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Modeling and analysis of an SI1I2R epidemic model with nonlinear incidence and general recovery functions of I1

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  • Thirthar, Ashraf Adnan
  • Naji, Raid Kamel
  • Bozkurt, Fatma
  • Yousef, Ali

Abstract

In this paper, we established a mathematical model of an SI1I2R epidemic disease with saturated incidence and general recovery functions of the first disease I1. Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that supported our theoretical findings.

Suggested Citation

  • Thirthar, Ashraf Adnan & Naji, Raid Kamel & Bozkurt, Fatma & Yousef, Ali, 2021. "Modeling and analysis of an SI1I2R epidemic model with nonlinear incidence and general recovery functions of I1," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921000990
    DOI: 10.1016/j.chaos.2021.110746
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    References listed on IDEAS

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    1. Yusuf, Abdullahi & Inc, Mustafa & Isa Aliyu, Aliyu & Baleanu, Dumitru, 2018. "Efficiency of the new fractional derivative with nonsingular Mittag-Leffler kernel to some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 220-226.
    2. Raid Kamel Naji & Reem Mudar Hussien, 2016. "The Dynamics of Epidemic Model with Two Types of Infectious Diseases and Vertical Transmission," Journal of Applied Mathematics, Hindawi, vol. 2016, pages 1-16, January.
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    Cited by:

    1. Huda Abdul Satar & Raid Kamel Naji, 2023. "A Mathematical Study for the Transmission of Coronavirus Disease," Mathematics, MDPI, vol. 11(10), pages 1-20, May.

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