Zero-Diffusion Domains in Reaction–diffusion Morphogenetic and Epidemiologic Processes

Abstract

Classical models of morphogenesis by Murray and Meinhardt and of epidemics by Ross andMcKendrick 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.

Temperature Decreases Spread Parameters of the New Covid-19 Case Dynamics

“…These seasonal changes could occur in exactly the same way as for other pathogens, like the common cold or influenza [9][10][11][12]. This phenomenon can be modelled and the deterministic as well as stochastic models [2,[13][14][15][16][17][18][19][20][21][22][23][24][25] include potentially temperature-dependent parameters, like the contagion coefficient increasing with cold, dry weather because of faster evaporation of aerosol droplets. The present paper aims to identify such parameters from the covid-19 spread dynamics.…”

Discrete dynamics of contagious social diseases: Example of obesity

“…This quadratic term is also present in the interaction potential of Hopfield like networks in which the study of the robustness with respect to the contagion parameter changes has been performed [59][60][61][62][63][64][65][66][67][68][69] as well as in recent studies taking into account the spatial character of the disease spread. [70][71][72][73][74][75][76][77][78] Confinement and Saturation The localization of contamination has been treated by different authors. 79,80 When contagion occurs in confined locations (like professional, educational or residence buildings), we can use saturation dynamics terms coming from the enzymatic kinetics (cf.…”

Fractal Approach to Forming of Modified Bifurcation Diagrams in Practical Applications

“…The great importance of a bifurcation diagram is caused by the fundamental idea -to represent the inhere property of Nature connected with the regularities during the evolution of a nonlinear system. Taking into account this idea, the bifurcation analysis is widely ised for scientific researches of nonlinear dynamics regarding different kinds of systems, for example: researching into dynamical processes keeping under observation in power [1,2], control [2,3] and information [4,5] parts of technical systems; researching into dynamical processes keeping under observation in biological [6] and natural [7,8] systems; revealing the evolution processes in social systems [9]; and so on. However, the restrictions concerning the use of bifurcation analysis results for practical applications remain yet quite hard.…”