Modeling COVID-19 Spread: Scenario Studies from Indiana Data
Post doc researcher Jithin Sreedharan with Purdue Computer Science professors Ananth Grama, and Wojtek Szpankowski, are working on initial research with epidemiological models and predictions of spread of COVID-19 infection, the impact of social distancing guidelines, and providing guidance for policy-making. These efforts are aimed at understanding the current state of the epidemic (is it waxing or waning?), estimating the state in the future (its expected progression under different policy scenarios), and impact of various interventions (e.g., reopening workplaces, schools, etc.)
A useful indicator of the current (local) state of the epidemic is the basic reproduction number (also sometimes referred to as the basic reproduction ratio). Typically represented by R0 (pronounced R-nought), this number is the expected number of individuals infected by each infected individual. One may observe that a value of R0 greater than 1 corresponds to a spreading infection, R0 less than 1 corresponds to a waning infection, and R0 equal to one corresponds to a stable infected count. Estimating R0, though, is hard because of sparse observational data, uncertainty associated with population parameters, and variability in responses to exposure and infection. Work at CSoI has focused not just on estimating values of R0, but also on characterizing the uncertainty associated with the value due to estimated uncertainty of population parameters. By building models (see Figure plotting values of R0 for various counties in Indiana) for each county, these results clearly demonstrate the conformance and effectiveness of social distancing. An important aspect of this work is its use of novel imputation techniques to estimate parameters for counties with sparse case reporting. These results indicate that the R0 value for various counties in Indiana is now less than one, although, there is a band of uncertainty around this value that potentially takes it above one. Overall, the R0 value for the state of Indiana as a whole is now trending to one, and lower, indicating that the peak of infection is near, due to the lag from time of infection to time of testing/ hospitalization. These results present a clear picture of the state of the epidemic in various county -- of particular note are counties like Lake County, where the value or R0 is still significantly greater than one.
"The figure shows the estimates of R0 up to April 10. The estimation is done with the New York Times COVID-19 data that is available until April 15 and discounts the time period requires for transition from exposed to infected state which is roughly 5 days "
Models are only as good as the data used to construct them. To this end, the CSoI team incorporates disparate data to fundamentally enhance the predictive accuracy of the models. Working with data from Facebook, mobility data across counties is being incorporated into new models. This data allows one to assess the impact of stay-at-home guidelines, as well as best approaches to relax these guidelines. With availability of data at increasingly refined scales (e.g., data on movement across campus buildings), they are building fine-grained models for controlled activities that minimize risk of subsequent spread. The ability to accurately scale models from the entire country down to individual buildings allows decision-making at various levels, and to assess the integrated impact of these decisions at coarser levels.
Sources: Wojciech Szpankowski, firstname.lastname@example.org
Ananth Grama, email@example.com
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