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These are replies submitted by jgray07m

@Carl Love 


I am now curious to look at the same model without the birth and death rates. What all in the code would I have to change for this since now dN/dt = 0 and N = S+I+R ? 

@Carl Love 

Yes, the N is total alive. I guess the parameters could be as follows:

0< beta < 2 

0< gamma < 0.8

I'm less sure about b, delta and d. b is the birth rate, delta is the infected death rate and d Is the natural death rate. I imagine these could all be between 0 and 1? 

@Carl Love 

Would it be reasonable to say that all of the population is susceptible (s(0)=1), 20% are infected (i(0) = .2) and no one is recovered in the beginning (r(0)= 0) ? 

@Carl Love 

I've never heard of an Explore app, but that sounds very helpful for visualizing. Thank you!

@Carl Love 

I've edited the question to maybe make a little more sense. Let me know if it still doesn't. 

@Rouben Rostamian  

This is a really useful visual! Thank you so much. 

@Christian Wolinski 

Thank you! Is there a way to do this with multiple transformations? 

For example 

  T[0] := [abs(z) < 1,  abs(z - 1)<1];

Then the first transformation would be  zeta(z) := (z - z1)/(z - z2);  z1:= exp(Pi*I/3);  z2:= exp(-Pi*I/3); 

and the second transfomation would be tau(zeta) := exp(2*Pi*I/3) * zeta 

I would like to plot each transfomation, so the original, zeta and tau. 

@Carl Love 

Thank you very much! One more question: Is there a reason it won't also work for this case?
A1 := plots:-inequal([evalc(abs(z)) < 1, evalc(abs(z - 1) < 1)], x = -2 .. 2, y = -2 .. 2)

z1 := e^(`&pi;i`/3);

z2 := e^(-`&pi;i`/3);

M := (z - z1)/(z - z2);

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