Mathematical models are being used by governments around the world to predict and respond to the spread of COVID-19.
The SMC asked experts to comment on the key data and assumptions which inform the development of COVID-19 modelling.
Professor Murray Cox, Te Pūnaha Matatini and Massey University, comments:
“Models play a central role in many scientific fields because they often provide the only way to explore alternative realities. What happens if we end the lockdown early? Or extend it? What happens if a few people ignore physical distancing? What if a lot of people ignore it? The usefulness of models is very clear in the current outbreak.
“Models can never show exactly how things will turn out, but the more information from the real world you can feed into them, the more accurate model predictions become. This is one reason why there has been such a strong call for much more community testing. Even if most tests come back negative (which of course is what we all hope for), how many uninfected versus infected people are out there is a critical part of the models. The level of community transmission, and how and where it is happening, are also crucial factors.
“Getting this information right makes predicting what might happen in the future more accurate. So the call for widespread community testing has two purposes: obviously to find people who are sick, but equally importantly to get key information for better evidence-based decision making. This close interplay between modelling and testing is perhaps not always appreciated.”
No conflict of interest.
Professor Michael Plank, Te Pūnaha Matatini and University of Canterbury, comments:
“Probably the biggest factor in a COVID model is what we call the basic reproduction number, which is the average number of people each infected person passes the virus on to. If this number is bigger than one, the chains of transmission grow exponentially and we will get an epidemic. But if the number is less than one, the number of cases declines over time, as we are currently seeing at Alert Level 4.
“Modellers need to try and quantify how much the different restrictions for New Zealand’s four Alert Levels reduce the reproduction number. The virus can only spread when two people come in close contact, so anything that reduces contacts between people reduces the reproduction number. By looking at what restrictions have been used in other countries and what happened to their case numbers as a result, we can start to piece together a model for their effect here. We can also use things like data on number of journeys or number of EFTPOS transactions to estimate how much of a reduction there has been in activities that lead to people coming into contact.
“Another big unknown is the proportion of people who spread COVID-19 without ever showing symptoms, because this makes it harder to trace and eliminate the virus. One thing models can do is look at a range of “what if…?” questions, like “what if 50% of COVID-19 carriers are asymptomatic?”, or “what if only 50% of people with symptoms go in for a test?”. There is always uncertainty but this approach can gives us an idea of best-case and worst-case scenarios for the weeks ahead.”
No conflict of interest.
Professor Mick Roberts, Massey University comments:
SEIR models
“A SEIR model is one in which the population is compartmentalised into those Susceptible to infection, those Exposed to infection (but not infectious), those Infectious and those Recovered.
“When a susceptible individual is in contact with an infectious individual there may be transmission of infection, and the S individual then progresses through E, I and R. The times spent in the E and I compartments can be inferred from clinical observations. The rate of infection transmission can be inferred from R0, the basic reproduction number – the average number of infections transmitted from a single infected individual when everybody is susceptible. The SEIR model may be solved on a computer, producing the now familiar epidemic curve. The value of R0 determines the proportion of the population that is infected throughout the epidemic, and reducing R0 flattens the epidemic curve.
“The SEIR model tracks infections, from which the burden of disease, hospitalisations, etc can be estimated. Interventions such as physical distancing and vaccination can be added to the model: physical distancing reduces R0 and vaccination reduces the size of the susceptible compartment.
“The SEIR model may be elaborated/complicated further, and there is a whole alphabet spaghetti of models in the literature. The basic structure imposes an unnatural distribution of residence times in each compartment – some may move on just after entering and others may linger for a long time. Further considerations include infectiousness before symptoms, a feature of COVID-19 requiring an extra compartment. There appears to be uncertainty over the proportion of those infected that show symptoms, and this has model implications. How infectious are those with mild or no symptoms compared to those clearly sick? Furthermore, do the sick tend to isolate themselves while the asymptomatic continue to contact others?
“When modelling small numbers of infected individuals, as we currently have in New Zealand, a stochastic model is required. This means that some uncertainty is involved, each time you run the model you get a different output. To make sense of that output you need to average over a number of model realisations. A stochastic model will be essential to explore the effects of contact tracing.”
International models
“The model developed by Te Pūnaha Matatini for the scenario of a COVID-19 epidemic in New Zealand follows the familiar SEIR format, but with an extra compartment for those pre-symptomatic but infectious, and one for those showing symptoms but no longer infectious.
“The Australian model, developed by a Melbourne-based consortium and published on the Peter Doherty Institute website has a similar SEIR structure, but with a parallel branch for those quarantined and therefore not contributing as much to transmission. Both models lead to similar outcomes.
“Another SEIR model has been released by Harvard T. H. Chan School of Public Health. This model is interesting because it addresses COVID-19 post-pandemic, its potential interaction with other coronaviruses, and explores the effects of physical distancing. Here the authors find that highly effective distancing could reduce the incidence of infection sufficiently to make contact tracing and quarantine feasible.”
No conflict of interest.