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. / Thesis / Master of Science (MSc) / This thesis explores a new way to model how diseases spread using a deterministic mathematical framework. We focus on estimating the changing transmission rate and the effective reproduction number, key factors in understanding and controlling disease outbreaks. Our method, incorporated into the `macpan2` software, uses advanced techniques to estimate these changing rates over time. We first prove the effectiveness of our approach with simulations and then apply it to real data from Scarlet Fever, COVID-19, and Measles. We also compare the model performance. Our results show that this flexible and user-friendly approach is a valuable tool for modelers working on disease dynamics.