On Fractional Model of an HIV/AIDS with Treatment and Time Delay

Hikal, M.M.; Zahra, Waheed K.

doi:10.18576/pfda/020106

Cited by 11 publications

(2 citation statements)

References 16 publications

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“…It is very useful to determine the basic reproduction number that plays an important role in spreading the disease and studying the stability behavior of the epidemic model. To compute the basic reproductive number of the system (1.1), we follow [21][22][23][24][25] by using the next-generation method. Hence we can rearrange system (1.1) to have the form:…”

Section: Theorem 21 Any Solution Of System (11) With Bounded Initial Conditions Is Uniformly Boundedmentioning

confidence: 99%

“…5 Time response of in S(t), E(t), I(t), R(t) and U(t) example 2, τ = 0, τ = 40 < τ 1 ∈ (0, 1] . Figure 2 presents the time response of the system (1.1) for α = 1, using the fourth-order Rung-Kutta method (FORKM) [26] for solving ordinary differential equations and the nonstandard finite difference method (NSFDM) [23,27] for solving the fractional-order differential equations. In Fig.…”

Section: Examplementioning

confidence: 99%

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Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

Hikal

El-Sheikh

Zahra

2021

J. Appl. Math. Comput.

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This study presents methods of hygiene and the use of masks to control the disease. The zero basic reproduction number can be achieved by taking the necessary precautionary measures that prevent the transmission of infection, especially from uninfected virus carriers. The existence of time delay in implementing the quarantine strategy and the threshold values of the time delay that keeping the stability of the system are established. Also, it is found that keeping the infected people quarantined immediately is very important in combating and controlling the spread of the disease. Also, for special cases of the system parameters, the time delay can not affect the asymptotic behavior of the disease. Finally, numerical simulations have been illustrated to validate the theoretical analysis of the proposed model.

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Section: Theorem 21 Any Solution Of System (11) With Bounded Initial Conditions Is Uniformly Boundedmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

Hikal

El-Sheikh

Zahra

2021

J. Appl. Math. Comput.

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Numerical simulation for time‐fractional nonlinear reaction–diffusion system on a uniform and nonuniform time stepping

Zahra

Hikal

Băleanu

2021

Math Methods in App Sciences

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In this article, two nonstandard high‐order schemes on a uniform and nonuniform time stepping combined with the multi‐parameter exponential fitting technique (MPEF) have been developed to solve the time‐fractional nonlinear reaction–diffusion system. The first method based on the MPEF combined with the 3‐weighted shifted‐Grünwald–Letnikov approximation with uniform time stepping, this scheme leads to a numerical solution that suffers from the singularity near t = 0. In order to frustrate this singularity, a nonstandard higher‐order L1‐approximation for a nonuniform time‐stepping scheme is developed. The developed scheme's convergence and unconditionally stability analysis have been verified. Numerical results effectively validate the theoretical aspects.

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SEIRS epidemic model with Caputo–Fabrizio fractional derivative and time delay: dynamical analysis and simulation

et al. 2021

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On Fractional Model of an HIV/AIDS with Treatment and Time Delay

Cited by 11 publications

References 16 publications

Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

Stability analysis of COVID-19 model with fractional-order derivative and a delay in implementing the quarantine strategy

Numerical simulation for time‐fractional nonlinear reaction–diffusion system on a uniform and nonuniform time stepping

SEIRS epidemic model with Caputo–Fabrizio fractional derivative and time delay: dynamical analysis and simulation

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