Forecasting of infectious disease epidemics in sexual networks using attenuated renewal processes

Forecasting emerging infectious disease outbreaks is particularly challenging for sexual networks of men who have sex with men (MSM), where transmission can be shaped by heterogeneous and overdispersed contact structures, mixing assortativity, and both one-time and recurrent partnerships. Using stochastic epidemic simulations on synthetic MSM networks and empirical mpox case data from major cities, we systematically evaluated five classes of short-term forecasting models, from random walk approaches to semi-mechanistic attenuated renewal processes. Model performance was assessed using the continuous ranked probability score (CRPS). Across both simulated and empirical epidemics in heterogeneous networks, renewal models attenuated by a reverse-sigmoid curve, to account for early depletion of highly-connected nodes, consistently outperformed alternatives, achieving more balanced and reliable forecasts. Our findings suggest a practical approach for robust forecasting in highly overdispersed networks, where distinguishing network effects from other factors remains challenging and usually requires additional data.