Abstract

Accurate assessment of epidemic severity requires uncertainty-aware indicators that quantify outbreak size and timing under uncertainty. Numerous studies have proposed stochastic epidemic models and associated epidemiological indicators coupled with offline estimation methods. However, most existing work assumes constant epidemic dynamics, which can limit accuracy and hinder real-time (online) estimation. In this paper, we introduce a SPIR (Susceptible, Presymptomatic, Infectious, Removed) model formulated as a three-dimensional Markov chain. Within this framework, we define uncertainty-aware descriptors including: (i) the total number of infections, (ii) the occurrence time of a specified number of deaths, and (iii) the number of infections generated by an index presymptomatic or infectious case. We then couple an augmented state-space representation with particle filtering to infer time-varying epidemiological parameters online from surveillance data. Using mpox data from Ghana (2022), the proposed time-varying approach improves predictive performance relative to a standard constant-parameter method. When using the proposed online method, the estimation error decreases from 12.497 to 5.480 for the expected total infections until extinction, and from 2.082 to 1.588 for the expected time to the first death. Overall, dynamically updating parameters improves the precision and realism of uncertainty-aware descriptors, supporting data-driven online assessment of emerging outbreaks.