Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation

Tabassum, Muhammad Farhan; Saeed, Muhammad; Akgül, Ali; Farman, Muhammad; Chaudhry, Nazir Ahmad

doi:10.1016/j.chaos.2020.109686

Cited by 16 publications

(4 citation statements)

References 23 publications

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“…The researchers utilized incidence data from Nigeria to calibrate the parameters of their model. Readers may refer to ( 28 – 34 ) for more HIV/AIDS related models.…”

Section: Introductionmentioning

confidence: 99%

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

Aldila,

Dhanendra,

Khoshnaw

et al. 2024

Front. Public Health

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In this article, we present a mathematical model for human immunodeficiency virus (HIV)/Acquired immune deficiency syndrome (AIDS), taking into account the number of CD4+T cells and antiretroviral treatment. This model is developed based on the susceptible, infected, treated, AIDS (SITA) framework, wherein the infected and treated compartments are divided based on the number of CD4+T cells. Additionally, we consider the possibility of treatment failure, which can exacerbate the condition of the treated individual. Initially, we analyze a simplified HIV/AIDS model without differentiation between the infected and treated classes. Our findings reveal that the global stability of the HIV/AIDS-free equilibrium point is contingent upon the basic reproduction number being less than one. Furthermore, a bifurcation analysis demonstrates that our simplified model consistently exhibits a transcritical bifurcation at a reproduction number equal to one. In the complete model, we elucidate how the control reproduction number determines the stability of the HIV/AIDS-free equilibrium point. To align our model with the empirical data, we estimate its parameters using prevalence data from the top four countries affected by HIV/AIDS, namely, Eswatini, Lesotho, Botswana, and South Africa. We employ numerical simulations and conduct elasticity and sensitivity analyses to examine how our model parameters influence the control reproduction number and the dynamics of each model compartment. Our findings reveal that each country displays distinct sensitivities to the model parameters, implying the need for tailored strategies depending on the target country. Autonomous simulations highlight the potential of case detection and condom use in reducing HIV/AIDS prevalence. Furthermore, we identify that the quality of condoms plays a crucial role: with higher quality condoms, a smaller proportion of infected individuals need to use them for the potential eradication of HIV/AIDS from the population. In our optimal control simulations, we assess population behavior when control interventions are treated as time-dependent variables. Our analysis demonstrates that a combination of condom use and case detection, as time-dependent variables, can significantly curtail the spread of HIV while maintaining an optimal cost of intervention. Moreover, our cost-effectiveness analysis indicates that the condom use intervention alone emerges as the most cost-effective strategy, followed by a combination of case detection and condom use, and finally, case detection as a standalone strategy.

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“…The researchers utilized incidence data from Nigeria to calibrate the parameters of their model. Readers may refer to ( 28 – 34 ) for more HIV/AIDS related models.…”

Section: Introductionmentioning

confidence: 99%

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

Aldila,

Dhanendra,

Khoshnaw

et al. 2024

Front. Public Health

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“…Ibtissem and Nouredine [20] hybrid the conjugate gradient with DE algorithm, Herein used local search and DE for the global search including conjugate gradient, Shahidi et al [21] collectively used GA with conjugate gradient, Wu and Yu used an evolutionary algorithm with gradient-based method [22]. Some recent applications of DE based hybried algorithms are reported in [23][24][25][26][27][28][29] and some recent applications regarding COVID-19 are reported in [30,31].…”

Section: Introductionmentioning

confidence: 99%

Optimal solution of engineering design problems through differential gradient evolution plus algorithm: a hybrid approach

Tabassum¹,

Akgül²,

Akram³

et al. 2022

Phys. Scr.

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It is very necessary and applicable to optimize all disciplines. In practical engineering problems the optimization has been a significant component. This article presents the hybrid approach named as differential gradient evolution plus (DGE+) algorithm which is the combination of differential evolution (DE) algorithm and gradient evolution (GE) algorithm. DE was used to diversify and GE was used for intensification with a perfect equilibrium between exploration and exploitation with an improvised distribution of dynamic probability and offers a new shake-off approach to prevent premature convergence to local optimum. To describe the success, the proposed algorithm is compared to modern meta-heuristics. To see the accuracy, robustness, and reliability of DGE+ it has been implemented on eight complex practical engineering problems named as: pressure vessel, belleville spring, tension/compression spring, three-bar truss, welded beam, speed reducer, gear train and rolling element bearing design problem, the results revealed that DGE+ algorithm can deliver highly efficient, competitive and promising results.

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“…Among those, Mukandavire et al [5] presented a mathematical model for the HIV/AIDS spread on sex-base as a delay-system of differential equations and gave the local and global stabilities for their model subjected to the value of basic reproduction number R 0 . Tabassum et al [6] developed a nonlinear mathematical model for the HIV/AIDS transmission and examined the necessary conditions required for the well-posedness and boundedness. Dutta and Gupta [7] presented a mathematical model for HIV/AIDS analysis with weak CD4+ T cells and studied the infection, infectionfree equilibrium situations.…”

Section: Introductionmentioning

confidence: 99%

A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

et al. 2021

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In this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solution, the stability analysis, and simulations. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the fractional order model is derived with the help of existing literature for the Hyers–Ulam stability. For the numerical computations, the Lagrange interpolation is utilized, and the simulations are obtained for specific parameters. The results are closer to the classical results for different orders.

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Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation

Cited by 16 publications

References 23 publications

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

Understanding HIV/AIDS dynamics: insights from CD4+T cells, antiretroviral treatment, and country-specific analysis

Optimal solution of engineering design problems through differential gradient evolution plus algorithm: a hybrid approach

A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

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