Quantitatively accurate epidemiology models are powerful tools for both understanding disease outbreak and informing public health policies. However, as models become increasingly sophisticated, there are more parameters to estimate and therefore less accurate predictions and more data-intensive requirements. This is especially true with COVID-19 because the disease parameters are (in most cases) unknown. Indeed, the emergence of new variants such as Delta and Lambda (with markedly different characteristics) demonstrate that even accurate measurements of parameters can become rapidly redundant. Another challenge is both the amount of, and bias in, data. Within each region, different sampling strategies are being pursued so that the observed case statistics must be carefully treated. 

To circumvent these difficulties in our proposal we proposed using a methodology that has seen recent success in molecular dynamics simulations?maximum entropy biasing methods. The advantage of such an approach is that it replaces model parameter optimization (requiring intensive data collection) with a biasing term that is independent of model parameters. This has the advantage of computational speedup---it makes the runtime complexity of model optimization linear in the amount of data; and more importantly, the formulation is independent of unknown parameters, allowing one to rapidly adapt the simulations to new realities. Thus, one can make reasonable estimates of a number of things including projecting disease dynamics forward, as well as inferring past history based on present observations without the need to get precise estimates of the numerous parameters governing epidemic spread.

The first aim of our proposal was to adapt the MaxEnt framework to families of compartmental models that describe the evolution of various types of pathogens, and validate our approach on known data and outcomes. We considered a model with 5 states: Susceptible, Exposed, Asymptomatic, Infected, Recovered (SEAIR), that has been used extensively in the literature to forecast the spread of COVID-19. We used the deterministic model as the ground truth, and then simulated uncertainty in the data by introducing noise in the temporal evolution of each of the states. Inputs to the MaxEnT framework corresponded to discrete observations in time serving as a proxy for imperfect knowledge of the evolution of the pandemic. We demonstrated that despite noisy and sparse inputs, as well as no knowledge of the disease parameters, the MaxEnT framework was able to accurately capture the complete trajectory of each of the disease states. This work titled "Simulation-Based Inference with Approximately CorrectParameters via Maximum Entropy" is available to view on https://arxiv.org/abs/2104.09668 and is currently in review with Nature Computational Science. Figure 1 illustrates the process of discrete sampling and projecting the disease dynamics forward.

Having validated our methodology our second aim involved deploying the framework in real-world settings of COVID-19 spread. To that effect we conducted an analysis of disease spread in New York State. Despite, sampling trajectories from a subset of counties, we were able to accurately reproduce the infection curves in other parts of the state. An important result we uncovered, was in inferring the origin of the pandemic in the state by sampling curves much later in the pandemic. Indeed, while the current belief is that the efficacy of contact-tracing in determining the source of the pandemic diminishes rapidly as the epidemic progresses, we demonstrate the existence of another temporal window much later in disease spread, where one can recover knowledge about the origins of the pandemic. This work is described in the manuscript "Maximum Entropy Epidemiology: Predicting Future Trajectories and Inferring Origin of Patient-Zero"  and is being prepared for submission to the Proceedings of the National Academy of Sciences. Figure 2 illustrates the sampling of counties in New York and the relative accuracy of inferring the origin of the infection.

Finally, in addition to the stated aims of our proposal, we also worked on phenomenological modeling. Specifically, we asked the question: "What is it that makes urban centers vulnerable to epidemics in the first place?". We proposed a metric that combines population density and mobility flow between high population centers and demonstrated it to be a accurate predictor of future outbreaks. We validated out metric in about a 160 cities worldwide and showed it predicted the severity of the initial outbreak in multiple countries. Based on this we proposed a number of non-pharmaceutical-intervention measures, much less severe than draconian lockdowns, that appeared to suppress the spread of the pandemic. This work is published in Communications Physics 4, 191 (2021). 

Last Modified: 08/23/2021
Modified by: Gourab Ghoshal