Dynamics of SARS-CoV-2 with waning immunity in the UK population

Abstract

The dynamics of immunity are crucial to understanding the long-term patterns of the SARS-CoV-2 pandemic. Several cases of reinfection with SARS-CoV-2 have been documented 48–142 days after the initial infection and immunity to seasonal circulating coronaviruses is estimated to be shorter than 1 year. Using an age-structured, deterministic model, we explore 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-hospitalized individuals, a year for hospitalized individuals, and the effective reproduction number after lockdown ends is 1.2 (our worst-case scenario), we find that the secondary peak occurs in winter 2020 with a daily maximum of 387 000 infectious individuals and 125 000 daily new cases; threefold greater than in a scenario with permanent immunity. Our models suggest 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 in June 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 wave. 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 as immunity to reinfection is not permanent. This article is part of the theme issue ‘Modelling that shaped the early COVID-19 pandemic response in the UK’.

Epidemic interventions: insights from classic results

“…These results are qualitatively robust to different assumptions on how the immunity has come about, but we know that different dynamics can arise depending on the duration of immunity [10], and how acquisition of immunity is correlated with transmission [11]. The sensitivity to the reproduction ratio is similar to that described in §4, above.…”

“…B 376: 20200263 this paper is based [3]. Later in the year the need for additional lockdowns, this time in the presence of immunity required additional consideration and some detailed modelling [10], and once again the approximations in this article helped communicate the dynamics of the epidemic in response to such interventions.…”

Modelling that shaped the early COVID-19 pandemic response in the UK

“…There are time-sensitive, changing policy questions, such as the impact of mass gatherings [38], reopening schools in May 2020 [39][40][41], the introduction of support bubbles [42] or the impact of contact tracing and lockdown [43]. We have evidence that drove the understanding of nosocomial and care home transmission [44,45], the importance of segmenting and shielding [46] as well as the possible impact of waning immunity [47]. The breadth of these topics reflects the experience of the modelling community involved in the response in the UK.…”

A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

“…Models developed by Xu, Wu, and Topcu (2021), Ghostine et al (2021), Wintachai andPrathom (2021), andAntonini, Calandrini, andBianconi (2021) are age-homogeneous. In the early stages of the pandemic in the UK, Crellen et al (2021) used an SEIR model to investigate the e↵ect of di↵erent mean durations of immunity (90-365 days), on short-term dynamics and long-term endemic behaviour, in an age-based model, in the absence of vaccination, under various assumptions about the time-varying e↵ective reproduction number. In Xu, Wu, and Topcu (2021), the authors consider a short-term SEIR model over 200 days, that optimises vaccination roll-out, subject to thresholds on death rates, cumulative deaths, and target numbers of those vaccinated.…”