Theoretical analysis of a SIRD model with constant amount of alive population and COVID-19 applications

Navid Amiri Babaei, Martin Kröger, Teoman Özer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This study deals with a theoretical analysis of the integrability properties and analytical solutions of an initial-value problem for a SIRD model with a constant amount of alive population (SIRD-CAAP), which is in the form of a fourth-dimensional and first-order coupled system of nonlinear ordinary differential equations, by using the partial Hamiltonian method. This research represents a COVID-19 study as a real-world problem by using the analytical results obtained in the study. The first integrals and the associated exact analytical solutions are investigated of the model with respect to algebraic relations among the model parameters. Then, for both cases, the dynamical behaviors of the model based on the analytical solutions are analyzed, and the graphical representations of the closed-form solutions are demonstrated and compared. In addition, it is shown that the SIRD-CAAP model can be decoupled based on its first integrals for all cases from the mathematical perspective point of view. Furthermore, the periodicity properties and the classification of the regimes of the solutions with respect to the model parameter constraints are discussed. Finally, the COVID-19 applications are given using the data related to the different countries.

Original languageEnglish
Pages (from-to)237-258
Number of pages22
JournalApplied Mathematical Modelling
Publication statusPublished - Mar 2024

Bibliographical note

Publisher Copyright:
© 2023 Elsevier Inc.


This work was supported by the research fund of the Istanbul Technical University , Project Number: MDK-2021-42911 for the Ph.D. Thesis of Navid Amiri Babaei. The following URL has been used to get information and data on the COVID-19 pandemic: .

FundersFunder number
Istanbul Teknik ÜniversitesiMDK-2021-42911


    • Analytical solutions
    • Artificial Hamiltonian
    • COVID-19
    • Decoupling
    • Epidemic models
    • First integrals
    • Lie groups
    • SIRD-model


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