Nonlinear equations with global differential and integral operators: Existence, uniqueness with application to epidemiology

Atangana, Abdon; Araz, Seda İğret

doi:10.1016/j.rinp.2020.103593

Cited by 68 publications

(40 citation statements)

References 13 publications

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“…• B 1 (t), Therefore, the associated stochastic model is given as follows: In this conversion, the function B i (t) represents the standard Brownian motions valid within the set of probability ( , A, {A t } t≥0 , P), where {A t } t≥0 is filtration valid under the condition described in [17]. Here, i,j∈ [1,2,3,4,5,6,7,8] are positive and are the intensities of the environmental random disturbance.…”

Section: Mathematical Model For Covid-19 Outbreakmentioning

confidence: 99%

“…To do this, we used the available data on the website of the World Health Organization (WHO) [1,2]. Although mathematicians cannot provide vaccine or cure the disease in an infected person, they can use their mathematical tools to foresee what could possibly happen in the near future with some limitations [3][4][5][6][7][8][9][10][11][12][13][14]. With the new trend of spread, it is possible that the world will face a second wave of COVID-19 spread, this will be the aim of our work.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Atangana

Araz

2021

Adv Differ Equ

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Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.

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Section: Mathematical Model For Covid-19 Outbreakmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Atangana

Araz

2021

Adv Differ Equ

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“…About the ABC-fractional calculus, we highlight the following useful literature from [21][22][23][24][25].…”

Section: (T) I(t) C(t) A(t) For This Model {S(t) I(t) C(t) A(t)}mentioning

confidence: 99%

A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

et al. 2021

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In this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solution, the stability analysis, and simulations. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the fractional order model is derived with the help of existing literature for the Hyers–Ulam stability. For the numerical computations, the Lagrange interpolation is utilized, and the simulations are obtained for specific parameters. The results are closer to the classical results for different orders.

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“…Since December 2019, a date when the world first witnessed the breakout of the novel Covid-19 that started in Wuhan, a China city, mathematicians as well as many others researchers in many academic disciplines have focused their attention in modelling a dynamic spread of Covid-19 [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] . The literature is now full of new mathematical models, of course all these mathematical models have their limitations, advantages and disadvantages.…”

Section: Introductionmentioning

confidence: 99%

A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial

Atangana

Araz

2021

Alexandria Engineering Journal

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To capture more complexities associated to the spread of Covid-19 within a given population, we considered a system to nine differential equations that include a class of susceptible, 5 sub-classes of infected population, recovered, death and vaccine. The mathematical model was suggested with a lockdown function such that after the lockdown, the function follows a fading memory rate, a concept that is justified by the effect of social distancing that suggests, susceptible class should stay away from infected objects and humans. We presented a detailed analysis that includes reproductive number and stability analysis. Also, we introduced the concept of fractional Lyapunov function for Caputo, Caputo-Fabrizio and the Atangana-Baleanu fractional derivatives. We established the sign of the fractional Lyapunov function in all cases, additionally we proved that, if the fractional order is one, we recover the results for the model with classical differential operators. With the nonlinearity of the differential equations depicting the complexities of the Covid-19 spread especially the cases with nonlocal operators, and due to the failure of existing analytical methods to provide exact solution to the system, we employed the newly introduced numerical method based on the Newton polynomial to derive numerical solutions for all cases and numerical simulations are provided for different values of fractional orders and fractal dimensions. Collected data from Turkey case for a period of 90 days were compared with the suggested mathematical model with Atangana-Baleanu fractional derivative and a agreement was reached for alpha .

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Nonlinear equations with global differential and integral operators: Existence, uniqueness with application to epidemiology

Cited by 68 publications

References 13 publications

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe

A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

A novel Covid-19 model with fractional differential operators with singular and non-singular kernels: Analysis and numerical scheme based on Newton polynomial

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