A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties

The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria. We apply the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.