SIR epidemic model

Reference

https://mp.weixin.qq.com/s/XXfsnuz1--ySFdSGRW3txg

The SIR model

• S for the number susceptible,指未得病者，但缺乏免疫能力，与感病者接触后容易受到感染。
• I for the number of infectious
• R for the number recovered
• N the constancy of population
• β the effective contact rate of the disease: an infected individual comes into contact with βN other individuals per unit time
• γ is the mean recovery rate: that is, 1/γ is the mean period of time during which an infected individual can pass it on. i.e. the transition rate between I and R. If the mean duration of the infection is denoted D, then γ = 1/D
• βI: transition rate between S and I

It's assumed that the permanence of each single subject in the epidemic states is a random variable with exponential distribution.

S(t)+I(t)+R(t)=N (consistent) # t is time