Trajectory of SARS-CoV-2 vaccination and immunity examined in new model

The coronavirus disease 2019 (COVID-19) pandemic has proven especially difficult to model accurately. In the early days, as the disease first spread around the world, public health policies changed rapidly, and many models were based on parameters that were no longer correct even one week after creation.

As the disease progressed, and new lockdowns and changes in policy were introduced and stabilized,  the introduction of new variants forced models to be adapted even further, and when vaccines were finally developed the models needed to include both vaccination rates and rates of loss of immunity – which were contentious at first.

Study: Measuring the impact of COVID-19 vaccination and immunity waning: a modelling study for Portugal. Image Credit:

Researchers have created a model that takes all of these into account and can be adjusted as factors change.

A preprint version of the group’s study is available on the medRxiv* server, while the article undergoes peer review.

The study

The researchers previously created a simplified version of the age-structured SEIR model, in which individuals begin as susceptible (S), and upon contact with an infected individual change to become infected (I), and then can later recover (R). The model also takes into account differences in symptomatic and asymptomatic infection, with asymptomatic infections passing the disease on at a lower rate. All asymptomatic individuals are expected to recover, while symptomatic individuals can recover or enter hospital, and hospitalized individuals can either recover, die, or progress to the ICU.

ICU-admitted individuals can recover or die. The scientists added another branch to the model to assess the effect of vaccination. Susceptible and recovered individuals are vaccinated at a certain rate (Y), before being moved to an analogous compartment in the new ‘vaccine protected’ branch of the model.

The model even takes into account vaccine breakthrough infections, with susceptible individuals still retaining a small chance of becoming infected and an even smaller chance of becoming symptomatic. Otherwise, the vaccinated branch behaves the same as the non-vaccinated branch.

The researchers present simulations in which individuals are vaccinated per age-group, mimicking the vaccination program. They assumed that the vaccine protects an individual for a certain period post-vaccination, and age-groups were assigned a coverage proportional to their size. The duration of both vaccine-induced and infection-induced immunity were included in the model, and the scientists examined multiple different scenarios assuming different lengths of immunity. This model was fitted to ICU and non-ICU hospitalization data between January and September 2021, and changes in contacts due to non-pharmaceutical interventions were estimated and added to the model.

The reproduction number was estimated with and without non-pharmaceutical interventions (NPIs) in place, assuming a 47% reduction in effective contacts according to mask effectiveness studies.

The researchers showed that with no NPIs, the possibility of keeping the reproduction number (Rt) of the disease below one is only possible if the entire population above age 12 is vaccinated, vaccine effectivity is above 85%, and the Delta variant shows similar transmission dynamics as the original strain. Bear in mind that this study was begun before the Omicron variant began threatening to become the most dominant strain, and figures have likely changed since. With NPIs in place, an Rt below one could be achieved at any level of transmission.

The scientists also examined the results for vaccine protection duration scenarios and booster shots. Their scenario for a 1-year immunity duration results in a wave of non-ICU hospitalizations at the end of 2021 – but the peak of this can be reduced dramatically if all above 65 years old receive a booster shot. 3-year immunity scenarios show a smaller magnitude of new hospitalizations, and the booster shots to the elderly only reduce peak hospitalization by 38%. The scenario assuming no immunity is lost still results in a peak of hospitalization at the end of the year but at a much lower magnitude. This is the only scenario that does not result in ICU occupancy rising higher than acceptable limits by the end of 2021.

The authors highlight that their model enables the analysis of possible outcomes dependent on different NPIs, social activity, vaccine effectiveness and vaccine allocation, and is adjustable for the different mechanics of different variants.

As an array of different possible values can be considered for each of the parameters that they were investigating, this model is an excellent way to explore the consequences for changes in law and can easily be adjusted if new data comes to light on vaccine effectivity against new variants, or if vaccination rates change. This model could be invaluable for public health policymakers, healthcare administrators and epidemiologists, and should help provide information for future plans to combat the pandemic.

*Important notice

medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Journal reference:
  • Constantino Caetano, et al. (2021). Measuring the impact of COVID-19 vaccination and immunity waning: a modelling study for Portugal. medRxiv. doi:

Posted in: Medical Research News | Disease/Infection News | Healthcare News

Tags: Coronavirus, Coronavirus Disease COVID-19, Healthcare, Hospital, immunity, Pandemic, Public Health, Reproduction, SARS, SARS-CoV-2, Vaccine

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Written by

Sam Hancock

Sam completed his MSci in Genetics at the University of Nottingham in 2019, fuelled initially by an interest in genetic ageing. As part of his degree, he also investigated the role of rnh genes in originless replication in archaea.

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