Modeliranje zaraze

undergraduate thesis

• Title (english): Modelling infectious disease
• Author: Petra Tomulić
• Mentor: Ivica Gusić (mentor)
• Committee member: Ivica Gusić (predsjednik povjerenstva)
• Committee member: Miroslav Jerković (član povjerenstva)
• Committee member: Dajana Kučić Grgić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2020-07-07, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Opisani su glavni epidemiološki matematički modeli u zatvorenoj populaciji: SIS model, SIR model i SIRS model. Detaljno je razrađen SIR model koji se temelji na sustavu od tri obične diferencijalne jednadžbe. U modelu se pojavljuju nezavisna varijabla t (vrijeme) i tri zavisne varijable (S – broj osoba podložnih zarazi, I – broj zaraženih osoba, R – broj oporavljenih osoba, s imunitetom) i dva pozitivna parametra: stopa zarazljivosti, β i stopa ozdravljenja, α. Sustav se numerički rješava pomoću programskog paketa MATLAB R2020a na primjeru podataka o gripi u jednom engleskom internatu za dječake. Rezultati su prikazani grafički i računski za nekoliko različitih vrijednosti parametara i uz fiksirane realne početne uvjete. Pokazano je da optimalni parametri koji su uzeti iz literature, najbolje opisuju danu situaciju. Ukoliko se parametar α smanji dva puta, tj. ako je stopa ozdravljenja dva puta manja, primjećuje se da se maksimalan broj zaraženih u teorijskom modelu bitno poveća i da zaraza unutar populacije traje duže. Daljnjom parametarskom analizom uočeno je da već mala promjena vrijednosti parametara osjetno utječe na dinamiku koju opisuje model.

Abstract (english)

This paper contains a description of basic epidemiological models: SIS model, SIR model and SIRS model. SIR model, based on three differential equations, is thoroughly analysed. The model contains independent variable t (time), three dependent variables (S - susceptibles, I - infected, R - recovered) and two positive parameters: the infection rate, β and the recovery rate, α. The system is solved numerically with the software package MATLAB R2020a using the data gathered from an English board school for boys. The results are presented graphically and numerically for various sets of parameters and with fixed initial conditions. Optimal parameters are taken from referred literature. It is concluded that these parameters describe given situation in the best way. If the value of α is reduced two times, it is noticeable that maximum number of infected people is higher in theoretical situation compared to the numbers obtained in the realistic case. Also, transmission of the infection lasts longer if the value of recovery rate is increased. Parameter analysis shows that even small changes of parameters’ values can have impact on dynamics of the model.

• Keywords: matematički model; epidemiologija; gripa; SIR model; SIS model; SIRS model
• Keywords (english): mathematical model; epidemiology; influenza; SIR model; SIS model; SIRS model
• Language: croatian
• URN:NBN: urn:nbn:hr:149:885746
• Study programme: Title: Environmental Engineering - Undergraduate study; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2023-05-09 09:49:16