Modelling and stability of HIV/AIDS epidemic model with treatment

Huo, Hai‐Feng; Chen, Rui; Wang, Xun-Yang

doi:10.1016/j.apm.2016.01.054

Cited by 112 publications

(71 citation statements)

References 19 publications

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“…The disease is very dangerous and can be fatal if untreated. Since the first AIDS case was discovered in 1981 [1], HIV has spread worldwide and over 35 million people have died from AIDS-related illness. At the end of 2016, approximately 36.7 million people were living with HIV, and approximately 1.8 million new infections were occurring globally each year [2].…”

Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo-Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theorem and an iterative method. The model is shown to have a disease-free and an endemic equilibrium point. Conditions are derived for the existence of the endemic equilibrium point and for the local asymptotic stability of the disease-free equilibrium point. The results confirm that the disease-free equilibrium point becomes increasingly stable as the fractional order is reduced. Numerical simulations are carried out using a three-step Adams-Bashforth predictor method for a range of fractional orders to illustrate the effects of varying the fractional order and to support the theoretical results.

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Section: Introductionmentioning

confidence: 99%

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

2019

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“…In order to continue study about the L‐V model of fractional order in ABC sense of derivative , we suggest the readers for reconsideration of for the study of exact traveling wave front, multiplicity, and exponential stability. Some more related results on dynamical models may be studied in …”

Section: Introductionmentioning

confidence: 99%

“…Some more related results on dynamical models may be studied in. [28][29][30][31] Organization of the paper: In this paper, we are presenting EU of the solution and HUS of an L-V fractional-order model in ABC sense of derivative. For these, the paper has five sections.…”

Section: Introductionmentioning

confidence: 99%

Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel

Khan

et al. 2019

Math Methods in App Sciences

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In the literature, many researchers have studied Lotka‐Volterra (L‐V) models for different types of studies. In order to continue the study, we consider a fractional‐order L‐V model involving three different species in the Atangana‐Baleanu‐Caputo (ABC) sense of fractional derivative. This new model has potentials for a large number of research‐oriented studies. The first point that arises is whether the new model has a solution or not. Therefore, to answer this question, we consider the existence and uniqueness (EU) of the solutions and then Hyers‐Ulam (HU) stability for the proposed L‐V model.

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“…Shen et al [18] to analyze the mathematical model of global dynamics with two lyapunov functions are constructed to prove the global stability of disease free and endemic equilibria. Treatment class of HIV/AIDS epidemic model is introduced by Huo et al [19].…”

Section: Introductionmentioning

confidence: 99%

Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

Singh¹

2016

AJAM

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The mathematical model for analyzing the transmission dynamics of HIV/AIDS epidemic with treatment is studied by considering the three latent compartments for slow, medium and fast progresses of developing the AIDS. By constructing the system of differential equations for the different population groups namely susceptible, three types of latent individuals, symptomatic stage group and full blown AIDS individuals, the mathematical analysis is carried out in order to understand the dynamics of disease spread. By determining the basic reproduction number (R 0 ), the model examines the two equilibrium points (i) the disease free equilibrium and (ii) the endemic equilibrium. It is established that if < 1, the disease free equilibrium is locally and globally asymptotically stable. The stability of endemic equilibrium has also been discussed.

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Modelling and stability of HIV/AIDS epidemic model with treatment

Cited by 112 publications

References 19 publications

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment

Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel

Epidemic Model of HIV/AIDS Transmission Dynamics with Different Latent Stages Based on Treatment

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