Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications. © 2022 Elsevier Ltd

Physical Education in the COVID-19 context. A tale from teachers of different educational stages

The way in which Physical Education (PE) is conceived has changed radically in a matter of months. This means that the professional identity of the teaching staff has had to be reconstructed and adapted to an unprecedented situation. The aim of this study is, under the theory of teaching identity and professional reconstruction, to contrast how three groups of teachers from different educational stages teach PE with COVID 19, analyzing the adaptations made in the classroom. Five university teachers, seven school teachers and eight future teachers took part. A qualitative analysis was employed, using reflective journals and discussion groups as data collection instruments. Three categories of analysis were used: (a) reconfiguration of the purpose of the subject;(b) reconstruction of professional identity;(c) main limitations of teaching and solutions found. The results show how teachers in the three educational stages agree on the negative implications of teaching the subject with physical distance. University teachers stress the need to reconsider the aims of the subject in order to adapt to this new situation, while school teachers admit to being very limited on the content to be taught. For their part, the future teachers express great insecurity about being able to apply what they have been taught throughout their university training. It is considered essential to continue researching and reflecting on the evolution of PE teaching in the situation of COVID 19, as well as the curricular and educational role that it should continue to play.