Mathematical study of SIR epidemic model under convex incidence rate
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 num...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020483/fulltext.html |
| _version_ | 1828943575994335232 |
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| author | Rahim ud Din Kamal Shah Manar A. Alqudah Thabet Abdeljawad Fahd Jarad |
| author_facet | Rahim ud Din Kamal Shah Manar A. Alqudah Thabet Abdeljawad Fahd Jarad |
| author_sort | Rahim ud Din |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T04:17:40Z |
| format | Article |
| id | doaj.art-022e071a4a2b46ea960fb296b28558dd |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-14T04:17:40Z |
| publishDate | 2020-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-022e071a4a2b46ea960fb296b28558dd2022-12-21T23:17:29ZengAIMS PressAIMS Mathematics2473-69882020-09-01567548756110.3934/math.2020483Mathematical study of SIR epidemic model under convex incidence rateRahim ud Din0Kamal Shah1Manar A. Alqudah2Thabet Abdeljawad3Fahd Jarad41 Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan1 Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan2 Department of Mathematical Sciences, Faculty of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia3 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, Taiwan6 Department of Mathematics, Çankaya University, Ankara, TurkeyIn 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.https://www.aimspress.com/article/10.3934/math.2020483/fulltext.htmlconvex incidence rateused dulac functionglobal analysissir modelreproductive number |
| spellingShingle | Rahim ud Din Kamal Shah Manar A. Alqudah Thabet Abdeljawad Fahd Jarad Mathematical study of SIR epidemic model under convex incidence rate AIMS Mathematics convex incidence rate used dulac function global analysis sir model reproductive number |
| title | Mathematical study of SIR epidemic model under convex incidence rate |
| title_full | Mathematical study of SIR epidemic model under convex incidence rate |
| title_fullStr | Mathematical study of SIR epidemic model under convex incidence rate |
| title_full_unstemmed | Mathematical study of SIR epidemic model under convex incidence rate |
| title_short | Mathematical study of SIR epidemic model under convex incidence rate |
| title_sort | mathematical study of sir epidemic model under convex incidence rate |
| topic | convex incidence rate used dulac function global analysis sir model reproductive number |
| url | https://www.aimspress.com/article/10.3934/math.2020483/fulltext.html |
| work_keys_str_mv | AT rahimuddin mathematicalstudyofsirepidemicmodelunderconvexincidencerate AT kamalshah mathematicalstudyofsirepidemicmodelunderconvexincidencerate AT manaraalqudah mathematicalstudyofsirepidemicmodelunderconvexincidencerate AT thabetabdeljawad mathematicalstudyofsirepidemicmodelunderconvexincidencerate AT fahdjarad mathematicalstudyofsirepidemicmodelunderconvexincidencerate |