Modelos matemáticos de propagação de epidemias baseados em redes sociais e detecção de clusters de doenças

Abstract

Theoretical studies to better understand mathematical epidemics are currently made in at least three distinct areas: the mathematical models of differential equations, the physics of their propagation models on networks and the statistics of disease cluster detection. Despite the common goal, those areas have little or no intersection. Our studies are directed at seeking tools within the intersection of those areas. Computer simulations of epidemics on hypothetical scenarios are valuable tools for understanding and predicting the behavior of epidemics. Thus, we have studied mathematical models that are able to describe the dynamics of epidemics in various scenarios. Direct transmission diseases from person to person (such as influenza, HIV, smallpox, etc.) depends on how individuals interact with each other. Moreover, infectious diseases behave differently in populations with different social structures. Mathematical models of differential equations usually do not take into account these aspects and, therefore, we propose a new individual based model (MBI), in order to consider different organizations within the community as complex networks. Studies of this kind of interactions have indicated difficulties when adjusting the parameters of the SIR to networks. We propose then a differential equation model, the SIR, able to describe the usual SIR model in any network. However, the SIR models needs complete information from the network, which could result in an impractical tool. Because of this, we developed the HMF-MC model, a multi-communities model whose required information consists of the frequencies of connectivity within each community and the number of edges between them. Methods for the early detection of geographic disease clusters of cases or symptoms are important tools in disease surveillance, endowing to the public health agencies the ability to intervene quickly in order to control outbreaks. We discuss two statistics: Kulldorffs spatial scan and the Workflow scan statistic. Both statistics are not ideally fitted for use in epidemics models employing differential equations. We thus propose the WEB statistic, based on the expected number of cases; our experiments showed good results for use in conjunction with models of differential equations. Kulldorffs spatial scan statistic, although well established, still requires improvement, and therefore, we propose a new technique, the datadriven inference. With this set of proposed tools, statistics and models in epidemiology, we hope to contribute to unify some of the current practices of the area.