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The dynamics of immunity are crucial to understanding the long-term patterns of the SARS-CoV-2 pandemic. While the duration and strength of immunity to SARS-CoV-2 is currently unknown, specific antibody titres to related coronaviruses SARS-CoV and MERS-CoV have been shown to wane in recovered individuals, and immunity to seasonal circulating coronaviruses is estimated to be shorter than one year. Using an age-structured, deterministic model, we explore different potential immunity dynamics using contact data from the UK population. In the scenario where immunity to SARS-CoV-2 lasts an average of three months for non-hospitalised individuals, a year for hospitalised individuals, and the effective reproduction number ( R t ) after lockdown is 1.2 (our worst case scenario), we find that the secondary peak occurs in winter 2020 with a daily maximum of 409,000 infectious individuals; almost three-fold greater than in a scenario with permanent immunity. Our models suggests that longitudinal serological surveys to determine if immunity in the population is waning will be most informative when sampling takes place from the end of the lockdown until autumn 2020. After this period, the proportion of the population with antibodies to SARS-CoV-2 is expected to increase due to the secondary peak. Overall, our analysis presents considerations for policy makers on the longer term dynamics of SARS-CoV-2 in the UK and suggests that strategies designed to achieve herd immunity may lead to repeated waves of infection if immunity to re-infection is not permanent.

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