Socio-spatial formalism and nonlinear interaction in the diffusion of epidemics in regional space

Abstract

The existence of nonlinear interaction in the spread of various infectious diseases is extensively discussed in mathematical biology literature. Since these models are predominantly based on the studies of biological objects with almost no reference to the complexity of social structures, the negligence of socio-spatial parameters in these models is often inherent. Present paper intends to contribute to the understanding of epidemical diffusion process from a socio-spatial perspective. The emphasize is on two directions, namely a qualitative description of the diffusion of epidemics in a regional setup in order to incorporate the spatial aspects of the diffusion process, and an analytical framework to bring together the spatial and nonlinear analysis into the study of irregular phenomena observed in the outbreak of epidemics in human geographic space. A general model is suggested and various hypothesis are tested by using monthly notification of the occurrence of various epidemics in Danish regions.