SIR Model Demography

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Great444
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#1
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#1
Does my graph looks right, not sure how to tes if it's correct , I used Euler method.

Thanks
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DFranklin
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It looks reasonable. It's mu, not meow, by the way!
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Great444
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(Original post by DFranklin)
It looks reasonable. It's mu, not meow, by the way!
Why did you think it's reasonable ? Thanks I will correct it.
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DFranklin
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(Original post by Great444)
Why did you think it's reasonable ? Thanks I will correct it.
Just looks roughly reasonable shapes for the diff equations and experience of what these kind of things typically look like.

I've not ever formally done SIR models, but Covid has made experts of us all...
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Great444
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(Original post by DFranklin)
Just looks roughly reasonable shapes for the diff equations and experience of what these kind of things typically look like.

I've not ever formally done SIR models, but Covid has made experts of us all...
Thanks
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Great444
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#6
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(Original post by Great444)
Thanks
(Original post by DFranklin)
It looks reasonable. It's mu, not meow, by the way!
How do I figure out the steady states from the graph?
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DFranklin
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(Original post by Great444)
How do I figure out the steady states from the graph?
Just read them off, surely? (You might want to run over a longer period).

Are you sure you're not supposed to get them from the diff eqns? At steady state the derivatives would all be 0 and you get some simultaneous equations to solve.
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Great444
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(Original post by DFranklin)
Are you sure you're not supposed to get them from the diff eqns? At steady state the derivatives would all be 0 and you get some simultaneous equations to solve.
Yes I am which I did , but I have also to get them from the graph and compare between them, how do I get them from the graph ?Just read them off, surely? (You might want to run over a longer period).
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DFranklin
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(Original post by Great444)
Yes I am which I did , but I have also to get them from the graph and compare between them, how do I get them from the graph ?Just read them off, surely? (You might want to run over a longer period).
Was going to be a bit more explicit and found myself doubting your graph after all.

Shouldn't S+I+R always sum to 1? (Looking at the DEs it seems the sum of the 3 derivatives should be 0).
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Great444
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(Original post by DFranklin)
Was going to be a bit more explicit and found myself doubting your graph after all.

Shouldn't S+I+R always sum to 1? (Looking at the DEs it seems the sum of the 3 derivatives should be 0).
Check now
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DFranklin
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#11
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(Original post by Great444)
Check now
Still doesn't look right. If S is almost zero dS/dt should be mu (and so S should be growing).

Note that I'm merely eyeballing your charts. I'm not going to do my own simulation just to troubleshoot yours.
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ghostwalker
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#12
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#12
(Original post by DFranklin)
Still doesn't look right. If S is almost zero dS/dt should be mu (and so S should be growing).

Note that I'm merely eyeballing your charts. I'm not going to do my own simulation just to troubleshoot yours.
Great444 for info.

wadr, I'd run the simulation on Excel and got identical results to the OP.

Although S gets close to zero, the \beta S I term of dS/dt is of the same order of magnitude as \mu at that point.
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Great444
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#13
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#13
(Original post by DFranklin)
Still doesn't look right. If S is almost zero dS/dt should be mu (and so S should be growing).

Note that I'm merely eyeballing your charts. I'm not going to do my own simulation just to troubleshoot yours.
Good idea, I'm waiting for the result I think it's right but not sure 100%
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Great444
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#14
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(Original post by ghostwalker)
Great444 for info.

wadr, I'd run the simulation on Excel and got identical results to the OP.

Although S gets close to zero, the \beta S I term of dS/dt is of the same order of magnitude as \mu at that point.
Does this mean it's correct?
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ghostwalker
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(Original post by Great444)
Does this mean it's correct?
Probably, or we both made the same mistake.
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ghostwalker
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#16
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(Original post by Great444)
Does this mean it's correct?
Although it shouldn't effect the steady state values, changing the step size does impact the graphs.

E.g. h=0.1 gives
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Great444
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(Original post by ghostwalker)
Probably, or we both made the same mistake.
I don't think so.
Any idea about this ? Using suitable sources find a disease that you believe can be modelled accurately with the SIR model with demography.
Thank you
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ghostwalker
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(Original post by Great444)
I don't think so.
Any idea about this ? Using suitable sources find a disease that you believe can be modelled accurately with the SIR model with demography.
Thank you
None. Think you might need a biologist on that one.
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Great444
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#19
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#19
(Original post by ghostwalker)
Although it shouldn't effect the steady state values, changing the step size does impact the graphs.

E.g. h=0.1 gives
S and I graph here look different than my graphs
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Great444
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#20
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#20
(Original post by Great444)
S and I graph here look different than my graphs
Similar to this one, I thought I have to divide mu by (70*365)
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