Μαθηματική προτυποποίηση για τη μετάδοση μολυσματικών ασθενειών

Γαλάνη, Κωνσταντίνα

Mathematical modelling for the transmission of infectious diseases

Master Thesis

Author

Γαλάνη, Κωνσταντίνα

Date

2026-01

Abstract

This master’s thesis focuses on the mathematical modeling of the spread of infectious diseases, aiming to understand the transmission of a virus within a population. Various models have been developed to describe the spread of an infection, which are classified into deterministic and stochastic models. Deterministic models include the epidemiological SIR and SEIR models, while stochastic models comprise continuous- and discrete-time Markov models, as well as branching processes. In this thesis, a theoretical study of the aforementioned models is carried out, along with the application of some of them to real-world data, with the aim of understanding and capturing the evolution of infectious diseases under real conditions. More specifically, Chapter 1 provides an introduction to epidemiology, including historical background, types of epidemiological studies, and risk measures. Chapter 2 develops the theory of stochastic processes, with an emphasis on discrete- and continuous-time Markov processes. In Chapter 3, branching processes are presented, focusing on the theory of discrete- and continuous-time branching process models. Subsequently, Chapter 4 offers a theoretical analysis of the deterministic models used in epidemiology, namely the SIR and SEIR models, as well as the SI and SIS models. In Chapter 5, the SIR and SEIR models are applied to data from the first wave of the COVID-19 pandemic in Greece, Italy, Spain, and Switzerland. Finally, Chapter 6 presents a summary of the thesis and the conclusions drawn from the study.

Postgraduate Studies Programme

Εφαρμοσμένη Στατιστική

Department

Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

Number of pages

178

Language

Greek

URI

https://dione.lib.unipi.gr/xmlui/handle/unipi/18831

Collections

Τμήμα Στατιστικής και Ασφαλιστικής Επιστήμης

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Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα