Mathematical analysis of HIV/AIDS infection model with Caputo-Fabrizio fractional derivative

Bushnaq, Samia; Khan, Sajjad Ali; Shah, Kamal; Zaman, Gul

doi:10.1080/23311835.2018.1432521

Cited by 39 publications

(27 citation statements)

References 9 publications

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“…A lot of scholars are investigating epidemic models related to different infectious diseases involving fractional operator because it shows the reasonable biphasic decline of contamination of diseases. [21,22,23,24,25].…”

Section: Mathematical Modelmentioning

confidence: 99%

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Shaikh

Nisar

2020

Preprint

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Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

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Section: Mathematical Modelmentioning

confidence: 99%

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Shaikh

Nisar

2020

Preprint

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“…The epidemic models of HIV differ in many aspects; ranging from different classifications of the total population to various terms used to represent transmission rates. Total population is generally divided into susceptible individuals, infected individuals and individuals with AIDS [1,19,20]. The infected individuals may further be divided into the individuals who are aware of their infection and who are not aware of their infection.…”

Section: Between-host Hiv Epidemic Modelsmentioning

confidence: 99%

“…HIV infects various body cells in the immune system, particularly CD 4 + T cells. Without any treatment, this infection leads to the failure of the host immune system and ultimately to death [1]. The spread of infection is considered to be a vital part of any infectious disease where the dynamics of the disease primarily depends on the rate of transmission from an infectious individual to a susceptible individual [2].…”

Section: Introductionmentioning

confidence: 99%

“…For example, to solve the immunological models, different techniques have been used, such as homotopy analysis method [13], quasilinearization-Lagrangian method [14], the shifted boubaker Lagrangian approach [15], Laplace-Adomian decomposition method [16], and Legendre wavelet method [17]. The epidemiological models are studied both from stability analysis perspective, as well as, their numerical solutions [1,[18][19][20][21]. In this paper, we propose Memetic computing approach to solve the HIV epidemic model.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Between-host HIV model: stability analysis and solution using memetic computing

Ahmed¹,

Qureshi²,

Saleem³

et al. 2019

Turk J Elec Eng & Comp Sci

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HIV poses a great threat to humanity for two major reasons. First it attacks the immunity system of the body and second, it is epidemic in nature. Mathematical models of HIV have been instrumental in understanding and controlling the infection. In this paper, we solve the between host epidemic model of HIV, described by nonlinear coupled differential equations, by using memetic computing. Under this model, the sexually active population is divided into four classes and we investigate the transfer of individuals from one class to another. The solution consists of Bernstein polynomials whose parameters have been optimized by using differential evolution as global and sequential quadratic programming as local optimizer. Our second contribution is the stability analysis of this model. The disease-free equilibrium is stable while endemic equilibrium is unstable within the practical range of the values of parameters.

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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 analysis of HIV/AIDS infection model with Caputo-Fabrizio fractional derivative

Cited by 39 publications

References 9 publications

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control

Between-host HIV model: stability analysis and solution using memetic computing

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

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