A fractional order SIR epidemic model with nonlinear incidence rate

Mouaouine, Abderrahim; Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura

doi:10.1186/s13662-018-1613-z

Cited by 58 publications

(35 citation statements)

References 26 publications

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“…The functional response of feeding prey by susceptible predator Not long ago, many researchers began to study fractional biological models [1,10,20,25]. In article [14], a dynamic system modelling a prey-predator with harvest area and reserve for prey in the presence of competition and toxicity.…”

Section: Parameters and Variables Explanationmentioning

confidence: 99%

Fractional order prey-predator model with infected predators in the presence of competition and toxicity

Lemnaouar

Khalfaoui

Louartassi

et al. 2020

Math. Model. Nat. Phenom.

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Section: Parameters and Variables Explanationmentioning

confidence: 99%

Fractional order prey-predator model with infected predators in the presence of competition and toxicity

Lemnaouar

Khalfaoui

Louartassi

et al. 2020

Math. Model. Nat. Phenom.

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“…(10) and (12), a new iterative technique can also be considered, which has been framed in the later sections. (13) in which N i is a nonlinear operator.…”

Section: Formulation Of the Modelmentioning

confidence: 99%

“…Hamdan and Kilicman [12] studied the dynamical behaviour of a virus dynamics model with general incidence rate and cure rate for dengue transmission. Mouaouine et al [13] studied the vigorous deportment of a virus dynamics model with broad occurrence rate and cure rate. Wang et al [14] presented the delayed fractional-order SIR (susceptible and removed) epidemic model with saturated incidence and treatment functions.…”

mentioning

confidence: 99%

Analysis of Fractional-Order Model of COVID-19 Pandemics With a Nonlinear Incidence Rate

Varghese¹,

Bhoyar²,

Nisar

2020

Innov Biosyst Bioeng

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Background. Several mathematical representations of contagious disease COVID-19 were evolved in order to capture the pragmatic aspect of unfurling of the disease. It is learned that individuals who became receptive were infected with a rate proportional to the fraction of the individuals affected by the infection, in the comprehensive population as well as the infected individuals recuperate at a sustained rate. It is also observed that in the SIR model, all contacts impart the disease with an identical probability. Objective. We will estimate the dynamic epidemic behaviour of inflected population for India with the use of fractional-order SIR simulations and compare our results with the results obtained for extrapolated actual cases of the infected people. Methods. We have obtained the approximate solutions of the fractional-order Susceptible-Infectious-Recovered model within the framework of the modified Riemann-Liouville fractional differential operator using a new iterative fractional complex transform technique. Results. The optimal values of the fractional-order SIR model parameters were identified with the use of the New Iterative Method. The dynamic incident rate with high and low reproduction number is predicted as well as the illustrated graphical with actual data is provided. To sum, the fractional calculus model for a complex system proposed here is just an indication to show what might happen if we do not control the reproduction number in the community. Conclusions. The control measures that have already been found like swift surveillance, quarantine and social distancing means, such as face masks and closures, assisted in curtailing coronavirus transmissionestimated by the average number of people each infected individual infects, or reproduction number, to close to the level of 1 in each month.

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“…As such, in recent years, fractional calculus has become an intriguing field. Several researchers have shown that models that utilize fractional calculus are more likely to replicate real-world problems compared those that use integer-order differential equations since fractional-order differential equations are able to capture memory effects [20,21].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for fall armyworm management on maize biomass

et al. 2021

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Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results.

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A fractional order SIR epidemic model with nonlinear incidence rate

Cited by 58 publications

References 26 publications

Fractional order prey-predator model with infected predators in the presence of competition and toxicity

Fractional order prey-predator model with infected predators in the presence of competition and toxicity

Analysis of Fractional-Order Model of COVID-19 Pandemics With a Nonlinear Incidence Rate

A mathematical model for fall armyworm management on maize biomass

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