Epidemic Forecasting on Networks: Bridging Local Samples with Global Outcomes

We study Susceptible-Infected (SI), Susceptible-Infected-Removed (SIR), and related epidemic models in which infected individuals transition to an absorbing state, such as recovery or permanent infectiousness. In addition to infectious diseases, these models are used for studying the diffusion of innovations in which new behaviors, opinions, conventions, and technologies propagate from person to person through a social network. We focus on the key challenge of forecasting epidemic trajectory and outbreak sizes and show that they can be predicted with a few samples from the network data. To this end, we propose a local algorithm for epidemic estimation, and prove the estimator's accuracy for both deterministic finite graphs and random networks, given certain neighborhood constraints. Further, leveraging the theory of local graph limits, we relate the time evolution in a sequence of graphs converging locally in probability with the epidemic in the limit graph. Finally, we validate our findings with experiments on synthetic models and real-world networks, such as Copenhagen and San Francisco's SafeGraph data.