Modeling the Dynamics of the Coronavirus SARS-CoV-2 Pandemic using Modified SIR Model with the 'Damped-Oscillator' Dynamics of the Effective Reproduction Number

Abstract: The COVID-19 pandemic has been a great catastrophe that upended human lives and caused millions of deaths all over the world. The rapid spread of the virus, with its early-stage exponential growth and subsequent 'waves', caught many medical professionals and decision-makers unprepared. Even though epidemiological models have been known for almost a century (since the 'Spanish Influenza' pandemic of 1918-20), the real-life spread of the SARS-CoV-2 virus often confounded the modelers. While the general framework of epidemiological models like SEIR (susceptible-exposed-infected-recovered) or SIR (susceptible-exposed-infected) was not in question, the behavior of model parameters turned out to be unpredictable and complicated. In particular, while the 'basic' reproduction number, R0, can be considered a constant (for the original SARS-CoV-2 virus, prior to the emergence of variants, R0 is between 2.5 and 3.0), the 'effective' reproduction number, R(t), was a complex function of time, influenced by human behavior in response to the pandemic (e.g., masking, lockdowns, transition to remote work, etc.) To better understand these phenomena, we model the first year of the pandemic (between February 2020 and February 2021) for a number of localities (fifty US states, as well as several countries) using a simple SIR model. We show that the evolution of the pandemic can be described quite successfully by assuming that R(t) behaves in a 'viscoelastic' manner, as a sum of two or three 'damped oscillators' with different natural frequencies and damping coefficients. These oscillators likely correspond to different sub-populations having different reactions to proposed mitigation measures. The proposed approach can offer future data modelers new ways to fit the reproduction number evolution with time (as compared to the purely data-driven approaches most prevalent today).