Projecting the transmission dynamics of SARS-CoV-2 through the post-pandemic period

Stephen M Kissler; Christine Tedijanto; Edward Goldstein; Yonatan H. Grad; Marc Lipsitch

Next, we incorporated a third strain into the dynamic transmission model to represent SARS-CoV-2. Using the maximum likelihood parameter values, we simulated transmission of HCoV-OC43 and HCoV-HKU1 for 20 years and then simulated the establishment of sustained SARS-CoV-2 transmission using another half-week pulse in the force of infection. We assumed that the incubation period and infectious period for SARS-CoV-2 were the same as the best-fit values for the other betacoronaviruses (5.0 and 4.9 days, respectively; see Table S7 ), in broad agreement with other estimates (23) (24) (25) . We allowed the cross immunities, duration of immunity, degree of seasonal variation in R0, and establishment time of SARS-CoV-2 to vary. In particular, we allowed the cross immunity from SARS-CoV-2 to the other betacoronaviruses to range from 0 to 1, the cross immunity from the other betacoronaviruses to SARS-CoV-2 to range from 0 to 0.5 (following the observation that SARS infection can induce long-lasting neutralizing antibodies against HCoV-OC43 but not vice-versa (15)),the duration of immunity to SARS-CoV-2 to range from 40 weeks to permanent, the seasonal variation in R0 to vary between none and equivalent to the other human betacoronaviruses, and the establishment time to vary throughout 2020. To adjust the amount of seasonal variation in R0, we held the maximum wintertime value of the sinusoid fixed and adjusted the minimum summertime (baseline) value. This way, smaller degrees of seasonal forcing translated into smaller summertime declines in R0; for the no-seasonality scenario, R0 was therefore held fixed at its maximal wintertime value. This choice was informed by observations on the seasonal variation in R0 for influenza, for which the wintertime R0 was similar between geographic locations with distinct climates, while the summertime R0 varied substantially between locations (11) . For a representative set of parameter values within these ranges, we measured the annual incidence of infection due to SARS-CoV-2 and the annual SARS-CoV-2 outbreak peak size for the five years following the simulated time of establishment. We summarized the post-pandemic SARS-CoV-2 dynamics into the categories of annual outbreaks, biennial outbreaks, sporadic outbreaks, or virtual elimination.