Fractional stochastic models for COVID-19: Case study of Egypt

Omar, O.A.; Elbarkouky, Reda A.; Ahmed, Hamdy M.

doi:10.1016/j.rinp.2021.104018

Cited by 21 publications

(20 citation statements)

References 18 publications

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“…Based on several plans carried out by the Saudi Arabian government to fight against COVID-19 at different levels, we generalize the susceptible – exposed – infectious – recovered – deaths (SEIRF) model in [11] to describe virus transmission. The expanded models consider the first and second vaccination doses.…”

Section: Methodsmentioning

confidence: 99%

“…In [10] , the authors generated a modified fractional-order epidemic model which partitioned the population into seven classes and applied it to the real data of COVID-19 for Wuhan city. Since the COVID-19 transmission differs everywhere and it has a stochastic effect, the authors in [11] established a fractional-order stochastic dynamical model for COVID-19 to describe the second virus wave behaviour in Egypt. In [12] , the authors constructed a stochastic mathematical model to investigate virus temporal dynamics in Oman.…”

Section: Introductionmentioning

confidence: 99%

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COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

Omar¹,

Alnafisah²,

Elbarkouky³

et al. 2021

Results in Physics

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In this paper, we investigate the stochastic nature of the COVID-19 temporal dynamics by generating a fractional-order dynamic model and a fractional-order-stochastic model. Initially, we considered the first and second vaccination doses as multiple vaccinations were initiated worldwide. The concerned models are then tested for the Saudi Arabia second virus wave, which is assumed to start on 1st March 2021. Four daily vaccination scenarios for the first and second dose are assumed for 100 days from the wave beginning. One of these scenarios is based on function optimization using the invasive weed optimization algorithm (IWO). After that, we numerically solve the established models using the fractional Euler method and the Euler-Murayama method. Finally, the obtained virus dynamics using the assumed scenarios and the real one started by the government are compared. The optimized scenario using the IWO effectively minimizes the predicted cumulative wave infections with a 4.4 % lower number of used vaccination doses.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

Omar¹,

Alnafisah²,

Elbarkouky³

et al. 2021

Results in Physics

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“…Some authors [24,25] propose to keep the model as simple as possible because of the thin data availability in early periods, with the purpose of focusing on specific local peculiarities. Simultaneously, some authors [8,[26][27][28][29][30] use fractional-order models and/or controllers instead of classical integer-order calculus to model the dynamics of the compartments, at the cost of increased complexity and required computational resources, because of the infinite memory problem and other aspects. Nevertheless, to control the system using a fractional model is a new trend which can be generally justified by the chaotic nature of the considered phenomena, as already tested for other nonlinear oscillating systems.…”

Section: Literature Reviewmentioning

confidence: 99%

Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability

2021

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Due to the worldwide outbreak of COVID-19, many strategies and models have been put forward by researchers who intend to control the current situation with the given means. In particular, compartmental models are being used to model and analyze the COVID-19 dynamics of different considered populations as Susceptible, Exposed, Infected and Recovered compartments (SEIR). This study derives control-oriented compartmental models of the pandemic, together with constructive control laws based on the Lyapunov theory. The paper presents the derivation of new vaccination and quarantining strategies, found using compartmental models and design methods from the field of Lyapunov theory. The Lyapunov theory offers the possibility to track desired trajectories, guaranteeing the stability of the controlled system. Computer simulations aid to demonstrate the efficacy of the results. Stabilizing control laws are obtained and analyzed for multiple variants of the model. The stability, constructivity, and feasibility are proven for each Lyapunov-like function. Obtaining the proof of practical stability for the controlled system, several interesting system properties such as herd immunity are shown. On the basis of a generalized SEIR model and an extended variant with additional Protected and Quarantined compartments, control strategies are conceived by using two fundamental system inputs, vaccination and quarantine, whose influence on the system is a crucial part of the model. Simulation results prove that Lyapunov-based approaches yield effective control of the disease transmission.

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“…The mathematical models suggest that doses will not be enough until 2023 due to limited sources and manufacturing capacity for population coverage [4] . In many recent studies , mathematical epidemiological modelling is used to predominantly develop mass-action models and suitable tools for analyzing COVID-19 dynamics [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] . Different mathematical models are used for this purpose as the transmission rates and virus behaviour depend on individuals' precautionary measures, daily vaccination rates, and vaccination efficiencies [15] , [16] , [17] , [18] , [19] , [20] , [21] .…”

Section: Introductionmentioning

confidence: 99%

Fractional stochastic modelling of COVID-19 under wide spread of vaccinations: Egyptian case study

Omar¹,

Elbarkouky²,

Ahmed³

2022

Alexandria Engineering Journal

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This work predicts the dynamics of the COVID-19 under widespread vaccination to anticipate the virus's current and future waves. We focused on establishing two population-based models for predictions: the fractional-order model and the fractional-order stochastic model. Based on dose efficacy, which is one of the main imposed assumptions in our study, some vaccinated people will probably be exposed to infection by the same viral wave. We validated the generated models by applying them to the current viral wave in Egypt. We assumed that the Egyptian current wave began on 10 th September 2021. Using current actual data and varying our models’ fractional orders, we generate different predicted wave scenarios. The numerical solution of our models is obtained using the fractional Euler method and the fractional Euler Maruyama method. At the end, we compared the current predicted wave under a high vaccination rate with the previous viral wave. Through this comparison, the vaccination control effect is quantified.

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Fractional stochastic models for COVID-19: Case study of Egypt

Cited by 21 publications

References 18 publications

COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

COVID-19 deterministic and stochastic modelling with optimized daily vaccinations in Saudi Arabia

Extension of SEIR Compartmental Models for Constructive Lyapunov Control of COVID-19 and Analysis in Terms of Practical Stability

Fractional stochastic modelling of COVID-19 under wide spread of vaccinations: Egyptian case study

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