The effect 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 so-called 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 first infective individual in each population. Moreover, we test our method and its accuracy by means of computer simulations.

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CHAPTER 1
Introduction and motivation
Throughout history, infectious diseases have profoundly aected human
development: for example, the Black Death (bubonic plague) that swept
Europe in several waves during the fourteenth century is estimated to have
caused the death of as much as one-third of the European population, re-
curring regularly for more than three centuries [9]. The defeat of the Aztecs
and Incas by invading Spaniards in 1519 and 1532, respectively, can also
be partially attributed to outbreaks of infectious diseases, such as smallpox,
measles and diphtheria, that were imported from Europe and to which the
invaders were mostly immune. It is estimated that the population of Mex-
ico was reduced to one-tenth of its previous size between 1519 and 1530 [9].
Further examples can be found in the book by McNeill [34], to which the
reader interested in the history of epidemics is referred. In view of the im-
portance of infectious diseases, people naturally started investigating their
causes and searching for treatments; one of the oldest accounts is the book
by Hippocrates [25] (see also [31]), who is often referred to as the father of
Western medicine. The existence of microorganisms was not discovered be-
fore the seventeenth century, with the aid of the rst microscopes; however,
their role in the spread of infectious diseases was understood much later [22]:
a rst theory of infectious agents (also called pathogens) was developed only
in the latter part of the nineteenth century [9].
The rst application of mathematical modelling to infectious diseases is
due to Bernoulli [5] (see also [6]), who developed models to understand the
eectiveness of a mass vaccination campaign against smallpox in increasing
life expectancy. The foundations of the mathematical epidemiology of in-
fectious diseases were laid only about a century later by En’ko [17] (see also
[15, 18]), Ross [38], and Kermack and McKendrick [27, 28, 29]; as we shall
see, some of their ideas, such as that of a threshold behaviour, can still be
found in more recent models.
The aim of mathematical epidemiology of infectious diseases is threefold
[13, Ch. 1]: (a) the rst objective is to understand the biological and so-
cial mechanisms of disease spread by means of an appropriate mathematical
structure that models available data; (b) the second goal is prediction of
future epidemics, including assessment of the possible impact of outbreaks
and estimation of associated medical costs; (c) the third aim is to under-
stand how the spread may be controlled, for example through education,
immunization and isolation, by introducing these measures in the model
1

Laurea liv.II (specialistica)

Facoltà: Faculdade de Ciências e Tecnologia

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Autore:
Gianluca Campanella
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