by Mark Bognanni, Douglas Hanley, Daniel Kolliner, and Kurt Mitman
We build on one of the workhorse epidemiological models, SIR, which stands for Susceptible-Infected-Recovered. In this case, as is also common, we include Asymptomatic and Death states, hence SAIRD. Each person in the population is in one of these 5 states at any given time, and they flow between them at certain rates shown below
Our main contribution is that rather than taking the transmission rate (β) as fixed or exogenously moving over time, we make it the results of optimizing behavior on the part of agents, as is common in economic models. Each day, agents have some exursion needs, say getting groceries or going to the doctor. The benefit arising from these needs is drawn randomly from some distribution. This benefit is weighed agains the possibility of infection, which is larger when the local disease prevalence is higher.
Thus when disease prevalence is high, people go out less and transmission rates are lower, and vice versa. This naturally leads to equilibration to a roughly constant disease prevalence. On top of this, government policies such as business closures and stay-at-home orders can further influence people's behavior. This dashboard allows you to play "social planner" and explore the models predictions for various policy options.
Check out our paper linked above for many more details, including additional features of the model and how we estimate the parameters of the model using daily data from US counties.