ZERO-DIFFUSION DOMAINS IN REACTION–DIFFUSION MORPHOGENETIC AND EPIDEMIOLOGIC PROCESSES

Abstract

Classical models of morphogenesis by Murray and Meinhardt and of epidemics by Ross and McKendrick can be revisited in order to consider the colocalizations favoring interaction between morphogens and cells or between pathogens and hosts. The classical epidemic models suppose, for example, that the populations in interaction have a constant size and are spatially fixed during the epidemic waves, but the presently observed pandemics show that the long duration of their spread during months or years imposes to take into account the pathogens, hosts and vectors migration in epidemics, as well as the morphogens and cells diffusion in morphogenesis. That leads naturally to study the occurrence of complex spatio-temporal behaviors in dynamics of population sizes and also to consider preferential zones of interaction, i.e. the zero-diffusion sets, for respectively building anatomic frontiers and confining contagion domains. Three examples of application will be presented, the first proposing a model of Black Death spread in Europe (1348–1350), and the last ones related to two morphogenetic processes, feather morphogenesis in chicken and gastrulation in Drosophila.