New dynamical behaviour of the coronavirus (COVID-19) infection system with nonlocal operator from reservoirs to people

Veeresha, P.; Prakasha, D. G.; Malagi, Naveen Sanju; Ilhan, Elif; Başkonuş, Hacı Mehmet

doi:10.21203/rs.3.rs-19500/v1

Cited by 18 publications

(14 citation statements)

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“…Also, I , A , and H denote the recovery rate of infected individuals, asymptomatic infected individuals, and quarantined infected individuals. So here, we consider the fractional order of Equation (1) with AB derivative which as follows: 24 ABC 0 D t P S (t) = − ( c + ca(1 − )) P S (P I + P A ) + P S a ,…”

Section: Mathematical Optimization and Miniaturementioning

confidence: 99%

“…Also, γ I , γ A , and γ H denote the recovery rate of infected individuals, asymptomatic infected individuals, and quarantined infected individuals. So here, we consider the fractional order of Equation () with AB derivative which as follows: 24

\begin{matrix} right_{0}^{A B C} D_{t}^{α} P_{S} (t) & left = - (β c + c a (1 - β)) P_{S} (P_{I} + θ P_{A}) + λ P_{S_{a}}, & right \\ right_{0}^{A B C} D_{t}^{α} P_{E} (t) & left = - β c (1 - a) P_{S} (P_{I} + θ P_{A}) + σ P_{E}, \\ right_{0}^{A B C} D_{t}^{α} P_{I} (t) & left = σ τ P_{E} - (δ_{I} + b + γ_{I}) P_{I}, \\ right_{0}^{A B C} D_{t}^{α} P_{A} (t) & left = σ (1 - τ) P_{E} - γ_{A} P_{A}, \\ right_{0}^{A B C} D_{t <...>} \end{matrix}

…”

Section: Mathematical Optimization and Miniaturementioning

confidence: 99%

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Analysis and numerical simulation of novel coronavirus (COVID‐19) model with Mittag‐Leffler Kernel

Padmavathi¹,

Prakash

Alagesan³

et al. 2020

Math Methods in App Sciences

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Every now and then, there has been natural or man-made calamities. Such adversities instigate various institutions to find solutions for them. The current study attempts to explore the disaster caused by the micro enemy called coronavirus for the past few months and aims at finding the solution for the system of nonlinear ordinary differential equations to which q−homotopy analysis transform method (q−HATM) has been applied to arrive at effective results. In this paper, there are eight nonlinear ordinary differential equations considered and to solve them the advanced fractional operator Atangana-Baleanu (AB) fractional derivative has been applied to produce better understanding. The outcomes have been presented in terms of plots. Ultimately, the present study assists in examining the real-world models and aids in predicting their behavior corresponding to the parameters considered in the models. KEYWORDS Atangana-Baleanu fractional derivative, coronavirus epidemic model, nonlinear differential equations, q−homotopy analysis transform method MSC CLASSIFICATION 37M05; 34F05; 92D30 1 INTRODUCTION Human history is facing a strange time, fighting with an invisible enemy called the novel coronavirus (COVID-19). This pandemic virus disease found in Wuhan, China. 1 It ensured where the animals and sea meat were sold and named as coronavirus on 31st of December, 2019. The Chinese Government and its health organization together insisted about its transformation from animals to human. 2,3 Coronavirus spread is rapidly increasing in all over the countries. Large number of people are affected by this deadly disease. The current status of coronavirus (COVID-19) is unimaginable, because enormous people have been suffered so far. Though people are recovering from this COVID-19, simultaneously the death ratio is increasing rapidly. World health organization is giving awareness among people through various factors. Scientist are also insisting its importance. The entire nation is joining together to overcome the disease, because even the developed countries couldn't get solution for this virus. This disease threat the people all over the world mentally, because vaccine didn't find yet for this dreadful disease. This study is not only on anticipating the results of the spread but also analyzing the spread of various disease. The study also focuses on to control the disease as possible. 1,4-8 In this paper, we are applying q-homotopy analysis transformation method (q-HATM) to the system of nonlinear equations and find suitable solution for this crucial disease. In order to consider the new fractional operator called

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Section: Mathematical Optimization and Miniaturementioning

confidence: 99%

\begin{matrix} right_{0}^{A B C} D_{t}^{α} P_{S} (t) & left = - (β c + c a (1 - β)) P_{S} (P_{I} + θ P_{A}) + λ P_{S_{a}}, & right \\ right_{0}^{A B C} D_{t}^{α} P_{E} (t) & left = - β c (1 - a) P_{S} (P_{I} + θ P_{A}) + σ P_{E}, \\ right_{0}^{A B C} D_{t}^{α} P_{I} (t) & left = σ τ P_{E} - (δ_{I} + b + γ_{I}) P_{I}, \\ right_{0}^{A B C} D_{t}^{α} P_{A} (t) & left = σ (1 - τ) P_{E} - γ_{A} P_{A}, \\ right_{0}^{A B C} D_{t <...>} \end{matrix}

…”

Section: Mathematical Optimization and Miniaturementioning

confidence: 99%

Analysis and numerical simulation of novel coronavirus (COVID‐19) model with Mittag‐Leffler Kernel

Padmavathi¹,

Prakash

Alagesan³

et al. 2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The emergence and reemergence of coronavirus epidemics sparked renewed concerns from global epidemiology researchers, public health administrators and Mathematical Modeling researchers to model this . In the present investigation, we consider the compartmental mathematical model (epidemic model) has been developed by Khan and Atangana [19] for understanding the transmission of virus and presented and derived some interesting results for the projected model by comparison with some practical values (see also [9,20,25,30]). In this epidemic model a total number of populations N at a time t, is divided into the following six compartments: s(t) the susceptible people; e(t) the exposed people; i(t) the infected strength; a(t) the asymptotically infected people; r(t) the recovered people; m(t) the reservoir.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

Christopher¹,

Magesh²,

Preethi³

2020

Preprint

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The aim of this paper is applying the Differential Transformation Method (DTM) to analyze and find the solution for the mathematical model described by the system of nonlinear ordinary differential equations which describe the epidemiology of the most threatening virus called Corona-virus later labelled as COVID-19. The behaviour of the outcomes is presented in terms of plots. Finally, the present study may help you to examine the wild class of real world models and also aid to predict their behaviour with respect to parameters considered in the model. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.

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“…Authors in [7] presented the impact on the environment of glob and effects on society with COVID-19 and also discussed and illustrated the possible ways of controlling its effect on humankind. A model-based analysis has been exemplified by authors in [8] and predictions and prevention approaches are presented and many researchers [9] .…”

Section: Introductionmentioning

confidence: 99%

A new study of unreported cases of 2019-nCOV epidemic outbreaks

Gao

Veeresha

Baskonus

et al. 2020

Chaos, Solitons & Fractals

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189

112

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2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q -homotopy analysis transform method ( q -HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

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New dynamical behaviour of the coronavirus (COVID-19) infection system with nonlocal operator from reservoirs to people

Cited by 18 publications

References 0 publications

Analysis and numerical simulation of novel coronavirus (COVID‐19) model with Mittag‐Leffler Kernel

Analysis and numerical simulation of novel coronavirus (COVID‐19) model with Mittag‐Leffler Kernel

Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

A new study of unreported cases of 2019-nCOV epidemic outbreaks

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