Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

Atangana, Abdon; Araz, Seda İğret

doi:10.1016/j.rinp.2021.104694

Cited by 39 publications

(3 citation statements)

References 21 publications

(24 reference statements)

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“…It is noteworthy that the notion of piecewise derivatives aligns closely with the concept of short memory in fractional calculus. In this context, significant recent contributions have been made, with references to notable works such as [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

Sweilam,

Al-Mekhlafi,

Hassan

et al. 2024

Fractal Fract

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In this paper, we improved a mathematical model of monkeypox disease with a time delay to a crossover model by incorporating variable-order and fractional differential equations, along with stochastic fractional derivatives, in three different time intervals. The stability and positivity of the solutions for the proposed model are discussed. Two numerical methods are constructed to study the behavior of the proposed models. These methods are the nonstandard modified Euler Maruyama technique and the nonstandard Caputo proportional constant Adams-Bashfourth fifth step method. Many numerical experiments were conducted to verify the efficiency of the methods and support the theoretical results. This study’s originality is the use of fresh data simulation techniques and different solution methodologies.

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Section: Introductionmentioning

confidence: 99%

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

Sweilam,

Al-Mekhlafi,

Hassan

et al. 2024

Fractal Fract

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“…Recently, Atangana and Seda updated a new theory by introducing the concept of piecewise differentiation and integration, where a derivative or an integral is defined as a piecewise within a given interval [4]. Subsequently, much research has been conducted based on this new approach; see, for example, [6,7,10,12,15] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

Alalhareth

Laksaci

Boudaoui

et al. 2023

Preprint

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Some real-world problems have complicated behaviors, so in the last twoyears, piecewise calculus has been developed to more accurately depict these issues. Thispaper will elaborate on and examine cancer tumor’s chaotic model from determinism torandomness. Several scenarios are considered. The existence and the uniqueness of thesolutions of the system are proved via Mao’s theorem. Graphics of numerical schemesand their numerical simulations. AMS (MOS) Subject Classifications: 92B05, 65P20, 26A33

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“…Differential equations of fractional order for the mathematical modeling of COVID-19 were used by Khan et al, where they provided a detailed analysis by considering Saudi Arabia as a case study [21]. An approach based on piecewise differential and integral operators was developed by Atangana, Seda and Prolonger [22,23]. The dynamics of COVID-19 with the fuzzy Caputo approach are discussed in [24].…”

Section: Introductionmentioning

confidence: 99%

Threshold of Stochastic SIRS Epidemic Model from Infectious to Susceptible Class with Saturated Incidence Rate Using Spectral Method

Ali

Khan

2022

Symmetry

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Stochastic SIRS models play a key role in formulating and analyzing the transmission of infectious diseases. These models reflect the environmental changes of the diseases and their biological mechanisms. Therefore, it is very important to study the uniqueness and existence of the global positive solution to investigate the asymptotic properties of the model. In this article, we investigate the dynamics of the stochastic SIRS epidemic model with a saturated incidence rate. The effects of both deterministic and stochastic distribution from infectious to susceptible are analyzed. Our findings show that the occurrence of symmetry breaking as a function of the stochastic noise has a significant advantage over the deterministic one to prevent the spread of the infectious diseases. The larger stochastic noise will guarantee the control of epidemic diseases with symmetric Brownian motion. Periodic outbreaks and re-infection may occur due to the existence of feedback memory. It is shown that the endemic equilibrium is stable under some suitable initial conditions, taking advantage of the symmetry of the large amount of contact structure. A numerical method based on Legendre polynomials that converts the given stochastic SIRS model into a nonlinear algebraic system is used for the approximate solution. Finally, some numerical experiments are performed to verify the theoretical results and clearly show the sharpness of the obtained conditions and thresholds.

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Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

Cited by 39 publications

References 21 publications

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

A Novel Hybrid Crossover Dynamics of Monkeypox Disease Mathematical Model with Time Delay: Numerical Treatments

Numerical Simulations for Deterministic-Stochastic Chaotic Cancer Model

Threshold of Stochastic SIRS Epidemic Model from Infectious to Susceptible Class with Saturated Incidence Rate Using Spectral Method

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