IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v170y2023ics0960077923003041.html
   My bibliography  Save this article

Threshold quantities and Lyapunov functions for ordinary differential equations epidemic models with mass action and standard incidence functions

Author

Listed:
  • Seidu, Baba
  • Makinde, Oluwole D.
  • Asamoah, Joshua Kiddy K.

Abstract

This paper presents a novel algebraic method for the construction of Lyapunov functions to study global stability of the disease-free equilibrium points of deterministic epidemic ordinary differential equation models with mass action and standard incidence functions. The method is named as Jacobian-Determinant method. In our method, a direct algebraic procedure that also relies only on determinant of the Jacobian matrix of the infected subsystem is developed to determine a threshold quantity, R0′ akin to the basic reproduction number, R0 of such class of models. The developed technique is applied on a wide variety of models to construct Lyapunov functions to study the global stability of the infection-free critical points. Further, implementation of our method reveals that the threshold quantity is the same as (or the square) of the basic reproduction numbers as obtained using the next-generation matrix method. It is further observed that even for models that do not use the standard or mass action incidence, the threshold quantity is still related to the basic reproduction numbers as obtained with the next-generation matrix method.

Suggested Citation

  • Seidu, Baba & Makinde, Oluwole D. & Asamoah, Joshua Kiddy K., 2023. "Threshold quantities and Lyapunov functions for ordinary differential equations epidemic models with mass action and standard incidence functions," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
  • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923003041
    DOI: 10.1016/j.chaos.2023.113403
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923003041
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.113403?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Okuonghae, D. & Omame, A., 2020. "Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Asamoah, Joshua Kiddy K. & Sun, Gui-Quan, 2023. "Fractional Caputo and sensitivity heat map for a gonorrhea transmission model in a sex structured population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohamed M. Mousa & Fahad Alsharari, 2021. "A Comparative Numerical Study and Stability Analysis for a Fractional-Order SIR Model of Childhood Diseases," Mathematics, MDPI, vol. 9(22), pages 1-12, November.
    2. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Ghanbari, Behzad, 2020. "On forecasting the spread of the COVID-19 in Iran: The second wave," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Mayra R Tocto-Erazo & Jorge A Espíndola-Zepeda & José A Montoya-Laos & Manuel A Acuña-Zegarra & Daniel Olmos-Liceaga & Pablo A Reyes-Castro & Gudelia Figueroa-Preciado, 2020. "Lockdown, relaxation, and acme period in COVID-19: A study of disease dynamics in Hermosillo, Sonora, Mexico," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-18, December.
    5. Kefan Xie & Benbu Liang & Maxim A. Dulebenets & Yanlan Mei, 2020. "The Impact of Risk Perception on Social Distancing during the COVID-19 Pandemic in China," IJERPH, MDPI, vol. 17(17), pages 1-17, August.
    6. Matouk, A.E., 2020. "Complex dynamics in susceptible-infected models for COVID-19 with multi-drug resistance," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Jinghan Yuan & Hansong Zou & Kefan Xie & Maxim A. Dulebenets, 2021. "An Assessment of Social Distancing Obedience Behavior during the COVID-19 Post-Epidemic Period in China: A Cross-Sectional Survey," Sustainability, MDPI, vol. 13(14), pages 1-16, July.
    8. Omame, A. & Abbas, M. & Onyenegecha, C.P., 2021. "A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    9. Okposo, Newton I. & Adewole, Matthew O. & Okposo, Emamuzo N. & Ojarikre, Herietta I. & Abdullah, Farah A., 2021. "A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Çaparoğlu, Ömer Faruk & Ok, Yeşim & Tutam, Mahmut, 2021. "To restrict or not to restrict? Use of artificial neural network to evaluate the effectiveness of mitigation policies: A case study of Turkey," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    11. Jiajia Li & Shiyu Yang & Changju Chen & Houjian Li, 2022. "The Impacts of COVID-19 on Distance Education with the Application of Traditional and Digital Appliances: Evidence from 60 Developing Countries," IJERPH, MDPI, vol. 19(11), pages 1-19, May.
    12. Omame, Andrew & Abbas, Mujahid, 2023. "Modeling SARS-CoV-2 and HBV co-dynamics with optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923003041. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.