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. 2020 Dec 17;10(1):22268.
doi: 10.1038/s41598-020-79405-9.

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

Zubair Ahmad  1 , Muhammad Arif  1 , Farhad Ali  2   3 , Ilyas Khan  4 , Kottakkaran Sooppy Nisar  5
Affiliations

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

Zubair Ahmad et al. Sci Rep. .

Abstract

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 [Formula: see text] 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 [Formula: see text] 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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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Flow chart of the given SEIR model.
Figure 2
Figure 2
WHO reported cases for COVID-19 from 19th March 2020 till 31st March 2020.
Figure 3
Figure 3
WHO reported deaths by COVID-19 from 19th March 2020 till 31st March 2020.
Figure 4
Figure 4
WHO reported recovered cases of COVID-19 from 19th March 2020 till 31st March 2020.
Figure 5
Figure 5
Comparative bar chart and line plot of reported deaths and recovered individuals of COVID-19.
Figure 6
Figure 6
WHO reported cases for COVID-19 from 19th March 2020 till 31st March 2020.
Figure 7
Figure 7
Real data verses model fitting.
Figure 8
Figure 8
The dynamics of COVID-19 in different classes with different values of fractional parameter α.
Figure 9
Figure 9
The dynamics of COVID-19 in different classes with different initial values.
See this image and copyright information in PMC

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