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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

hello.. i'm just confused about how to transform continuous form(differential equation) to discrete form

ex :

dS/dt = (alpha)*n- (alpha)*S - (beta)*S*I

dI/dt = (beta)*S*I- (gamma)*I

dR/dt = (gamma)*I

become

S = ??

I = ??

R =??

thank you very much...

*Last edited by pococz (2010-07-18 14:32:40)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi pococz;

I am a little confused here. As far as I know you can convert a DE ( continuous ) into a Recurrence ( discrete ), you don't convert the constants. I don't understand what you are trying to accomplish. Can you give more? What textbook or webpage are you studying from?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

i'm sorry.. i've just read epidemic modelling books by daley and gani... there are some discrete model on that book...

my exercise is to analyze the fixed point stability from discrete time epidemic model.but the model on that book can't be anlyzed, so i think to change from the continuous model to discrete model.. i'm so thankful..

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi pococz;

I have that book, please tell me where in it are you exactly working! Maybe I can help out.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

ooohh.. you have that book. please open the 50th page.. there is a deterministic model in discrete time for epidemics problem. can you show me how to find the stability of the model. especially if you can solve the stability depends on the Ro (reproduction number)...

so please.. help me dude..

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi pococz;

I have the 1999 edition. My pahe 50 has a figure 2.12 on the top. Am I in the right spot?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

yes.. you are on the spot... thank's

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi;

I am already stuck on how he derived:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

yup.. but from the first model at above (continuous model ) can you change it to discrete form (like in 50th page)..

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi;

Do you have some initial conditions for post#1. If I have initial conditions I might be able to.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**pococz****Member**- Registered: 2010-07-18
- Posts: 8

hmmm.... how about semi discretization??

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,257

Hi pococz;

Okay you got me, what is a semi discretization?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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