Herd immunity of Covid 19 in dynamic environments with vaccination: a model based study

DOI: https://doi.org/10.21203/rs.3.rs-136268/v1



The first wave of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in Canada is entering the last stage, while the development of vaccine is still ongoing. A thorough analysis on the potential effect of restoring to the normal life was needed.


We used an infectious disease model which optimized for individual immunity to investigate the potential impact of the vaccine on the number of cases, ℛ𝑡, and the duration of the epidemic. We modeled the severity of the cases with three intervention measures and the effect of herd immunity. The combined intervention strategies with the vaccination, speed of vaccination, and the proportion of population pre-vaccinated before reopening were modeled to give an overview of the effect of the vaccination. For each simulation, we set the observation range to be from Feb, 2020 to Oct. 2021, and modeled the number of cases after the first wave, the change of reproduction number (ℛ𝑡), and the proportion of immunized population under the effect of waning immunity.


We found the proportion of immunized population to reach herd immunity in a dynamic environment to be between 1−1ℛ0and 1−1ℛ02; for Covid-19, the threshold proportion is 64·16%, the final proportion of infections could be up to 87·15% when basic reproduction number (ℛ0) is 2·79. The average number of cases predicted in Canada after the first wave was 285590, 90260, 163057, and 60082 with no intervention, social distancing, quarantining severe cases, and combined strategies; 122261, 89903, 49276, 39856, and 10983 cases with 0·1%, 0·2%, 0·3%, 0·4%, and 1·0% of the population vaccinated per day; 117475, 93502, 91634, 79418, and 8713 cases with 10%, 20%, 30%, 40%, and 50% of population immunized before reopening. Assuming the half-life of the effectivity of the antibody is 48 weeks for symptomatic cases, 24 weeks for asymptomatic cases.


Neither of these strategies cannot prevent the second wave solely nor together. However, the third wave can be prevented with both social distancing and quarantining severe cases in practice. The speed and timing of vaccination has a direct impact on the reduction of the final number of cases. Unexpectedly, the proportion of population immunized before reopening did not lead to a huge shift of the number of cases after the first wave when the immunized proportion is lower than the critical proportion (49·6%) when social distancing is in practice.

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