SIR model

Epidemiološki modeli širjenja nalezljivih bolezni so matematični modeli, ki poskušajo pojasniti, kako se širijo nalezljive bolezni. Eden najbolj znanih modelov je model SIR. Leta 1927 sta ga oblikovala Kermack in McKendrick, zapišemo pa ga lahko s sistemom treh diferencialnih enačb. Proučevanje le-teh nam omogoča napovedovanje obnašanja določene bolezni v populaciji in s tem napoved, ali bo epidemija izbruhnila ali ne. V diplomskem delu predstavimo in analiziramo omenjeni model ter poskušamo napovedati obnašanje določene bolezni v populaciji. Vpeljemo najpomembnejši faktor v matematični epidemiologiji, tj. osnovni reprodukcijski faktor, ki nam pove, ali bo prišlo do izbruha epidemije ali ne. Poleg modela SIR predstavimo še druge modele širjenja nalezljivih bolezni, ki vključujejo dodatne razrede. Ti modeli nam omogočajo natančnejše proučevanje širjenja določene bolezni.Epidemic models for the spread of infectious diseases are mathematical models that try to explain the spread of infectious diseases. The most famous mathematical model for the spread of an infectious disease is the SIR model. It was first publushed by Kermack in McKendrick in 1927 and is formulated as a system of differential equations. Study of epidemic models enables us to predict the outcome of a disease spread within population and by that gives us a prediction wheather the disease dies out or turns into an epidemic. In this diploma paper we analyze the SIR model and try to predict the outcome of a certain disease in a population. We define the most important quantity in mathematical epidemiology, the basic reproduction number, which/that determines wheather there is an epidemic or not. Besides the SIR model, we introduce other disease spread models which in its analysis include additional population classes. These models give a more accurate prediction of a disease spread