Webinar Series — Reasoning Under Uncertainty (Part 3): Epidemic Modeling with Temporal Bayesian Networks
"Flatten the curve" has become the motto of the moment. From policymakers and the media, we hear that it's all about keeping the peak of COVID-19 infections below the maximum capacity of healthcare systems.
There appears to be a consensus regarding the default shape of the curve and that an intervention, e.g., social distancing, would reduce the peak of infections while extending the duration of the epidemic, i.e., the curve flattens.
Given that the curve does resemble a normal distribution, one may speculate that there is an underlying function with "disease" parameters. As it turns out, the curve is impractical to characterize with a closed-form expression. Instead, the curve is the result of a simulation of a compartmental epidemic model that is defined by a set of differential equations.
The simplest model of this kind is the so-called SIR model. S stands for the number of susceptible, I for the number of infectious, and R for the number recovered. Infection and recovery rates determine how individuals in a population move between the "compartments," i.e., S->I and I->R, from one time step to the next.
While the infection and recovery rates for a typical flu season are known, COVID-19 is novel, and these parameters have yet to be estimated from observations. However, health policy decisions may be required long before estimates can be established with any degree of certainty. It is a prototypical situation of reasoning under uncertainty.
In this webinar, we show how to implement the SIR model as a temporal Bayesian network and how to use BayesiaLab for simulating the curves as a function of different infection and recovery rates. In this context, we also demonstrate the Bayesia Expert Knowledge Elicitation Environment for combining experts' assumptions to parameterize the Bayesian network model.
Please also check out our next webinar in the series about reasoning under uncertainty:
During the webinar today, someone raised a point about the models shown not being comprehensive enough and missing many important interactions, e.g., between the number of susceptible and infectious individuals for calculating the beta parameter. Yes, absolutely. All the models we showed today were very simplistic. However, our objective was not to improve on epidemiological models — we are not qualified for that, but rather to translate existing models into Bayesian networks. We hope that the Bayesian network framework will make it easier for epidemiologists to formulate and estimate more sophisticated models in the future.
In the webinar, I forgot to provide the links to the self-study courses:
Learn Bayesian networks during the lockdown!
Germán Riaño and Lionel Jouffe pointed out that I omitted the interaction between Susceptible and Infectious in the dynamic model I presented, and they are absolutely correct. I have attached a corrected model (with random values for beta, gamma, lambda, and mu), which now includes an arc from Susceptible to the function node beta.