LAUSR

Significance We show that under widely believed complexity theoretic hypotheses, one cannot expect to find provably correct and efficient algorithms for predicting epidemic dynamics on general networks. These results hold even under idealized problem formulations, where all the model parameters are known and are insensitive to changes in environment. Further, they hold even for a small time horizon with just one random parameter, namely, the transmission probability. Thus, computational complexity poses an inherent challenge to effective and efficient epidemic forecasting in network models. Our results do not rule out heuristics that work well in practice or algorithms that provide provable guarantees for restricted networks. Rather, they suggest that algorithms working across a range of inputs should exploit properties of problem instances. The ongoing COVID-19 pandemic underscores the importance of developing reliable forecasts that would allow decision makers to devise appropriate response strategies. Despite much recent research on the topic, epidemic forecasting remains poorly understood. Researchers have attributed the difficulty of forecasting contagion dynamics to a multitude of factors, including complex behavioral responses, uncertainty in data, the stochastic nature of the underlying process, and the high sensitivity of the disease parameters to changes in the environment. We offer a rigorous explanation of the difficulty of short-term forecasting on networked populations using ideas from computational complexity. Specifically, we show that several forecasting problems (e.g., the probability that at least a given number of people will get infected at a given time and the probability that the number of infections will reach a peak at a given time) are computationally intractable. For instance, efficient solvability of such problems would imply that the number of satisfying assignments of an arbitrary Boolean formula in conjunctive normal form can be computed efficiently, violating a widely believed hypothesis in computational complexity. This intractability result holds even under the ideal situation, where all the disease parameters are known and are assumed to be insensitive to changes in the environment. From a computational complexity viewpoint, our results, which show that contagion dynamics become unpredictable for both macroscopic and individual properties, bring out some fundamental difficulties of predicting disease parameters. On the positive side, we develop efficient algorithms or approximation algorithms for restricted versions of forecasting problems.