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A restricted epidemic SIR model with elementary solutions

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  • Turkyilmazoglu, Mustafa

Abstract

The mathematical epidemic SIR (Susceptible–Infected–Recovered) model is targeted to obtain full elementary solutions under restrictive assumptions in this paper. To achieve the aim, the traditional SIR model is modified in such a manner that the interaction between the susceptible and infected leading to new infected person takes place proportional to the susceptible square root and infected compartments, in place of the product of susceptible and infected class as in the classical model. First, equilibrium points of the new model are identified and their stability analysis is examined. Such a variant of the SIR model enables us to define a basic reproduction number in terms of the ratio of squares of infection and recovery rates. Elementary solutions of the model are next formed based on the simple hyperbolic functions. Solutions of this form are shown to be valid for a confined interval of basic reproduction number. Graphical illustrations are finally given for some selected epidemic parameters. The present analytical solutions can be used to test the accuracy of a number of numerical simulation methods being developed for various other SIR models recently being investigated.

Suggested Citation

  • Turkyilmazoglu, Mustafa, 2022. "A restricted epidemic SIR model with elementary solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    • Handle: RePEc:eee:phsmap:v:600:y:2022:i:c:s037843712200396x
    DOI: 10.1016/j.physa.2022.127570
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    References listed on IDEAS

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    1. Liu, Liya & Jiang, Daqing & Hayat, Tasawar, 2021. "Dynamics of an SIR epidemic model with varying population sizes and regime switching in a two patch setting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    2. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Wei, Wei & Xu, Wei & Song, Yi & Liu, Jiankang, 2021. "Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    5. Jang, Junyoung & Kwon, Hee-Dae & Lee, Jeehyun, 2020. "Optimal control problem of an SIR reaction–diffusion model with inequality constraints," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 136-151.
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    Cited by:

    1. Kaniadakis, G., 2024. "Novel class of susceptible–infectious–recovered models involving power-law interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).
    2. Saha, Sangeeta & Dutta, Protyusha & Samanta, Guruprasad, 2022. "Dynamical behavior of SIRS model incorporating government action and public response in presence of deterministic and fluctuating environments," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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