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

Overview & Synopsis

In epidemiology, accurately assessing epidemic events deserves particular attention and becomes more and more urgent. Numerous studies have introduced different stochastic models and associated epidemiological 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 the 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. Analytical expressions are obtained along with corresponding algorithms based on recursive algorithmic schemes. A new methodology is described to provide more precise estimates, which is based on an augmented state space model with dynamically updated parameters. The effectiveness of the proposed methodology is compared to the standard approach (with fixed parameters) by evaluating two descriptors: the total number of infectious cases and the time until the first death, using real monkeypox (mpox) data from Ghana in 2022. Additionally, the impact of infections due to contact with presymptomatic or an infectious case is investigated. In summary, incorporating time-varying parameter estimates through the filtering process enhances the precision of descriptors, allowing for more realistic epidemic scenarios. The ability to provide data-driven, online predictions while managing the inherent uncertainty of physical phenomena is a crucial tool in addressing emerging public health challenges.