Mathematical study of SIR epidemic model under convex incidence rate

Rahim ud Din; Kamal Shah; Manar A. Alqudah; Thabet Abdeljawad; Fahd Jarad; Rahim ud Din; Kamal Shah; Manar A. Alqudah; Thabet Abdeljawad; Fahd Jarad

doi:10.3934/math.2020483

AIMS Mathematics

2020, Volume 5, Issue 6: 7548-7561. doi: 10.3934/math.2020483

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Research article

Mathematical study of SIR epidemic model under convex incidence rate

1.
Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan
2.
Department of Mathematical Sciences, Faculty of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia
4.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
5.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
6.
Department of Mathematics, ?ankaya University, Ankara, Turkey

Received: 25 July 2020 Accepted: 17 September 2020 Published: 24 September 2020
MSC : 92Bxx, 92B05

In this manuscript, we examine the SIR model under convex incidence rate. We first formulate the famous SIR model under the aforesaid incidence rate. Further, we develop some sufficient analysis to examine the dynamical behavior of the model under consideration. We compute the basic reproductive number $\mathcal{R}_0.$ Also we study the global attractivity results via using Dulac function theory. Further, we also provide some information about the stability of the endemic and disease free equilibria for the considered model. In addition, we use nonstandard finite difference scheme to perform numerical simulation of the considered model via using Matlab. We provide different numerical plots for two different values of contact rate and taking various initial values for compartments involved in the considered model.
- convex incidence rate,
- used Dulac function,
- global analysis,
- SIR model,
- reproductive number
Citation: Rahim ud Din, Kamal Shah, Manar A. Alqudah, Thabet Abdeljawad, Fahd Jarad. Mathematical study of SIR epidemic model under convex incidence rate[J]. AIMS Mathematics, 2020, 5(6): 7548-7561. doi: 10.3934/math.2020483

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Abstract

In this manuscript, we examine the SIR model under convex incidence rate. We first formulate the famous SIR model under the aforesaid incidence rate. Further, we develop some sufficient analysis to examine the dynamical behavior of the model under consideration. We compute the basic reproductive number $\mathcal{R}_0.$ Also we study the global attractivity results via using Dulac function theory. Further, we also provide some information about the stability of the endemic and disease free equilibria for the considered model. In addition, we use nonstandard finite difference scheme to perform numerical simulation of the considered model via using Matlab. We provide different numerical plots for two different values of contact rate and taking various initial values for compartments involved in the considered model.

References

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