Inferring the time-varying transmission rate and effective reproduction number by fitting semi-mechanistic compartmental models to incidence data

Abstract

This thesis presents a novel approach to ecological dynamic modeling using non-stochastic compartmental models. Estimating the transmission rate (\(\beta\)) and the effective reproduction number (\(R_t\)) is essential for understanding disease spread and guiding public health interventions. We extend this method to infectious disease models, where the transmission rate varies dynamically due to external factors. Using Simon Wood's partially specified modeling framework, we introduce penalized smoothing to estimate time-varying latent variables within the `R` package `macpan2`. This integration provides an accessible tool for complex estimation problems. The efficacy of our approach is first validated via a simulation study and then demonstrated with real-world datasets on Scarlet Fever, COVID-19, and Measles. We infer the effective reproduction number (\(R_t\)) using the estimated \(\beta\) values, providing further insights into the dynamics of disease transmission. Model fit is compared using the Akaike Information Criterion (AIC), and we evaluate the performance of different smoothing bases derived using the `mgcv` package. Our findings indicate that this methodology can be extended to various ecological and epidemiological contexts, offering a versatile and robust approach to parameter estimation in dynamic models.