A possible method of selecting spatial epidemic models based on Turing’s diffusive threshold

Abstract

Spatial epidemic has increasingly become the focus of attention of the global population, and epidemics modeling is an important tool for its prevention and control. However, how to choose the better model has always the challenge faced by modelers. This paper provides a possible method of model selection based on two Turing’s diffusive thresholds of a spatial epidemic model: the inherent diffusive threshold and the practical diffusive threshold. It is a new classification in terms of original Turing region obtained by linear analysis. The inherent diffusive threshold of the model is mathematical without realistic significance; on the contrary, the practical diffusive threshold is the physical diffusive threshold. The region between two thresholds has both realistic and mathematical significance. For a classical spatial epidemic model, we derive these two types of thresholds, and find that the larger the area size between two thresholds, the more models contain dynamical behaviors possibly describing spatial epidemic transmission dynamics which are also the models needed by modelers. Our approach may provide a new insight into the selection of spatial epidemic models.