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## #1 2010-07-19 12:32:00

pococz
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### continuous to discrete

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 (2010-07-19 12:32:40)

## #2 2010-07-19 17:11:23

bobbym

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### Re: continuous to discrete

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #3 2010-07-20 20:05:05

pococz
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### Re: continuous to discrete

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..

## #4 2010-07-21 00:25:47

bobbym

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### Re: continuous to discrete

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #5 2010-07-21 15:32:55

pococz
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### Re: continuous to discrete

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)...

## #6 2010-07-21 17:18:56

bobbym

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### Re: continuous to discrete

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #7 2010-07-21 17:29:24

pococz
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### Re: continuous to discrete

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

## #8 2010-07-21 18:10:56

bobbym

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### Re: continuous to discrete

Hi;

I am already stuck on how he derived:

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

## #9 2010-07-21 23:14:24

pococz
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### Re: continuous to discrete

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

## #10 2010-07-22 01:17:29

bobbym

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### Re: continuous to discrete

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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.

pococz
Novice

Offline

## #12 2010-07-25 00:35:47

bobbym

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### Re: continuous to discrete

Hi pococz;

Okay you got me, what is a semi discretization?

In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.