Dynamic estimation of stochastic descriptors in the SPIR model using particle filtering

• Introduction of a new stochastic model for the assessment of epidemic severity. • Construction of new algorithms for the computation of distributions of interest. • Combination with a Bayesian method for dynamic parameter estimation. • Estimation of key epidemiological descriptors. • Estimates of increased precision that can improve decision-making. Accurate assessment of epidemic severity requires stochastic indicators that quantify outbreak size and timing under uncertainty. Numerous studies have introduced different stochastic models and associated epidemic descriptors, providing explicit formulas and algorithms that enable their calculation. Most of the studies consider constant epidemic dynamics, which limit the accuracy and the possibility of providing online estimates. In this paper, we introduce a SPIR (Susceptible, Presymptomatic, Infectious, Removed) model based on a 3-dimensional Markov chain. In the framework of this model, stochastic descriptors are introduced including the total number of infections, the occurrence time of a specific number of deaths and the number of infections generated from an index presymptomatic or an infectious case. The paper then integrates an augmented state-space formulation with particle filtering to estimate time-varying epidemiological parameters from surveillance data. Using mpox data from Ghana (2022), the time-varying approach improves predictive accuracy compared with a standard constant parameter method. The root mean squared error (RMSE) 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. In summary, incorporating time-varying parameter estimates through the filtering process enhances the precision of descriptors, allowing for more realistic epidemic scenarios. Overall, incorporating dynamically updated parameters improves the precision of stochastic descriptors and supports data-driven online assessment of emerging outbreaks.