Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan

Qureshi, Sania; Memon, Zaib-un-Nisa

doi:10.1016/j.chaos.2019.109478

Cited by 43 publications

(21 citation statements)

References 44 publications

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“…Using equation (11), model (1) becomes: Similarly, EE of model (1) is obtained from system (12) and is given by:…”

Section: Equilibrium Points Basic Reproduction Number and Local Stabmentioning

confidence: 99%

“…Recently, many researchers have chosen AB fractional model for dynamics of different infectious diseases, like the dynamics of HIV [6], chicken pox [7], hepatitis E [8], dengue fever [9], rubella disease [10], measles [11], tuberculosis [12]. The applications of AB fractional derivative is not only limited to study the dynamics of infectious diseases but it has many applications in modern sciences and technologies e.g.…”

Section: Introductionmentioning

confidence: 99%

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A Report on COVID-19 Epidemic in Pakistan: An SEIR Fractional Model

Ahmad

Arif

Ali

et al. 2020

Preprint

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Recently, novel coronavirus is a serious global issue and having a negative impact on the economy of the whole world. Like other countries, it also effected the economy and people of Pakistan. According to the publicly reported data, the first case of novel corona virus in Pakistan was reported on 27th February 2020. The aim of the present study is to describe the mathematical model and dynamics of COVID-19 in Pakistan. To investigate the spread of coronavirus in Pakistan, we develop the SEIR time fractional model with newly, developed fractional operator of Atangana-Baleanu. We present briefly the analysis of the given model and discuss its applications using world health organization (WHO) reported data for Pakistan. We consider the available infection cases from 19th march 2020, till 31st march 2020 and accordingly, various parameters are fitted or estimated. It is worth noting that we have calculated the basic reproduction number which shows that virus is spreading rapidly. Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter on the model, various graphs are plotted. It is worth noting that the base of our investigation, we have predicted the spread of disease for next 200 days.

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“…Using equation (11), model (1) becomes: Similarly, EE of model (1) is obtained from system (12) and is given by:…”

Section: Equilibrium Points Basic Reproduction Number and Local Stabmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Report on COVID-19 Epidemic in Pakistan: An SEIR Fractional Model

Ahmad

Arif

Ali

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“… [26] and Qureshi et al. [21] . In recent years, many papers have been published on the subject of Caputo-Fabrizio fractional derivative [18] (see for example, Dokuyucu et al.…”

Section: Introductionmentioning

confidence: 96%

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

Tuan¹,

Mohammadi

Rezapour

2020

Chaos, Solitons & Fractals

305

157

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Highlights COVID-19 is transmitted from asymptomatic individuals to susceptible individuals. COVID-19 is transmitted from symptomatic individuals to susceptible individuals. Since R0=1.6 is greater than 1, the COVID-19 will spread exponentially. If COVID-19 is not controlled, it is estimated that about 20 million people will become infected in the next three years.

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“…Recently, many researchers have chosen AB fractional model for dynamics of different infectious diseases, like the dynamics of HIV 18 , chicken pox 19 , hepatitis E 20 , dengue fever 21 , rubella disease 22 , measles 23 , tuberculosis 24 . Besides this, AB fractional operator is also used by many researchers to investigate the dynamics of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

A report on COVID-19 epidemic in Pakistan using SEIR fractional model

Ahmad

Arif

Ali

et al. 2020

Sci Rep

View full text Add to dashboard Cite

Recently, novel coronavirus is a serious global issue and having a negative impact on the economy of the whole world. Like other countries, it also effected the economy and people of Pakistan. According to the publicly reported data, the first case of novel corona virus in Pakistan was reported on 27th February 2020. The aim of the present study is to describe the mathematical model and dynamics of COVID-19 in Pakistan. To investigate the spread of coronavirus in Pakistan, we develop the SEIR time fractional model with newly, developed fractional operator of Atangana–Baleanu. We present briefly the analysis of the given model and discuss its applications using world health organization (WHO) reported data for Pakistan. We consider the available infection cases from 19th March 2020, till 31st March 2020 and accordingly, various parameters are fitted or estimated. It is worth noting that we have calculated the basic reproduction number $${\mathfrak{R}}_{0} \approx 2.30748$$ R 0 ≈ 2.30748 which shows that virus is spreading rapidly. Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter $$\alpha$$ α on the model, various graphs are plotted. It is worth noting that the base of our investigation, we have predicted the spread of disease for next 200 days.

show abstract

Monotonically decreasing behavior of measles epidemic well captured by Atangana–Baleanu–Caputo fractional operator under real measles data of Pakistan

Cited by 43 publications

References 44 publications

A Report on COVID-19 Epidemic in Pakistan: An SEIR Fractional Model

A Report on COVID-19 Epidemic in Pakistan: An SEIR Fractional Model

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

A report on COVID-19 epidemic in Pakistan using SEIR fractional model

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