [5][6][7][8]. Many following models have been introduced for seeking the controlling and preventing the spread of HIV infection, for example, one can see [9][10][11][12][13][14][15][16][17][18][19][20]. The main components of the immune system are C D4 + T cells which play a critical role in the suppression of immune reaction.…”

Section: Introductionmentioning

confidence: 99%

A nonstandard finite difference scheme and optimal control for an HIV model with Beddington–DeAngelis incidence and cure rate

Salman

2020

Eur. Phys. J. Plus

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In this paper, we incorporate the Beddington-DeAngelis incidence rate to a continuous-time HIV infection model with cure rate and a full logistic proliferation rate of C D4 + T cells in both uninfected and infected cells. Equilibria and their local stability analysis are discussed. It is shown that the HIV-free equilibrium point is locally asymptotically stable if R 0 < 1 and unstable if R 0 ≥ 1, where R 0 is the basic reproduction number. Whereas, the HIV equilibrium point is locally asymptotically stable if R 0 > 1. A nonstandard finite difference method is applied to the continuous model to obtain its discrete counterpart. The scheme applied preserves the main features of the continuous model such as positivity, boundedness of the solutions, equilibria and their local stability. Moreover, an optimal control strategy is applied to the discrete-time model in order to reduce the number of infected cells as well as the number of free HIV particles. Numerical simulations are performed to verify the theoretical analysis obtained.

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Mathematical modeling of the HIV/AIDS epidemic in Cuba

Cited by 20 publications

References 8 publications

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Modeling the effect of delay strategy on transmission dynamics of HIV/AIDS disease

Optimal control of a fractional order model for the COVID – 19 pandemic

A nonstandard finite difference scheme and optimal control for an HIV model with Beddington–DeAngelis incidence and cure rate

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