[Mathematics in Medicine Based Around Epidemic]

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ACKNOWLEDGEMENT

I would take this opportunity to thank my research supervisor, family and friends for their support and guidance without which this research would not have been possible.

DECLARATION

I, [type your full first names and surname here], declare that the contents of this dissertation/thesis represent my own unaided work, and that the dissertation/thesis has not previously been submitted for academic examination towards any qualification. Furthermore, it represents my own opinions and not necessarily those of the University.

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Abstract

Here we present the Global Epidemic and Mobility (GLEaM) model that integrates socio-demographic and population mobility data in a spatially structured stochastic disease approach to simulate the spread of epidemics at the worldwide scale. We discuss the flexible structure of the model that is open to the inclusion of different disease structures and local intervention policies. This makes GLEaM suitable for the computational modeling and anticipation of the spatio-temporal patterns of global epidemic spreading, the understanding of historical epidemics, the assessment of the role of human mobility in shaping global epidemics, and the analysis of mitigation and containment scenarios.

Table of Contents

CHAPTER 1: INTRODUCTION6

CHAPTER 2: LITERATURE REVIEW10

Mathematics in Medical Imaging12

Mathematics as innovation factor15

Mathematics in Cardiology and Cardial Surgery16

Mathematics as innovation factor18

Perspective: the virtual heart19

Disease metaphors in new epidemics20

Metaphors, medicine and policy21

Case Example24

UK SARS coverage26

SARS and its metaphors28

CHAPTER 3: METHODOLOGY29

Population layer30

Mobility layers32

Worldwide Airport Network33

Commuting networks33

CHAPTER 4: MATHEMATICAL MODEL36

Epidemic and mobility dynamics38

Effective force of infection40

CHAPTER 5: SIMULATION AND IMPLEMENTATION43

Long distance travel43

Compartment transitions44

Aggregation and post-processing45

Model calibration and simulation47

Conclusions52

REFERENCES54

APPENDIX57

CHAPTER 1: INTRODUCTION

The increasing computational and data integration capabilities witnessed in recent years have enabled the development of computational epidemic models of great complexity and realism. Generally accepted methodologies are represented by very detailed agent-based models and large-scale spatial meta-population models. These two major classes of computational models have different resolutions and limitations. Agent-based models are stochastic, spatially explicit, discrete-time, simulation models where the agents represent single individuals (Barrat, 2004, 3747).

The infection can spread among individuals by contacts within household members, within school and workplace colleagues and by random contacts in the general population. One of the key features of the model is the characterisation of the network of contacts among individuals based on a realistic model of the socio-demographic structure of the population (see for instance for a comparison between several models based on this approach). The second scheme relies on meta-population structured models that consider the system divided into geographical regions defining a subpopulation network where connections among subpopulations represent the individual fluxes due to the transportation and mobility infrastructures. Infection dynamics occurs inside each subpopulation and is described by compartmental schemes that depend on the specific etiology of the disease and the containment interventions considered (Shortridge, 1997, 637).

Agent-based models provide a very rich data scenario but the computational cost and most importantly the need for very detailed input data has limited their use to a few country level scenarios so far, up to continent level. On the opposite side, the structured meta-population models are fairly scalable and can be conveniently used ...