Threshold dynamics and epidemic-informed machine learning for forecasting of mpox: A U.S. case study

Mpox (monkeypox) is a re-emerging viral disease with increasingly sustained human transmission, particularly in previously unaffected regions. In this study, we develop a compartmental epidemic model that captures mpox transmission dynamics and incorporates a treatment function to assess the impact of medical interventions on disease progression and recovery. The model is calibrated using U.S. case data, with parameters estimated via the Trust Region Reflective optimization method to ensure close alignment with observed trends. We perform global sensitivity analysis using partial rank correlation coefficients to identify key parameters influencing transmission. The model's bifurcation structure is examined through the basic reproduction number RM0, revealing both forward and backward bifurcations that highlight threshold behavior and the potential for complex endemic dynamics. For real-time forecasting, we incorporate prior knowledge of mpox dynamics into machine learning models, ARNN (Autoregressive Neural Network), ARIMA (Autoregressive Integrated Moving Average), and LSTM (Long Short-Term Memory), achieving improved predictive accuracy over traditional methods. These epidemic-informed models benefit from mechanistic insights, enhancing their responsiveness to changing trends. Our results emphasize the importance of timely treatment, hygiene, and vaccination in mitigating mpox spread. The integrated modeling and the forecasting framework provide valuable tools for anticipating outbreaks and informing public health strategies.