Stability of a fractional HIV/AIDS model

Silva, Cristiana J.; Torres, Delfim F. M.

doi:10.1016/j.matcom.2019.03.016

Cited by 64 publications

(36 citation statements)

References 28 publications

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“…Suppose that t 0 � 0, m � 2, and one period is ω � 1 with ω 1 � 0.9 and ω 2 � 0.1. Most of the parameter values are taken from those in [2,7,8,17]. Assume that constant parameter values are λ � 0.029 and u � 0.02.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Pitchaimani and Monica [7] incorporated three time delays into a HIV-1 infection model and gave the existence of Hopf bifurcation of the model. Silva and Torres [8] introduced the fractional order into an HIV/AIDS model and surveyed local and uniform stability of its disease-free equilibrium. Huo et al [9] added anti-HIV preventive vaccines into a fractional order HIV model and showed that the model has rich phenomenon of backward bifurcation with different dosages of vaccines and fractional derivative orders.…”

Section: Introductionmentioning

confidence: 99%

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Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

Wang

2021

Discrete Dynamics in Nature and Society

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In this paper, we formulate and investigate new switched HIV/AIDS models with drug treatment involving Caputo-fractional derivatives. Initially, due to the fractional derivative order related to the memory and hereditary effects and supposing that the model coefficients are time-varying parameters, we develop a Caputo-fractional order HIV/AIDS models with switching parameters and study their dynamics utilizing Lyapunov–Razumikhin technique. Furthermore, the results show that the fractional derivative α ( 0 < α < 1 ) and the switching parameters are related to the critical threshold value ( R ^ or R ¯ ) which ensures disease eradication under the condition of R ^ < 1 or R ¯ < 1 . Then, a treatment compartment is introduced into the above model from the asymptomatic infected individuals until the full blown AIDS individuals. Novel sufficient conditions on the threshold value are derived to verify that the disease is eventually cleared as the critical threshold parameter is below unity. Finally, some simulations are employed to support the main results and one future research direction is presented.

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Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

Wang

2021

Discrete Dynamics in Nature and Society

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“…Mallela et al proposed an HIV‐TB coinfected model for the mathematical analysis, and they established numerical study of their model for different aspects of the model. Silva and Torres proposed a fractional order model for HIV/AIDS transmission, and the local and uniform stability of the model were studied. Some authors studied HIV models in the presence and treatment of many other diseases.…”

Section: Introductionmentioning

confidence: 99%

A fractional order HIV‐TB coinfection model with nonsingular Mittag‐Leffler Law

Khan

Gómez‐Aguilar

Alkhazzan

et al. 2020

Math Methods in App Sciences

122

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The biological models for the study of human immunodeficiency virus (HIV) and its advanced stage acquired immune deficiency syndrome (AIDS) have been widely studied in last two decades. HIV virus can be transmitted by different means including blood, semen, preseminal fluid, rectal fluid, breast milk, and many more. Therefore, initiating HIV treatment with the TB treatment development has some advantages including less HIV‐related losses and an inferior risk of HIV spread also having difficulties including incidence of immune reconstitution inflammatory syndrome (IRIS) because of a large pill encumbrance. It has been analyzed that patients with HIV have more weaker immune system and are susceptible to infections, for example, tuberculosis (TB). Keeping the importance of the HIV models, we are interested to consider an analysis of HIV‐TB coinfected model in the Atangana‐Baleanu fractional differential form. The model is studied for the existence, uniqueness of solution, Hyers‐Ulam (HU) stability and numerical simulations with assumption of specific parameters.

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“…Thus, Sousa and de Oliveira (2018a) introduced the ψ-Hilfer fractional derivative. Presently, fractional calculus is consolidated and numerous applications of fractional derivatives and fractional integrals have been obtained, among which several relevant and important works published in high-quality journals (Machado et al 2010;Rasheed and Anwar 2018;Sousa and De Oliveira 2018b;Sousa and de Oliveira 2019c;Sousa et al 2017;Wang et al 2019;Luo et al 2018;Babaei et al 2020;Sayevand and Tenreiro Machado 2018;Silva and Torres 2019;Nemati et al 2019;Salati et al 2019;Frederico and Lazo 2016;Frederico and Torres 2008).…”

Section: Introductionmentioning

confidence: 99%

$$\psi $$-Hilfer pseudo-fractional operator: new results about fractional calculus

2020

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In this paper, we introduce the ψ-Hilfer pseudo-fractional operator, motivated by the ψ-Hilfer fractional derivative and the theory of pseudo-analysis. We investigate a wide class of important and essential results for pseudo-fractional calculus in a semiring ([a, b], ⊕,) and some particular cases are discussed. Specifically, we present a class of pseudo-fractional operators which are particular cases of the ψ-Hilfer pseudo-fractional operator. In addition, we present the pseudo-Leibniz-type rules I and II and pseudo-Leibniz rules and some particular cases of Leibniz-type rules I and II are discussed. Finally, we obtain formulas for the Hilfer pseudofractional derivative, for the pseudo-Laplace transform, and for the g-integration by parts of the ψ-Hilfer pseudo-fractional operator.

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Stability of a fractional HIV/AIDS model

Abstract: We propose a fractional order model for HIV/AIDS transmission. Local and uniform stability of the fractional order model is studied. The theoretical results are illustrated through numerical simulations.

Cited by 64 publications

References 28 publications

Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

Global Stability of Switched HIV/AIDS Models with Drug Treatment Involving Caputo-Fractional Derivatives

A fractional order HIV‐TB coinfection model with nonsingular Mittag‐Leffler Law

$$\psi $$-Hilfer pseudo-fractional operator: new results about fractional calculus

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