Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model
An exact solution of an initial value problem for the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model is derived, and various properties of the exact solution are obtained. It is shown that the parametric form of the exact solution satisfies some linear differential system...
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| Format: | Article |
| Language: | English |
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University of Szeged
2024-01-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10599 |
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| author | Norio Yoshida |
| author_facet | Norio Yoshida |
| author_sort | Norio Yoshida |
| collection | DOAJ |
| description | An exact solution of an initial value problem for the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model is derived, and various properties of the exact solution are obtained. It is shown that the parametric form of the exact solution satisfies some linear differential system including a positive solution of an Abel differential equation of the second kind. In this paper Abel differential equations play an important role in establishing the exact solution of the SEIRD differential system, in particular the number of infected individuals can be represented in a simple form by using a positive solution of an initial value problem for an Abel differential equation. Uniqueness of positive solutions of an initial value problem to SEIRD differential system is also investigated, and it is shown that the exact solution is a unique solution in the class of positive solutions. |
| format | Article |
| id | doaj-art-a1c5c67bc03e4c19b86bcc38050b7b84 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-a1c5c67bc03e4c19b86bcc38050b7b842025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-01-012024813710.14232/ejqtde.2024.1.810599Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic modelNorio Yoshida0https://orcid.org/0000-0001-8696-3040University of Toyama, Toyama, JapanAn exact solution of an initial value problem for the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model is derived, and various properties of the exact solution are obtained. It is shown that the parametric form of the exact solution satisfies some linear differential system including a positive solution of an Abel differential equation of the second kind. In this paper Abel differential equations play an important role in establishing the exact solution of the SEIRD differential system, in particular the number of infected individuals can be represented in a simple form by using a positive solution of an initial value problem for an Abel differential equation. Uniqueness of positive solutions of an initial value problem to SEIRD differential system is also investigated, and it is shown that the exact solution is a unique solution in the class of positive solutions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10599exact solutionseird epidemic modelinitial value problemlinear differential systemabel differential equationuniqueness of positive solutions |
| spellingShingle | Norio Yoshida Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model Electronic Journal of Qualitative Theory of Differential Equations exact solution seird epidemic model initial value problem linear differential system abel differential equation uniqueness of positive solutions |
| title | Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model |
| title_full | Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model |
| title_fullStr | Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model |
| title_full_unstemmed | Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model |
| title_short | Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model |
| title_sort | exact solution of the susceptible exposed infectious recovered deceased seird epidemic model |
| topic | exact solution seird epidemic model initial value problem linear differential system abel differential equation uniqueness of positive solutions |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10599 |
| work_keys_str_mv | AT norioyoshida exactsolutionofthesusceptibleexposedinfectiousrecovereddeceasedseirdepidemicmodel |