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

Abstract

AbstractThe dynamics of epidemiological phenomena associated to infectious diseases have long been modelled with different approaches. However, recent pandemic events exposed many areas of opportunity to improve over the existing models. We develop a model based on the idea that transitions between epidemiological stages are alike sampling processes. Such processes may involve more than one subset of the population or they may be mostly dependent on time intervals defined by infectious or clinical criteria. We apply the model to simulate epidemics and obtain realistic case fatality ratios. We also analyse the impact of the proportion of asymptomatic of infected people in the distribution of the total infected population and define a basic reproductive number, which determines the existence of a probabilistic phase transition for the pandemics 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.