Simulation of the spread of infectious diseases in a geographical environment

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. cellular automata, infectious disease, modeling, geographic information systems, spatial weighting function

Modelling the global spread of diseases: A review of current practice and capability

“…Record [78] is a cellular automaton model (CA). CA models involve a grid lattice made up of cells and, at each discrete time step, the state of an individual cell is affected by the states of its neighbours according to a predefined mathematical rule (Wolfram Math World).…”

“…Infectious disease cellular automata models could involve each cell representing an individual who, at each time step, will be either susceptible, infected, or recovered; see, for instance, Keeling and Rohani (2008) for a more detailed description. Alternatively, in the case of [78], each cell represents one of a number of discrete spatial regions each with corresponding population. At each time step, the population for a discrete region is split into susceptible, infected, and recovered individuals and the sizes of these subpopulations vary dependent upon disease dynamics both within and between spatial regions.…”

Binary opinion dynamics with noise on random networks

“…In recent years, much effort has been invested in social dynamics formulated with concepts and methods from statistical physics [1][2][3]. Opinion dynamics is one of the social problems well-studied by physicists based on the famous Ising model from three decades ago [4].…”

Disease spreading in complex networks: A numerical study with Principal Component Analysis

“…Given the flexible adaptability of this framework, a wide range of problems started to use some complex network models, for instance: analysis of zooplankton community ( Raymond & Hosie, 2009 ), Buruli ulcer in Victoria, Australia ( van Ravensway et al, 2012 ) and swine shipments in Ontario, Canada ( Dorjee et al, 2013 ); exploration of network formed by dogs in a community ( Westgarth et al, 2009 ) and a study of the epidemic data of SARS (Severe Acute Respiratory Syndrome) in Beijing, China ( Zhong, Huang, & Song, 2009 ). By using complex networks in these circumstances, it is possible to find relations between the population structure and disease characteristics.…”

“…Complex networks have been frequently used to model populations in disease spreading models ( Albert & Barabasi, 2002;Boccaletti et al, 2006;May, 2006;Zhou, Fu, & Wang, 2006;Trapman, 2007;Zhong et al, 2009 ). Although the proposed methodology is an innovative approach to handle with any type of network, it does not consider some specific attributes and results.…”