1) The number of people n remains unchanged, and the proportions of healthy people, patients and migrants are S (t), I (t) and R (t) respectively.

2) Daily contact rate λ and daily cure rate λ? 0? 8. The number of contacts during infection σ = λ/? 0? eight

Model building:

s(t)+i(t)+r(t)= 1

di/dt=λsi-？ 0? 8i

ds/dt=-λsi

I(0)= i0； s(0)=s0