Integrability properties and invariant solutions of some biological models

Navid Amiri Babaei, Gülden Gün Polat, Teoman Özer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


In this research, we deal with the biological population-related models called two-dimensional Easter Island, Verhulst, and Lotka–Volterra and four-dimensional MSEIR (M: Population, S: Suspected, E: Under Supervision, I: Infectious, R: Recovered) and SIRD (S: Suspected, I: Infectious, R: Recovered, D: Death) models by applying the artificial Hamiltonian method constructed for dynamical systems involving ordinary differential equations (ODEs) known as a partial Hamiltonian or nonstandard Hamiltonian system in the literature. This novel approach enables the investigation of the exact closed-form solutions to dynamical systems of first-order and second-order ODEs that can be written as a nonstandard Hamiltonian system by utilizing common methods feasible to the nonstandard Hamiltonian systems. The first integrals and associated invariant solutions of the aforementioned biological and population models for some cases under the constraint of system parameters via the artificial Hamiltonian method for not only two-dimensional but also four-dimensional nonlinear dynamical systems are considered. Additionally, graphs of all population fractions for the SIRD model that show how they change over time for the subcase are presented and discussed.

Original languageEnglish
Pages (from-to)3631-3650
Number of pages20
JournalMathematical Methods in the Applied Sciences
Issue number5
Publication statusPublished - 30 Mar 2024

Bibliographical note

Publisher Copyright:
© 2023 John Wiley & Sons, Ltd.


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.

FundersFunder number
Istanbul Teknik Üniversitesi


    • Integrability
    • Lie point symmetries
    • artificial Hamiltonian
    • biological models
    • epidemic models
    • first integrals
    • partial Hamiltonian


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