Individual-based lattice model for spatial spread of epidemics

We present a lattice gas cellular automaton (LGCA) to study spatial and temporal dynamics of an epidemic of SIR (susceptible-infected-removed) type. The automaton is fully discrete, i.e. space, time and number of individuals are discrete variables. The automaton can be applied to study spread of epidemics in both human and animal populations. We investigate effects of spatial inhomogeneities in initial distribution of infected and vaccinated populations on the dynamics of epidemic of SIR type. We discuss vaccination strategies which differ only in spatial distribution of vaccinated individuals. Also, we derive an approximate, mean-field type description of the automaton, and discuss differences between the mean-field dynamics and the results of LGCA simulation.Comment: 13 pages, 5 figure

Lattice Gas Automata for Reactive Systems

Reactive lattice gas automata provide a microscopic approachto the dynamics of spatially-distributed reacting systems. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a simple physical picture to show how an automaton can be constructed to capture the essentials of a reactive molecular dynamics scheme. The statistical mechanical theory of the automaton is then developed for diffusive transport and for reactive processes, and a general algorithm is presented for reactive LGA. The method is illustrated by considering applications to bistable and excitable media, oscillatory behavior in reactive systems, chemical chaos and pattern formation triggered by Turing bifurcations. The reactive lattice gas scheme is contrasted with related cellular automaton methods and the paper concludes with a discussion of future perspectives.Comment: to appear in PHYSICS REPORTS, 81 revtex pages; uuencoded gziped postscript file; figures available from [email protected] or [email protected]

Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Common metrics for cellular automata models of complex systems

The creation and use of models is critical not only to the scientific process, but also to life in general. Selected features of a system are abstracted into a model that can then be used to gain knowledge of the workings of the observed system and even anticipate its future behaviour. A key feature of the modelling process is the identification of commonality. This allows previous experience of one model to be used in a new or unfamiliar situation. This recognition of commonality between models allows standards to be formed, especially in areas such as measurement. How everyday physical objects are measured is built on an ingrained acceptance of their underlying commonality. Complex systems, often with their layers of interwoven interactions, are harder to model and, therefore, to measure and predict. Indeed, the inability to compute and model a complex system, except at a localised and temporal level, can be seen as one of its defining attributes. The establishing of commonality between complex systems provides the opportunity to find common metrics. This work looks at two dimensional cellular automata, which are widely used as a simple modelling tool for a variety of systems. This has led to a very diverse range of systems using a common modelling environment based on a lattice of cells. This provides a possible common link between systems using cellular automata that could be exploited to find a common metric that provided information on a diverse range of systems. An enhancement of a categorisation of cellular automata model types used for biological studies is proposed and expanded to include other disciplines. The thesis outlines a new metric, the C-Value, created by the author. This metric, based on the connectedness of the active elements on the cellular automata grid, is then tested with three models built to represent three of the four categories of cellular automata model types. The results show that the new C-Value provides a good indicator of the gathering of active cells on a grid into a single, compact cluster and of indicating, when correlated with the mean density of active cells on the lattice, that their distribution is random. This provides a range to define the disordered and ordered state of a grid. The use of the C-Value in a localised context shows potential for identifying patterns of clusters on the grid

Autômatos Celulares e Sistema Multiagente para Simulação da Propagação de Doenças

Nestetrabalhoéapresentadoumestudosobremodeloscomputacionais epidemiológicos enfocando o tipo Suscetível-Infectado-Removido, SIR, e diferentes estratégias de solução à simulação computacional da propagação de doenças transmissíveis. Mostra-se que modelos baseados em autômatos celulares tipo Lattice Gas Cellular Automata, LGCA, têm soluções assemelhadas às obtidas por sistemas multiagentes, diferentemente de autômatos celulares difusivos. Os resultados obtidos da literatura, bem como aqueles decorrentes deste trabalho, apontam que tais metodologias têm potencial à simulação da dinâmica de fenômenos ecológicos, biológicos e físicos que possam assim ser modelados. Indicam, contudo, que resultados mais condizentes com dados reais dependem do desenvolvimento e da parametrização de modelos que adicionem características essenciais ao fenômeno, como a interação entre indivíduos e meio ambiente, e a heterogeneidade do sistema relacional de contatos.

Complex event types for agent-based simulation

This thesis presents a novel formal modelling language, complex event types (CETs), to describe behaviours in agent-based simulations. CETs are able to describe behaviours at any computationally represented level of abstraction. Behaviours can be specified both in terms of the state transition rules of the agent-based model that generate them and in terms of the state transition structures themselves. Based on CETs, novel computational statistical methods are introduced which allow statistical dependencies between behaviours at different levels to be established. Different dependencies formalise different probabilistic causal relations and Complex Systems constructs such as ‘emergence’ and ‘autopoiesis’. Explicit links are also made between the different types of CET inter-dependency and the theoretical assumptions they represent. With the novel computational statistical methods, three categories of model can be validated and discovered: (i) inter-level models, which define probabilistic dependencies between behaviours at different levels; (ii) multi-level models, which define the set of simulations for which an inter-level model holds; (iii) inferred predictive models, which define latent relationships between behaviours at different levels. The CET modelling language and computational statistical methods are then applied to a novel agent-based model of Colonic Cancer to demonstrate their applicability to Complex Systems sciences such as Systems Biology. This proof of principle model provides a framework for further development of a detailed integrative model of the system, which can progressively incorporate biological data from different levels and scales as these become available