Aplicação de autômatos celulares em sistemas complexos: um estudo de caso em espalhamento de epidemias

• Ano de defesa: 2009
• Autor(a) principal: Gledson Melotti
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Engenharia Elétrica; Engenharia elétrica
• Link de acesso: http://hdl.handle.net/1843/BUOS-8CDFAB

Many systems in nature and society can not be understood by examining the behavior of their individual components, but only by examining the overall behavior generated by interactions of individual components. Such systems are known as complex systems. The study of these systems has become recognized in recent years as a newscientific discipline, the latest of interdisciplinary fields. These are concepts that range from psychology to the exact sciences. Many of the systems that surround us are complex, such as ecosystems, economies, climate, nervous systems and the spread of disease in a population.To understand complex systems, various mathematical tools are used. Among them is the cellular automata (CA), which is used as an alternative in modeling systems. This mathematical tool is a discrete system, because states vary regularly spaced-time. They are groups of cells (vector/matrix) in which each cell is characterized by a certain state.The value of each cell of the group at the next instant depends on neighboring cells via a set of rules, known as local rules of transitions.An example of ACs able to represent natural phenomena are CAs for spreading of epidemics, the goal of study of this dissertation. This research proposes simple rules that simulate the spread of a generic disease among individuals of a population by means of CA. These individuals are characterized by the states of the system: susceptible, infected and recovered. Besides the neighbours, as local contacts has been infected individuals ability to move and have the chance to infect a susceptible to a certain distance. This distance is obtained by means of fuzzy rules, which includes a probability of displacement and a parameter of the SIR (susceptible-infected-recovered) epidemiological model known as basic rate of reproduction. To illustrate the behavior of the system eight scenarios were simulated with different starting conditions. The first and second scenarios present the evolution of AC with different parameters of infection, the third scenario shows the outbreaks of epidemics that arise. The fourth and fifth scenarios exhibit the evolution considering four different regions in CA. They illustrate how the same disease spreads in different natural environments, that is, the rate of spread of the disease may be different if they include natural different environmental conditions, such as climate. The sixth and seventh scenarios show the behaviour of the population when is performed a strategy of control to eradicate the disease. The strategy of control used was the vaccination pulsed. The last scene exhibit the behavior of the AC when was included the period of latency and the incubation period.To analyse and, in some cases, validate the AC was compared with two epidemiological models: the SIR mathematical model and the MBI model. Such validation was made qualitatively (behavior of time series) and quantitatively (numerical values of the time series). With these comparisons is possible to say that the adopted rules provide a satisfactory result for the study of epidemiology.