Using a modified version of the susceptible-infectious-recovered (SIR) model to include effects of prevention measures, researchers show patterns in the increase and decrease of coronavirus disease 2019 (COVID-19) cases in the UK.
The SIR model has been generally used to understand the transmission dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative pathogen of COVID-19. Although the model is simple and flexible, it has some limitations. It does not take into account any interventions, such as social distancing or mask-wearing. Furthermore, to determine if new virus variants are more transmissible, data for the entire outbreak should be included as well as preventive measures, which is not possible in the model.
Fitting data to a model that does not capture public health measures can lead to different reproductive rates for the same virus under different preventive measures. SIR modeling for the UK from September to December 2020 suggests much higher values for transmission and reproductive rate. But, the predictions are not very accurate as the model cannot fit the data for the entire time of the pandemic with its multiple waves and it cannot predict further waves. Thus, an alternative approach is needed for better prediction of COVID-19 cases.
Researchers from the Imperial College London, UK, report a modified model that can overcome the limitations of the SIR model. They have recently released their results on the medRxiv* preprint server.
Modifying model to include preventive measures
They used a model that includes population dynamics, with the population split into four groups: susceptible, infected, recovered, and vaccinated, where the groups followed a delayed dynamical system. They also included parameters for the effectiveness of preventive measures and the different waves in the number of cases.
This modified SIR model captures how the so-called ‘new normal’ of non-pharmaceutical interventions (NPIs) affects the number of infected people. This led to a constant transmission and reproductive rate for the entire pandemic, different from the varying values seen with the traditional SIR model.
Although there have been many mutant strains of the virus, the new UK strain B. 1.1.7 is reported to be significantly more transmissible, leading to an upsurge in the number of cases. However, for the UK, the modified model predicts an increased number of cases even without a virus variant with heightened transmissibility. Thus, it’s likely that the genomic data may have been overestimated.
The model includes characteristic parameters that could be crucial in the coming months. For example, “inertia of society” seems to play a role in flattening the curve. Preventive measures should be introduced early, taking into account this factor, which can lead to about a three-week delay until society becomes fully alert to the measures and follows them.
When the authors included the effect of vaccination, they found that social relaxation in March 2021 without completing a sufficient vaccination rate would lead to a surge of new cases from May to June 2021.
Insufficient number of vaccinations will cause a future surge
The unmodified SIR model fits the data for the initial days of the pandemic between March and June 2020, but does not predict any further waves. The modified SIR not only fits the data for the initial days of the pandemic well, but it also captures the decrease in the number of cases from mid-April to August 2020, caused by more “social awareness.”
The model further predicts the sudden increase in positive cases as society relaxes, as the decreasing trend is not because the pandemic has ended but because susceptible persons have been removed from the system. This happened between July and September 2020, leading to an increase in September 2020. The increasing cases led to another set of restrictions, but these were not enough to curb transmission, and another increase in cases appeared in December 2020 because of gradual relaxation in November 2020. Thus, the model accurately predicts transmission by including preventive measures implemented at different times.
Modeling the effects of vaccination and the third lockdown imposed in the UK in January 2021 indicates unless 200,000 vaccinations are performed per day, a fourth wave is unavoidable. Furthermore, the model predicts if less than 100,000 people are immunized per day, the next wave will be as severe as the previous ones.
The authors also analyzed the data for other European countries like Spain and Italy that were severely hit by the pandemic, and they found the same patterns as those in the UK. Thus, social relaxation generally for about two to three months causes a surge in the number of cases, followed by increased awareness and implementation of preventive measures, which leads to a decrease, and following the same pattern, a subsequent increase in the number of cases.
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.