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

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  • 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
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    References listed on IDEAS

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    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.
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    4. 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.
    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.
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