  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).
