Faculty Affiliate, ISSP
Full Professor, Department of Mathematics and Faculty of Medicine, uOttawa
On Thursday, February 25, the ISSP hosted Food for Thought: How modelling potential COVID-19 outcomes on campus helped uOttawa. This blog is an adaptation of the speaker’s remarks.
On January 22, 2020 Wuhan, China had 425 laboratory-confirmed cases of COVID-19. By February 16, there were 51,857 infections globally. When the World Health Organization declared a global pandemic on March 11, there were over 118,000 infections globally. The very next day, I was contacted by the uOttawa administration, who urgently needed some modelling to better understand their options for addressing the virus on campus. The administration wanted to know if they should do nothing, if they should do something, and if so, what? What combination of factors make for the best-case scenario? What makes for the worst-case scenario? What are the consequences for outbreak size and potential mortality on campus if we wait or if we’re proactive?
These are the exact types of questions that mathematical modelling can help with when time is short. Mathematical modelling has one great advantage: it's cheap. It’s also fast; you don't have to run clinical studies to get what you’re looking for. The trade-off is imperfect data and uncertainty. In March 2020, we still didn’t know much about the virus, so incorporating asymptomatic individuals in the model was a challenge. Did they even infect people? Today, of course, we know they do, but that was up in the air at the time. If so, how much less (or potentially even more) infectious could they be than people who are showing symptoms? What if they recover faster or slower? Without data, we need to make assumptions. The real question is whether these assumptions are reasonable or not. To compensate, we can run multiple scenarios to stress-test our assumptions. We can throw lots of questions at the problem, and the models can easily adapt to them.
In this type of modelling, there are variables and parameters. Variables are things that are always changing, such as the number of infections. Then there are parameters, which are constants that we may happen not to know, and which can be tweaked; for instance, the transmissibility of the virus or the level of social distancing. This is a subtle but importance difference. All of boxes in the figure below were our variables, and they're variables because they have derivatives. If it does not have a derivative, it's a parameter. In order to build a model, we combine the variables and parameters using a mechanistic understanding of the disease, based on the biology.
Here’s what we knew on March 12:
- About 17% of the infections were asymptomatic
- The death rate for low-risk groups was 0.2%
- Most, though not all, individuals on campus are very young, healthy people
Based on the above data, our assumption was that the uOttawa population was a healthy group. This presented a best-case scenario, since it didn’t address population outliers like professors over 70 or immune-compromised people. There is of course some heterogeneity among the campus population, but time was a constraint. This example shows the importance, ethically, of being clear about what these assumptions are so that anyone making decisions based on the modelling has as much information as possible. We also modelled the worst-case scenario, in which asymptomatic individuals spread the disease as much as symptomatic individuals; in reality we’ll always end up somewhere between the two extremes. Past epidemiological models for SARS, MERS, H1N1, and Ebola have been surprisingly accurate for the first wave (though less good at predicting second waves), so we had some strong evidence that this approach would be effective for COVID-19.
We ran several simulations to try and determine possible long-term outcomes without interventions like shutting down campus. In the worst-case scenario, without interventions, the model estimated that the first death would appear on campus about 115 days later, with a total of 6,000 cases and 63 deaths. In the long run, most people got infected. In the best-case scenario without interventions, the model showed 7,000 cases and 58 deaths. Cases actually went up in the best-case scenario because symptomatic individuals were actually transmitting more (to compensate for the lack of infections by asymptomatic people). But in either scenario, we would have had a disaster on our hands if we hadn’t done anything.
Modelling 50% contact reduction between people on campus produced fascinating results. There was talk at one point of going to 3-day weeks, which could serve as a rough approximation for this modelling scenario. With 50% contact reduction, the model showed cases dropping by more than a factor of 10 relative to no intervention, but still with 25 deaths (keep in mind the model assumed the population was all in the low-risk group). Basically, if you halve the contacts, you halve the deaths, but you cut cases by a factor of 10. The more we reduced contacts, the longer the pandemic lasted. With both interventions and reduced contact, the model shows we would not have seen the first death until day 1,850 of the pandemic, and just 5 deaths in total. Conversely, if we had done nothing, COVID-19 would have passed through and killed a lot of us, and we'd be out of it by now. Of course, we don't want it to kill people, so we’re weathering a longer pandemic with fewer deaths as a result.
I delivered the results from this modelling at 2:00am on March 13th. The next morning, uOttawa campus was shut down. It remains shut down, except for essential services such as labs that cannot be left unattended. The first case on campus eventually appeared on July 17, with no deaths to date.
There are also a few important limitations to this type of modelling that will constrain decision-makers. Most importantly, it represents a snapshot in time with limited data. It did not consider biodynamics, like mutations to the virus or changes in the population’s susceptibility to it. But even with the limited data we had, we were able to give clear answers to the specific questions the uOttawa administration had asked. Here we really see the value of models on a fast-moving ride. They can make predictions, and they can inform policy, particularly when people are brought in early on to build the models collaboratively from the ground up. It's not enough to just make a model, send it out into the world and hope that the right person sees it.
Since these results go straight to the interface between theoretical mathematics, numerical simulations, real-world data and human behavior, it really speaks to the need to integrate social scientists into this upfront work. When social scientists, biologists and mathematicians meet and co-develop, that’s where models can truly become a powerful, fast and effective tool for decision-making.