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Global stability analysis of a two-strain epidemic model with non-monotone incidence rates

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  • Meskaf, Adil
  • Khyar, Omar
  • Danane, Jaouad
  • Allali, Karam

Abstract

In this paper, we study an epidemic model describing two strains with non-monotone incidence rates. The model consists of six ordinary differential equations illustrating the interaction between the susceptible, the exposed, the infected and the removed individuals. The system of equations has four equilibrium points, disease-free equilibrium, endemic equilibrium with respect to strain 1, endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of suitable Lyapunov functions. Two basic reproduction numbers R01 and R02 are found; we have shown that if both are less than one, the disease dies out. It was established that the global stability of each endemic equilibrium depends on both basic reproduction numbers and also on the strain inhibitory effect reproduction number(s) Rm and/or Rk. It was also shown that any strain with highest basic reproduction number will automatically dominate the other strain. Numerical simulations were carried out to support the analytic results and to show the effect of different problem parameters on the infection spread.

Suggested Citation

  • Meskaf, Adil & Khyar, Omar & Danane, Jaouad & Allali, Karam, 2020. "Global stability analysis of a two-strain epidemic model with non-monotone incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    • Handle: RePEc:eee:chsofr:v:133:y:2020:i:c:s0960077920300461
    DOI: 10.1016/j.chaos.2020.109647
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    References listed on IDEAS

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    1. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
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    Cited by:

    1. Farah, El Mehdi & Amine, Saida & Allali, Karam, 2021. "Dynamics of a time-delayed two-strain epidemic model with general incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    2. Gilberto Gonzalez-Parra & Abraham J. Arenas, 2021. "Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness," Mathematics, MDPI, vol. 9(13), pages 1-22, July.
    3. Han, Dun & Wang, Xiao, 2023. "Vaccination strategies and virulent mutation spread: A game theory study," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Wang, Chaoqian, 2020. "Dynamics of conflicting opinions considering rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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