Stochastic approximate inference of latent information in epidemic model: A data-driven approach

Precise estimates of disease transmissibility, made using mathematical methods, are a critical part of epidemiology. This paper proposes a stochastic compartmental model based on a Discrete-Time Markov chain (DTMC) to estimate the transmission rate and important latent variables, such as the number of hidden patients. To find the transmission rate that best represents the reported data (e.g., the number of confirmed cases), we formulate a maximum log-likelihood estimation problem. However, this problem is challenging because it includes the posterior distribution of the reported data, which is mathematically intractable. Therefore, we relax the problem by proposing surrogate optimization with stochastic approximation, which allows us to successfully estimate the transmission rate and latent variables. To assess the proposed inference model, extensive simulations are performed using datasets from COVID-19, seasonal influenza, and mpox. The results confirm that the proposed algorithm finds a transmission rate explaining the macroscopic and microscopic variations in the waves of infectious diseases. Compared with existing solutions, the proposed algorithm better explains real-world disease evolution, such as reinfection and microscopic fluctuations in waves.