A topological approach to the study of COVID-19 pandemic: qualitative models for understanding and helping taking decisions

Mathematical models are either strategic, simplified, to study global qualitative properties, or tactic, detailed, appropriate for fine quantitative adjustment to reality. When complex systems interact with their medium or undergo parameter perturbations, they can suffer changes of order making qualitative and quantitative studies difficult. Epidemiological processes allow distinguishing between topological and dynamical alterations, and establishing precedence among them. In this essay we approach COVID-19 this way, to separate topological transformations inducing changes of order in the system, from dynamic transformations themselves. We then develop a visual metaphor, a sequence of images to support a stop-motion, allowing distinguishing the stages, identifying and classifying sceneries, and suggest actions to improve the understanding and control, of the pandemic.