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...

Full description

Saved in:
Bibliographic Details
Main Author: Norio Yoshida
Format: Article
Language:English
Published: University of Szeged 2024-01-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=10599
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1846091028895891456
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&paramtipus_ertek=publication&param_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&paramtipus_ertek=publication&param_ertek=10599
work_keys_str_mv AT norioyoshida exactsolutionofthesusceptibleexposedinfectiousrecovereddeceasedseirdepidemicmodel