Thinking Inside the Box: The Role of a Simple Compartmental Model in Planning for – and Preventing – Epidemics

Can math save your life? Eric Westhus, PhD, Data Scientist, Global Research and Data Analytics thinks so.

He uses mathematical models to simulate the spread of infectious diseases and help insurers quantify the risk posed by pandemic tail events. RGA recently sat down with Eric to discuss his video (above) about the role of compartmental modeling in epidemiology. How can simple mathematical models help the medical community to plan for, or even prevent, epidemics – and insurers to assess the risk of one. 

Headlines make it seem as though infectious diseases appear suddenly and spread at terrifyingly and unpredictably fast speeds. Mathematical models, by contrast, are elegant and precise. How then can math accurately predict something so uncontrolled as a pandemic?

There’s a saying by the statistician George Box: “All models are wrong, but some are useful.” Insurers and the public health and medical communities can use models to assess the risk posed by epidemic and pandemic events and plan for their severity. But no model of a complex natural system is ever going to be 100% accurate. That said, simple compartmental disease models have been in place since the early 20th century. In fact, these models are used in a variety of fields, from physics and economics to biology and epidemiology, and that’s because they work.

Explain the math behind the “compartmental” model.

Let’s look at the S-I-R compartmental model. It’s based on an important premise: An outbreak occurs when conditions allow the infection rate to exceed the recovery rate. S-I-R effectively simulates flows between disease states, from Susceptible to Infectious to Removed, or S-I-R compartments. Everyone starts out Susceptible to infection, except for a single infectious individual, who becomes the so-called “patient zero.” This individual introduces the new disease into the population. As people become sick, they join patient zero in our Infectious box until they recover and acquire immunity or lose their lives. Either way, they become Removed. We’re basically tracing out the classic immune response: a person’s immune system fights off the initial infection and then, in doing so, produces antibodies that enable the individual to fight off future exposures.

So with those transition states in mind, we can mathematically define an epidemic as any time people are being infected faster than they are recovering. Another way to look at this is the ratio of the rate at which people are infected divided by the rate of those being removed. An epidemic will deliver a value greater than one. If the result is less than one, the outbreak is going to burn itself out. It’s a really beneficial way to look at a complex problem.

This seems like an academic exercise in a way. How can these models actually help clinicians stop epidemics – or enable insurers to better understand them?

These models are so powerful because they allow clinicians and insurers to tell a story – and test multiple different endings. You can enter various interventions to slow, or even stop, the progress of a particular epidemic into the model. For example, establishing a quarantine or encouraging a prophylactic measure such as hand washing or other required hygiene might be effective in reducing the flow of individuals from one compartment to the next, reducing the spread of the disease and its duration within the population.

We can also model what vaccination rate in the general population could confer so-called “herd immunity,” or when a sufficiently high proportion of individuals become immune through prior exposure and enable an entire population to effectively resist the further spread of an infectious disease. In other words, if enough people are vaccinated, patient zero can sneeze over everybody in the subway and we’re still not going to have an epidemic – because we have herd immunity. It’s why vaccinations are so powerful.

What can insurers do with this information?

Outbreaks generally end long before all individuals in a population become sick. With that said, outbreaks inflict immense human and economic damage. By watching the progression of the disease using a model like this, the healthcare community can see paths to prevention by reducing the proportion of encounters that actually result in transmission or the Beta value in the model.

As insurers, we have a responsibility to better understand the risks of a globalizing world. Dangerous pathogens are often just a quick plane flight away from entering new populations, and many communities are unprepared to mitigate such unforeseen dangers. Through the sound use of data, modeling, and insight, insurers can provide an important line of defense.