Modeliranje širenja epidemija SIR modelom

master's thesis

• Title (english): Modeling the spread of epidemics by the SIR model
• Author: Branimir Marijan
• Mentor: Josip Tambača (mentor)
• Committee member: Josip Tambača (predsjednik povjerenstva)
• Committee member: Marko Radulović (član povjerenstva)
• Committee member: Zlatko Drmač (član povjerenstva)
• Committee member: Bojan Basrak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovome diplomskom radu detaljno smo analizirali SIR model i na osnovu podataka s početka epidemije formirali model za prvi i drugi val epidemije. Iz dobivenih rezultata možemo zaključiti da model ne opisuje dobro stvarne podatke, što znači da ćemo u početku epidemije imati jako loša predviđanja o razvoju epidemije. Vjerojatan razlog tome je uvođenje mjera. Nakon toga posvetili smo se modeliranju baziranom na osnovu svih dosadašnjih podataka vezanih uz koeficijent strogosti mjera zaštite protiv... More virusa. Ovakav način interpretacije epidemije daje točnije podatke stoga smo odlučili primjenjivati ovu interpretaciju na ostale modele u ovom radu. Zatim smo detaljno odradili analizu za ASIR model, baziranu na koeficijentu strogosti mjera. Pomoću ASIR modela dobivali smo podatke koji su bliže stvarnim podacima nego u SIR modelu. Nakon toga posvetili smo se SIRS, SIRW i SIR modelu s konstantnim cijepljenjem. Ove modele nismo detaljno analizirali nego smo ih predstavili kao modele koji na zanimljiv način opisuju epidemiju. U SIRS i SIRW modelu možemo uočiti da se populacija zaraženih, oporavljenih i podložnih zarazi javljaju u valovima što je zanimljivo jer se epidemija virusne bolesti COVID-19 u Republici Hrvatskoj također javljala u valovima. U ovim modelima zaraza i dalje kruži populacijom što će se, pored cijepljenja, moguće dogoditi i u stvarnosti. Na kraju možemo zaključiti da ni jedan od navedenih modela neće aproksimirati stvarno stanje potpuno točno. Razlog tomu je možda u nepreciznom određivanju parametara modela, te uvođenju mjera koje mijenjaju parametre. Kod svakog od modela možemo shvatiti na koji način će se ponašati epidemija ukoliko se promijene karakteristike virusa (mutacije virusa koje utječu na trajanje imuniteta) ili ukoliko se promijeni naš stav prema epidemiji (uvođenje ili ukidanje mjera). Less

Abstract (english)

In this thesis, we analyzed the SIR model in detail and based on the data from the beginning of the epidemic formed a model for the first and second wave of the epidemic. From the obtained results we can conclude that the model does not describe well the actual data, which means that at the beginning of the epidemic we will have very poor predictions about the development of the epidemic. Probable reason for this is introduction of epidemic measures. After that, we focused on modeling based on... More all previous data related to the stringency coeffcient. This way of interpreting the epidemic provides more accurate data, so we decided to apply this interpretation to other models in this paper. We then performed a detailed analysis for the ASIR model, based on the stringency coeffcient. Using the ASIR model, we obtained data that are closer to the actual data than in the SIR model. After that, we dedicated ourselves to the SIRS, SIRW and SIR models with constant vaccination. We did not analyze these models in detail, but presented them as models that describe the epidemic in an interesting way. In the SIRS and SIRW model, we can see that the population of infected, recovered and susceptible to infections occurs in waves, which is interesting because the epidemic of the viral disease COVID-19 in the Republic of Croatia also occurred in waves. In these models, the infection is still circulating in the population, which, in addition to vaccination, is possibly to happen in reality. In the end, we can conclude that none of the above models will approximate the actual situation completely accurately. The reason for this may be in the imprecise determination of the model parameters, and the introduction of measures that change the parameters. In each of the models, we can understand how the epidemic will behave if the characteristics of the virus change (virus mutations that affect the duration of immunity) or if our attitude towards the epidemic changes (introduction or abolition of measures).. Less

• Keywords: ASIR model; IRS; SIRW; SIR model; COVID-19; Hrvatska
• Keywords (english): ASIR model; SIRS; SIRW; SIR model; COVID-19; Croatia
• Language: croatian
• URN:NBN: urn:nbn:hr:217:914289
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-09-15 11:56:05