Matematičko modeliranje demografskih procesa

master's thesis

• Author: Eva Karačić
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-09-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu predstavljeni su matematički modeli koji opisuju promjene u veličini te u dobnom i spolnom sastavu stanovništva uzrokovane demografskim procesima kao što su rađanje, umiranje i migracije. Modeli koji opisuju prirodno kretanje stanovništva predstavljaju temelj za razvoj složenijih modela. Analizom modela prirodnog rasta koji dijeli stanovništvo prema spolu zaključujemo da stanovništvo može postati stabilno, odnosno da je omjer muškaraca i žena u stanovništvu jednak, jedino ako su za oba spola stope nataliteta i mortaliteta jednake. U modelima prirodnog rasta dvaju populacija podijeljenih prema dobi promatramo njihove dobne distribucije u slučajevima kada se njihove dobno specifične stope fertiliteta, odnosno mortaliteta razlikuju. Takvi modeli zanemaruju migracije i pretpostavljaju konstantnu stopu rasta pa se često ne mogu primijeniti u stvarnim situacijama. U posljednjem poglavlju predstavljeni su modeli koji su prikladniji za opisivanje stvarnog kretanja stanovništva. U svrhu modeliranja prema dobi, stanovništvo je podijeljeno u tri dobne skupine te su promatrane interakcije među grupama. Testiranjem linearnog determinističkog modela na stvarnim podacima o kretanju stanovništva Hrvatske, zaključujemo da se testirani model može koristiti za opisivanje kretanja stanovništva u Hrvatskoj.

Abstract (english)

The aim of this thesis is to present various mathematical models describing human population changes in size and changes in age and sex composition due to demographic processes such as births, deaths and migrations. Models of natural growth of the population are the foundation for the development of more complicated models. By analyzing the models of sex composition in which migrations are excluded, we conclude that the only way a population could become stabilized (i.e. to have the same number of males and females) is if the birth and death rates of both sexes are equal. In natural growth models of two populations divided into age groups, we observe their age distributions when their fertility schedules or mortality schedules differ. These models do not take migrations into account and also in these models constant growth rate is assumed, so they often cannot be applied to real populations. In the last chapter, we present mathematical models which are more convenient for describing the actual changes in population. For the purpose of modeling the age composition, the population is divided into three age groups and interactions between these groups are observed. By comparing the results of linear deterministic model with the actual data of the population of Croatia, we conclude that the tested model can be employed to describe population movement in Croatia.

• Keywords: matematički modeli; demografski procesi; linearni deterministički model
• Keywords (english): mathematical models; demographic processes; linear deterministic model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:014217
• Study programme: Title: Finance and Business 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: 2019-05-16 10:03:38