Mathematical Modeling of Periodic Outbreaks with Waning Immunity: A Possible Long-Term Description of COVID-19

Alex Viguerie, Margherita Carletti (), Guido Silvestri and Alessandro Veneziani
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Alex Viguerie: Division of Mathematics, Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L’Aquila, AQ, Italy
Margherita Carletti: Department of Pure and Applied Sciences, University of Urbino C. Bo, Piazza della Repubblica 13, 61029 Urbino, PU, Italy
Guido Silvestri: Department of Pathology and Laboratory Medicine, Emory University School of Medicine, Atlanta, GA 30322, USA
Alessandro Veneziani: Department of Mathematics, Emory University, 400 Dowman Drive NE, Atlanta, GA 30322, USA

Mathematics, 2023, vol. 11, issue 24, 1-15

Abstract: The COVID-19 pandemic is still ongoing, even if the emergency is over, and we now have enough data to analyze the outbreak over a long timeline. There is evidence that the outbreak alternates periods of high and low infections. Retrospectively, this can help in understanding the nature of an appropriate mathematical model for this dramatic infection. The periodic behavior may be the consequence of time-dependent coefficients related to seasonal effects and specific political actions, or an intrinsic feature of the model. The present paper relies on the assumption that the periodic spikes are an intrinsic feature of the disease, and, as such, it should be properly reflected in the mathematical model. Based on the concept of waning immunity proposed for other pathologies, we introduce a new model with (i) a compartment for weakly immune people subject to immunity booster, represented by a non-linear term; (ii) discrimination between individuals infected/vaccinated for the first time, and individuals already infected/vaccinated, undergoing to new infections/doses. We analyze some preliminary properties of our model, called SIRW2, and provide a proof-of-concept that it is capable of reproducing qualitatively the long-term oscillatory behavior of COVID-19 infection.

Keywords: modeling of infectious diseases; limit cycle; COVID-19 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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