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

Dynamic transmission model. We implemented a two-strain ordinary differential equation (ODE) susceptible-exposed-infectious-recovered (SEIR) compartmental model to describe the transmission dynamics of HCoV-OC43 ('strain 1') and HCoV-HKU1 ('strain 2') in the United States. Exposed individuals became infectious at rate ν and infectious individuals recovered at rate γ. Immunity waned at rates σ1 and σ2 for HCoV-OC43 and HCoV-HKU1, respectively. The basic reproduction number, R0, was assumed to be seasonal with a period of 52 weeks, specified by the equation where a is the amplitude of the seasonal forcing term, b is the minimum value, and Φ is the phase shift in weeks. The transmission rate β(t) is related to the basic reproduction number by the formula (11) Cross immunity of HCoV-OC43 against HCoV-HKU1 was captured by χ1,2 such that the transmission rate of HCoV-HKU1 to an individual who is exposed to, infected with, or recovered from HCoV-OC43 was reduced by a factor of 1-χ1,2, and vice-versa. Individuals died at rate μ such that the average lifespan was 1/μ = 80 years. Fully-susceptible individuals were born at the same rate μ to keep the population size constant. A schematic of the model structure is depicted in Fig S3. The entire population was assumed to be susceptible at the start of the simulation period Table 1 .