Deciphering Memory Patterns in Eco-Epidemiological systems through the lens of BaFOMS: A Bayesian Fractional Order Model Selection Method

The evolution of eco-epidemiological systems is significantly influenced by the memory or previous history of the system. These non-Markovian dynamics are effectively modelled using fractional derivatives (FDs), incorporating memory kernels that reflect long-term or short-term memory characteristics in corresponding nonlinear fractional differential evolution equations. We introduce BaFOMS, a framework for identifying and selecting the optimal FD model for eco-epidemiological processes based on historical data. Specifically, we evaluate a class of fractional logistic growth models defined by their time correlation functions and determine the optimal model through Bayesian inference, selecting the one with the highest posterior probability. We also demonstrated BaFOMS efficiency in parameter estimation and forecasting, producing reliable results with quantified uncertainties. The method is shown to be robust across a range of eco-epidemiological datasets, offering computational efficiency and reliable inference about the evolution dynamics.