Model thinking lecture note (4)

Percolation model

If the model can be seen as a net, then we can use this model. For example, in information transmission, the y axis can be how many people will hear your information and the x axis can be what's the value of our information. Now we can see a threshold of x axis there, below the threshold ,it seems that nobody would know your information , over the threshold, and we will find that the probability of people who would hear your information would increase rapidly.

Diffusion model

It has the equation like below:

W(t+1) = W(t) + c*N * tau * (W(t)/N) * ((N-W(t))/N )

W(t) : how many people are infected at time t.

c: transmission rate

tau: infected rate

N:how many people are there in the model

 it seems a little sophisticated , And we just remember that : it's like the percolation model except it has no threshold.

SIR model

It has the equation like below:

W(t+1) = W(t) + c*N * tau * (W(t)/N) * ((N-W(t))/N ) - alpha * W(t) 

It looks like the equation in diffusion model except it minus alpha * W(t)

And we define the threshold R0

R0 = c * tau / alpha

R0 < 1 , W(t) will be zero otherwise W(t) will be its max value N.

And we just remember that there is a threshold, lower than the threshold we shouldn't worry.   

Kinds of tips

(1) discrete tip

It means a small vibration in input can have a strong effect in the end.

(2)contextual tip

Just like the change in the threshold in the percolation model.

How to measure tips?

(1) 

D means how many types of things 

(2)

S shows how many information we know to identify the outcome.

How many years to take to double the GDP?

There's a formula to compute this :

72 / x (x stands for x% increase every year)