A Mathematical Model of Epidemics—A Tutorial for Students
This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emph...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/7/1174 |
| _version_ | 1797562169235079168 |
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| author | Yutaka Okabe Akira Shudo |
| author_facet | Yutaka Okabe Akira Shudo |
| author_sort | Yutaka Okabe |
| collection | DOAJ |
| description | This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths. |
| first_indexed | 2024-03-10T18:24:38Z |
| format | Article |
| id | doaj.art-531526d3c4bf4a5ab6e2b4d8ae2f0f7f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:24:38Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-531526d3c4bf4a5ab6e2b4d8ae2f0f7f2023-11-20T07:04:28ZengMDPI AGMathematics2227-73902020-07-0187117410.3390/math8071174A Mathematical Model of Epidemics—A Tutorial for StudentsYutaka Okabe0Akira Shudo1Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, JapanDepartment of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, JapanThis is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.https://www.mdpi.com/2227-7390/8/7/1174SIR modelnumerical solutionexact solutionBernoulli differential equationAbel differential equation |
| spellingShingle | Yutaka Okabe Akira Shudo A Mathematical Model of Epidemics—A Tutorial for Students Mathematics SIR model numerical solution exact solution Bernoulli differential equation Abel differential equation |
| title | A Mathematical Model of Epidemics—A Tutorial for Students |
| title_full | A Mathematical Model of Epidemics—A Tutorial for Students |
| title_fullStr | A Mathematical Model of Epidemics—A Tutorial for Students |
| title_full_unstemmed | A Mathematical Model of Epidemics—A Tutorial for Students |
| title_short | A Mathematical Model of Epidemics—A Tutorial for Students |
| title_sort | mathematical model of epidemics a tutorial for students |
| topic | SIR model numerical solution exact solution Bernoulli differential equation Abel differential equation |
| url | https://www.mdpi.com/2227-7390/8/7/1174 |
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