IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921009917.html
   My bibliography  Save this article

Analysis and simulation of a two-strain disease model with nonlinear incidence

Author

Listed:
  • Kuddus, Md Abdul
  • McBryde, Emma S.
  • Adekunle, Adeshina I.
  • Meehan, Michael T.

Abstract

We analysed and simulated a two-strain Susceptible-Infected-Recovered (SIR) disease model with varying population size and nonlinear incidence. We found that in addition to the infection-free and two single-strain endemic equilibria, the non-linear incidence term induces a fourth equilibrium point where the two strains co-exist. We determined the conditions for the existence and stability of each of the four equilibrium points, and showed that these depend on both the traditional basic reproduction numbers (R0) of each strain and a set of generalized threshold parameters (ψand γ). In particular, we used appropriate Lyapunov functions to show that these generalized quantities define strict boundaries that separate regions of parameter space in which each of the equilibrium points are unstable or globally asymptotically stable. Further, we used sensitivity analysis and the Partial Rank Correlation Coefficient (PRCC) method to identify the most influential model parameters on transmission and disease prevalence, finding that the contact rate of both strains had the largest influence on both. Finally, numerical simulations were carried out to support the analytic results.

Suggested Citation

  • Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & Meehan, Michael T., 2022. "Analysis and simulation of a two-strain disease model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921009917
    DOI: 10.1016/j.chaos.2021.111637
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009917
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111637?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. Qianqian Li & Shengshan Cao & Xiao Chen & Guiquan Sun & Yunxi Liu & Zhongwei Jia, 2012. "Stability Analysis of an HIV/AIDS Dynamics Model with Drug Resistance," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, December.
    2. Ullah, Saif & Khan, Muhammad Altaf & Farooq, Muhammad & Gul, Taza, 2019. "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 181-199.
    3. Md Abdul Kuddus & Michael T Meehan & Lisa J White & Emma S McBryde & Adeshina I Adekunle, 2020. "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-26, July.
    4. Li, Xue-Zhi & Li, Wen-Sheng & Ghosh, Mini, 2009. "Stability and bifurcation of an SIS epidemic model with treatment," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2822-2832.
    5. Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & White, Lisa J. & Meehan, Michael T., 2021. "Mathematical analysis of a two-strain disease model with amplification," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Sara Bidah & Omar Zakary & Mostafa Rachik, 2020. "Stability and Global Sensitivity Analysis for an Agree-Disagree Model: Partial Rank Correlation Coefficient and Latin Hypercube Sampling Methods," International Journal of Differential Equations, Hindawi, vol. 2020, pages 1-14, April.
    Full references (including those not matched with items on IDEAS)

    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. Liu, Yue, 2022. "Extinction, persistence and density function analysis of a stochastic two-strain disease model with drug resistance mutation," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    2. Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & White, Lisa J. & Meehan, Michael T., 2021. "Mathematical analysis of a two-strain disease model with amplification," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
    4. Fatima Sulayman & Farah Aini Abdullah & Mohd Hafiz Mohd, 2021. "An SVEIRE Model of Tuberculosis to Assess the Effect of an Imperfect Vaccine and Other Exogenous Factors," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    5. Misra, A.K. & Mishra, S.N. & Pathak, A.L. & Srivastava, P.K. & Chandra, Peeyush, 2013. "A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 41-53.
    6. Yongxue Chen & Hui Zhang & Jingyu Wang & Cheng Li & Ning Yi & Yongxian Wen, 2022. "Analyzing an Epidemic of Human Infections with Two Strains of Zoonotic Virus," Mathematics, MDPI, vol. 10(7), pages 1-27, March.
    7. Srivastav, Akhil Kumar & Ghosh, Mini, 2019. "Assessing the impact of treatment on the dynamics of dengue fever: A case study of India," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    8. Ren, Jianguo & Yang, Xiaofan & Yang, Lu-Xing & Xu, Yonghong & Yang, Fanzhou, 2012. "A delayed computer virus propagation model and its dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 74-79.
    9. Qureshi, Sania, 2020. "Periodic dynamics of rubella epidemic under standard and fractional Caputo operator with real data from Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 151-165.
    10. Md Abdul Kuddus & Michael T Meehan & Lisa J White & Emma S McBryde & Adeshina I Adekunle, 2020. "Modeling drug-resistant tuberculosis amplification rates and intervention strategies in Bangladesh," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-26, July.
    11. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    12. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.

    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:155:y:2022:i:c:s0960077921009917. 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.