Estimation of infection rate in epidemic models with multiple populations

Dissertação para obtenção do Grau de Mestre em Matemática e Aplicações Especialização em Actuariado, Estatística e Investigação Operacional

The e ect of infectious diseases on human development throughout history is well established, and investigation on the causes of infectious epidemics { and plagues in particular { dates back at least to Hippocrates,the father of Western medicine. The mechanisms by which diseases spread, however, could not be fully understood until the late nineteenth century, with the discovery of microorganisms and the understanding of their role as infectious agents. Eventually, at the turn of the twentieth century, the foundations of the mathematical epidemiology of infectious diseases were laid by the seminal work of En'ko, Ross, and Kermack and McKendrick. More recently, the application of graph theory to epidemiology has given rise to models that consider the spread of diseases not only at the level of individuals belonging to a single population (population models), but also in systems with multiple populations linked by a transportation network(meta-population models). The aim of meta-populations models is to understand how movement of individuals between populations generates the geographical spread of diseases, a challenging goal whose importance is all the greater now that long-range displacements are facilitated by inexpensive air travel possibilities. A problem of particular interest in all epidemic models is the estimation of parameters from sparse and inaccurate real-world data, especially the socalled infection rate, whose estimation cannot be carried out directly through clinical observation. Focusing on meta-population models, in this thesis we introduce a new estimation method for this crucial parameter that is able to accurately infer it from the arrival times of the rst infective individual in each population. Moreover, we test our method and its accuracy by means of computer simulations.