For many years, ISE professor Carolyn Beck has been building mathematical models to predict how epidemics spread through populations, and her research has gained renewed relevance in the wake of the worldwide COVID-19 pandemic. Beck explains how epidemic models can inform policymaking and how her research improves their accuracy.

In this interview, she discusses an epidemic model she helped design that considers how networks of human interaction change over time. She collaborated on this research with Philip Paré, her former Ph.D. student, and Angelia Nedić, an Arizona State University engineering professor.

**Can you describe what an epidemic model is, and how your new network model differs from others that are used?**

We're looking at how infectious diseases and viruses propagate in a population. For a couple hundred years, modelers have used what they call compartment models, which for the simplest model say the population is divided into two groups: They're either susceptible, meaning they're healthy and susceptible to infection, or they're infected. There are also different simulation models that describe this process and tell you what proportion of the population will be susceptible or infected over time — or if you're talking about just an individual, the probability that they'll be infected or healthy. These models assume the population mixes evenly — that is, everyone interacts with everyone else roughly to the same extent.

But rather than assuming the population is mixing evenly, we're assuming that there's an underlying network structure that affects how these viral processes are distributed in the population. The compartment models assume everyone is interacting with everyone else equally, but the network models try to take into account the fact that we're not equally in contact with each other. In our models, we impose network structures on the population and then look at how different network structures affect how quickly people get infected and healthy, and whether they stay healthy.

I had a Ph.D. student, Philip Paré, who graduated about a year and a half ago, and this was the basis for his thesis work. He said, let's consider what happens if these networks themselves change over time. For example, during the week, we may be going to work and interacting with one group of people, but on the weekend, we may be interacting with a different group of people. So there's a time-varying nature to the network. Then he looked at what network structures will lead the population to converge to a healthy state, or alternatively converge to a state where we can't get rid of the disease.

**Can you give a couple examples of these networks?**

At the finest level, you can model human contact networks; that would be on the level of every single person. That would make it pretty hard to run a lot of simulations, due to the size of the population under consideration, but you might be able to do it for, say, small towns. Another level might be aggregated populations. You can aggregate at the household level, the neighborhood level, the city level, the state level, the country level, etc. Then you can look at these different levels to get multiscale models of the interconnections between the population groups. You can also take into account where people are commuting and how they're commuting, and that can change the network dynamics as well. So we try to capture some of these varying levels in our network models to look at how diseases are propagating in a larger population.

**Looking at your most recent research, what do you gain by creating a model that includes time-varying aspects, and what outcomes does it create?**

It's more precise. If you take into account traffic flow, that actually has a pretty prevalent effect in our society today since we're globally connected. If you take this into account, you realize that if a sick person gets on a plane in one country and lands in another country, it creates and opportunity for a virus to become pandemic quickly.

We're able to capture some of these effects and see what the results of them are. If you assume we're all mixing equally countrywide or worldwide, as in compartment models, then you're assuming we're all connected, but people typically aren’t. So the network models give us a more realistic way to understand how diseases are going to spread to other places and how fast they might spread. Then we can quantify the effects of our movements and over what timeframes these matter, and we can do this at a more precise level.

**What motivated you to study this? Why is it important to do epidemic modeling?**

After the first SARS epidemic epidemiologists started thinking more seriously about networks playing a role in disease transmission; that was in 2004. Interestingly, around the same time researchers studying computer virus propagation also started to consider network structure effects. We realized about 10 years later that no one was taking into account mobility, or any sort of time-varying nature in the networks, or thinking about including, for example, traffic flow, etc. So we thought we'd try to understand what happens when networks themselves are time-varying.

The reason we want to study this is to better understand what conditions we need to meet, as a society, for the disease to be eradicated or controlled. So if we think about quarantine, for example, or shelter-in-place rules, these things are localizing us to our own little individual groups. And it means that the strength of connection that we have to other small population groups becomes much weaker, which makes it harder for the disease to spread widely. So we think of this as a network in a mathematical sense with weak links, and we try to analyze the overall system mathematically to develop some concrete understanding as to just how isolated we need to be, and for how long, to control or eliminate the disease.

We can also look at the effect of treatments and how best to use them. For example, let's say we have a limited number of vaccines, then we can try to determine to what parts or members of the population would we all be best served by giving them a vaccine? And so we want to study how allocation of these types of resources is going to change the parameters in the system so that the diseases can be eradicated most quickly.

I**n the context of COVID-19, are these models being used to better understand the current pandemic, or is it in preparation for the next one?**

Yes, absolutely. Many researchers are using these types of models along with data to better understand COVID-19. We are looking at some data from Spain and some from China, and developing models in which the parameters are estimated from the data, so it’s somewhat naturally correct for this particular virus, and then we can use these to do simulations going forward for different hypothetical scenarios and use the results to suggest control policies. What we’ve looked at so far — what I will say is obvious, but it really is true — the stay-at-home, shelter-in-place policies are really helping to decrease the transmission and control the epidemic.

What we'll try to do going forward is see, when can we relax some of these policies? To what extent can we relax them? What will happen next if or when we do relax them?

**Is there anything else people might find helpful for understanding this strange time?**

It is worth listening to the medical and epidemiological experts. They've studied these problems for many years. They have built-up a lot of knowledge and experience. There are people who seem to discard what the experts have to say, but they are experts because they have spent a lot of time thinking about these types of problems and these types of processes. We should listen to what they have to say.