Abstract
The study of mathematical models for the spread of infectious diseases is an important issue in epidemiology. Given the fact that most existing models cannot comprehensively depict heterogeneities (e.g., the population heterogeneity and the distribution heterogeneity) and complex contagion patterns (which are mostly caused by the human interaction induced by modern transportation) in the real world, a theoretical model of the spread of infectious diseases is proposed. It employs geo-entity based cellular automata to simulate the spread of infectious diseases in a geographical environment. In the model, physical geographical regions are defined as cells. The population within each cell is divided into three classes: Susceptible, Infective, and Recovered, which are further divided into some subclasses by states of individuals. The transition rules, which determine the changes of proportions of those subclasses and reciprocal transformation formulas among them, are provided. Through defining suitable spatial weighting functions, the model is applied to simulate the spread of the infectious diseases with not only local contagion but also global contagion. With some cases of simulation, it has been shown that the results are reasonably consistent with the spread of infectious diseases in the real world. The model is supposed to model dynamics of infectious diseases on complex networks, which is nearly impossible to be achieved with differential equations because of the complexity of the problem. The cases of simulation also demonstrate that efforts of all kinds of interventions can be visualized and explored, and then the model is able to provide decision-making support for prevention and control of infectious diseases.