Models for COVID-19 Daily Confirmed Cases in Different Countries

Ahmed, Hamdy M.; Elbarkouky, Reda A.; Omar, O.A.; Ragusa, Maria Alessandra

doi:10.3390/math9060659

Cited by 25 publications

(19 citation statements)

References 14 publications

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“…In recent years, extensive studies [17][18][19] have been conducted on the mathematical analysis of fractional derivatives and integrals. The fractional-order derivative is nonlocal and includes the historical and long-term memory effect of the system, and this is one of its most important advantages over the integer-order derivative, which helps to model natural phenomena better [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Mohammadi

Kaabar

Alzabut

et al. 2021

Journal of Function Spaces

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Crimean-Congo hemorrhagic fever is a common disease between humans and animals that is transmitted to humans through infected ticks, contact with infected animals, and infected humans. In this paper, we present a boxed model for the transmission of Crimean-Congo fever virus. With the help of the fixed-point theory, our proposed system model is investigated in detail to prove its unique solution. Given that the Caputo fractional-order derivative preserves the system’s historical memory, we use this fractional derivative in our modeling. The equilibrium points of the proposed system and their stability conditions are determined. Using the Euler method for the Caputo fractional-order derivative, we calculate the approximate solutions of the fractional system, and then, we present a numerical simulation for the transmission of Crimean-Congo hemorrhagic fever.

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Section: Introductionmentioning

confidence: 99%

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

Mohammadi

Kaabar

Alzabut

et al. 2021

Journal of Function Spaces

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“…Mathematical epidemiology may be said to have started with the SIR ODE model, which saw its birth in the works of . This was initially applied to model the Bombay plague of 1905-06, and later to measles [2], smallpox, chickenpox, mumps, typhoid fever and diphtheria, and recently to the COVID-19 pandemic-see, for example in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], to cite just a few representatives of a huge literature.…”

Section: Introductionmentioning

confidence: 99%

A Review of Matrix SIR Arino Epidemic Models

2021

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Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “(x,y,z)” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number R has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for (x,y,z) models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity Y(t) which satisfies “classic SIR relations”, which may be useful to obtain approximate control policies.

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“…Mathematical modelling is a powerful tool for predicting and controlling epidemics. Many mathematical models have demonstrated their ability to predict daily infections and deaths with pinpoint accuracy [1] , [2] . The main two mathematical models used for this object are statistical models and dynamical models.…”

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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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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Models for COVID-19 Daily Confirmed Cases in Different Countries

Cited by 25 publications

References 14 publications

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

A Complete Model of Crimean-Congo Hemorrhagic Fever (CCHF) Transmission Cycle with Nonlocal Fractional Derivative

A Review of Matrix SIR Arino Epidemic Models

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

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