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Two-strain epidemic model with two vaccinations and two time delayed

Author

Listed:
  • Bilgen Kaymakamzade

    (Near East University)

  • Evren Hincal

    (Near East University)

Abstract

In this paper, a delayed epidemic model consisting of two strains with vaccine for each strain is formulated. The model consist of four equilibrium points; disease free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 and R 2 are found, and we have shown that, if both are less than one, the disease dies out, if one of the ratios is less than one, epidemic occurs with respect to the other. It was also shown that, any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Condition for the existence of endemic equilibria was also given. Numerical simulations were carried out to support the analytic results and to show the effect of vaccine for strain 1 against strain 2 and the vaccine for strain 2 against strain 1. It is found that the population for infectives to strain 2 increases when vaccine for strain 1 is absent and viceversa.

Suggested Citation

  • Bilgen Kaymakamzade & Evren Hincal, 2018. "Two-strain epidemic model with two vaccinations and two time delayed," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 695-709, December.
    • Handle: RePEc:spr:qualqt:v:52:y:2018:i:1:d:10.1007_s11135-017-0647-8
    DOI: 10.1007/s11135-017-0647-8
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    References listed on IDEAS

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    1. Xu, Zhiting & Qu, Liangcheng & Huang, Yehui, 2016. "Global dynamics of a two-strain flu model with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 44-59.
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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. Hui Chen & Xuewen Tan & Jun Wang & Wenjie Qin & Wenhui Luo, 2023. "Stochastic Dynamics of a Virus Variant Epidemic Model with Double Inoculations," Mathematics, MDPI, vol. 11(7), pages 1-29, April.
    3. Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.
    4. Baba, Isa Abdullahi & Abdulkadir, Rabiu Aliyu & Esmaili, Parvaneh, 2020. "Analysis of tuberculosis model with saturated incidence rate and optimal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

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    1. Chen, Zhenwu & Xu, Zhiting, 2019. "A delayed diffusive influenza model with two-strain and two vaccinations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 439-453.
    2. 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).

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