Mathematical modeling

Question 1

Describe SIR model

Answer 1

Our first model for the infectious diseases is quite simple. It could be improved in the SIR model. In this framework the total population is divided into three subgroups:
the susceptible S
the infectious I
the recovered R

Question 2

equation of SIR model

Answer 2

susceptible ones:
dS
dt = -aSI
Infectious:
dI
dt = aSI -bI
Recovered:
dR
dt = bI
a= rate of birth 
b= rate of death

Question 3

why a certain population may increase?

Answer 3

Food, reproduction

Question 4

why a certain population may decrease?

Answer 4

Disease, no resurses, migration, wars