SIR Model of Epidemic Spread

U ovome radu proučavat ćemo matematički model prijenosa zarazne bolesti u nekoj populaciji poznat pod nazivom SIR model. Najprije ćemo se baviti osnovnim pretpostavkama koje SIR model zahtjeva te na osnovu njih ćemo konstruirati sustav nelinearnih običnih diferencijalnih jednadžbi proučavanog modela. U drugom poglavlju detaljno ćemo analizirati SIR model. Pokazat ćemo da epidemija uvijek izumire, da možemo izračunati maksimalan broj zaraženih tijekom epidemije te dobiti približnu vrijednost maksimalnog broja osjetljivih osoba u populaciji. Na kraju ćemo uvesti i diskretnu verziju SIR modela koja je vrlo korisna zbog načina prikupljanja podataka iz stvarnog svijeta.In this paper, we will study a mathematical model of infectious disease transmission in a population known as the SIR model. We will first deal with the basic assumptions required by the SIR model and on the basis of which we will construct a system of nonlinear ordinary differential equations of the studied model. In the second chapter, we will analyze the SIR model in detail. We will show that an epidemic is always extinct, that we can calculate the maximum number of infected during an epidemic and obtain an approximate value of the maximum number of susceptible in the population. Finally, we will introduce a discrete version of the SIR model which is very useful due to the way we collect real world data