Seasonal forcing and waning immunity drive the sub-annual periodicity of the COVID-19 epidemic

Seasonal trends in infectious diseases are shaped by climatic and social factors, with many respiratory viruses peaking in winter. However, the seasonality of COVID-19 remains in dispute, with significant waves of cases across the United States occurring in both winter and summer. Using wavelet analysis of COVID-19 cases, we find that the periodicity of epidemic COVID-19 varies markedly across the U.S. and correlates with winter temperatures, indicating seasonal forcing. However, seasonal forcing alone cannot explain the pattern of multiple waves per year that has been so disruptive and unique to COVID-19. Using a modified SIRS model that allows specification of the tempo of waning immunity, we show that specific forms of non-durable immunity can sufficiently explain the sub-annual waves characteristic of the COVID-19 epidemic.