Applying the SIR Model of Epidemics to the Covid-19 Pandemic
Source: https://www.medrxiv.org/content/10.1101/2020.05.26.20114058v3.full.pdf
While we are still living through the Covid-19 pandemic, understanding the characteristics of the disease is central to developing control strategies. As the pandemic progresses and more data is released, epidemiologists will be able to develop accurate and thorough models of the virus’s spread. In the meantime, containing the virus is crucial to inform decision-making for many governments across the world. To slow infection rates, governments have taken significant measures. The spread of the disease is dependent on R0, or the basic reproductive number of the disease. It is the expected number of new cases of the disease caused by a single individual. This measure consists of two components: p, the probability that the disease infects and k, the number of new people that an infected person comes into contact with. As a result, efforts to slow the infection rate have targeted these two characteristics. To reduce p, governments have encouraged better sanitation practices. To reduce k, governments have supported or even forced social distancing, quarantining, identifying, tracking, and isolating. However, there is no uniform policy, and some governments have reacted later than others. Also, some governments have made a deliberate decision to keep the country open and leave counter-measures up to individuals.
To assess the different governmental responses, researchers in the paper Analysis of Covid-19 Data for Eight European Countries and the United Kingdom Using a Simplified SIR Model attempt to model the Covid-19 pandemic. They use a simplified version of the SIR model. This article has been published in MedRxiv without peer review because of the urgency and relevance of this issue. Using the SIR model, the researchers partitions the population into three compartments: Susceptible (S), Infectious (I) and Removed (R). A susceptible individual is capable of getting the virus but, at the specific time, does not have it. An infectious individual has the virus and is capable of spreading it to susceptible individuals. A removed individual has either recovered from the disease or died after being infected. By looking at the first peak of the virus that happened over the summer, the researchers predict how long the pandemic will last if a government were to maintain its Covid-19 restrictions after the peak. Using data from an EU agency established in 2005 aimed to strengthen Europe’s defense against infectious disease, the researchers analyze eight countries: Netherlands, Denmark, Sweden, Norway, United Kingdom, Spain, Germany, France, and Italy. Because of the lack of thorough data, the researchers must rely on a simplified SIR model. This model strictly relies on the proportions of the populations that belong to the three compartments.
Using their model, the researchers predict when different countries would be able to end the pandemic within their population. The researchers define the end of the pandemic as less than five cases per day in the country. This model differentiates itself from other studies done because of its rigorous identification of parameters and by making a number of useful predictions very easily. These useful predictions include the duration of the pandemic in different countries. Of the eight countries studied, Italy was estimated to end the pandemic among its population the slowest. According to the model, if Italy had continued its measures to control the virus after the initial peak, the virus would still persist for more than 250 days after the first day of a documented case. According to the model, Norway was the only country that could end its pandemic within 200 days if it had continued its restrictions after the first peak. While the model generally tracks, countries like the United Kingdom and Spain both relaxed its restriction during the first peak. As a result, the results for these countries were inaccurate. According to the researchers, differences in getting over the first peak speaks to the efficiency of the healthcare systems in these different countries. The researchers suggest that countries like Norway were more successful than countries like Italy because of the competence and professionalism of healthcare workers. After creating the model, the researchers predict that only Norway would have been able to end the pandemic among its population within 200 days of its first case.
Another important implication of the study is that this model rests on the assumption that countries would continue their efforts to control the spread after the first peak. Of course, all the countries relaxed their restrictions after the first peak, and most have seen peaks even higher than the first one. These results suggest that, despite strong early efforts, there was poor success in limiting the spread after the first peak. These measures aimed at reducing p and k are extremely important to reducing the spread of the virus. With them, it would have still taken almost an entire year to stop the spread of the virus. Without them, the virus is free to spread as long as a vaccine is unavailable.
This implication of the study should inform Cornell’s Covid-19 policy going forward. With vaccinations hopefully around the corner, more and more people will continue to call for the relaxation of restrictions. However, problems with distribution and effectiveness are certain to slow the dissemination of the vaccine. While the first peak may seem to have passed, relaxing these restrictions have allowed for much worse numbers than before. As we hopefully approach the light at the end of the tunnel, Cornell administrators and students must not fumble. Even if the government relaxes restrictions, those who can manage them must persist, or the virus will spike right back up. Otherwise, until a vaccination is fully delivered to everyone, the pandemic will persist.
This figure shows the model’s prediction for Norway in the red line. X2 on the Y-axis is cases per day. The X-axis measures the number of days since the first documented case. As we see by the blue circles on the graph, the prediction did not hold as countries relaxed their Covid-19 restrictions and quarantines.