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SIRSi compartmental model for COVID-19 pandemic with immunity loss

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  • Batistela, Cristiane M.
  • Correa, Diego P.F.
  • Bueno, Átila M
  • Piqueira, José Roberto C.

Abstract

The coronavirus disease 2019 (Covid-19) outbreak led the world to an unprecedented health and economic crisis. In an attempt to respond to this emergency, researchers worldwide are intensively studying the dynamics of the Covid-19 pandemic. In this study, a Susceptible - Infected - Removed - Sick (SIRSi) compartmental model is proposed, which is a modification of the classical Susceptible - Infected - Removed (SIR) model. The proposed model considers the possibility of unreported or asymptomatic cases, and differences in the immunity within a population, i.e., the possibility that the acquired immunity may be temporary, which occurs when adopting one of the parameters (γ) other than zero. Local asymptotic stability and endemic equilibrium conditions are proved for the proposed model. The model is adjusted to the data from three major cities of the state of São Paulo in Brazil, namely, São Paulo, Santos, and Campinas, providing estimations of duration and peaks related to the disease propagation. This study reveals that temporary immunity favors a second wave of infection and it depends on the time interval for a recovered person to be susceptible again. It also indicates the possibility that a greater number of patients would get infected with decreased time for reinfection.

Suggested Citation

  • Batistela, Cristiane M. & Correa, Diego P.F. & Bueno, Átila M & Piqueira, José Roberto C., 2021. "SIRSi compartmental model for COVID-19 pandemic with immunity loss," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307827
    DOI: 10.1016/j.chaos.2020.110388
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    References listed on IDEAS

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    Cited by:

    1. Tu, Yunbo & Meng, Xinzhu & Alzahrani, Abdullah Khames & Zhang, Tonghua, 2023. "Multi-objective optimization and nonlinear dynamics for sub-healthy COVID-19 epidemic model subject to self-diffusion and cross-diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Giovanni Dieguez & Cristiane Batistela & José R. C. Piqueira, 2023. "Controlling COVID-19 Spreading: A Three-Level Algorithm," Mathematics, MDPI, vol. 11(17), pages 1-39, September.
    3. Bimal Kumar Mishra, 2022. "Stochastic models on the transmission of novel COVID-19," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 599-603, April.
    4. Erdoğan, Güneş & Yücel, Eda & Kiavash, Parinaz & Salman, F. Sibel, 2024. "Fair and effective vaccine allocation during a pandemic," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    5. Grass, D. & Wrzaczek, S. & Caulkins, J.P. & Feichtinger, G. & Hartl, R.F. & Kort, P.M. & Kuhn, M. & Prskawetz, A. & Sanchez-Romero, M. & Seidl, A., 2024. "Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses," Theoretical Population Biology, Elsevier, vol. 156(C), pages 46-65.
    6. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.
    7. Tri Nguyen-Huu & Pierre Auger & Ali Moussaoui, 2023. "On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect," Mathematics, MDPI, vol. 11(13), pages 1-25, June.

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