Euler method and SIR model (Excel)

[krisjoergensen]

Hey guys

I have this assigment for tomorrow and its my final assigment combined with 2 classes and I'm almost done but I'm stuck at this spot.

The question i have to answer is in another language but i will try to translate and explain it to english.

"Describe the S-I-R model of the spread of an epidemic, and by using the Euler method, explain how the model can be applied to the cholera epidemic. Involve calculations with data from the cholera epidemic in 1853."

I know there was 130000 inhabitants in Copenhagen in 1853 where 7219 was infected and 4737 out of the 7219 died. The whole cholera epidemic lasted for 16 weeks and started from 12 June to 1 October.

So in S-I-R model the S = 130000 inhabitants, I = 7219, R = the rest which is the survivors from infection + rest of the inhabitants which is 130000 - 4737 = 125263 inhabitants after the epidemic or 7219 - 4737 = 2482 who survived after catching the disease.

In the first week of the epidemic there was 5 who catched the disease and 3 of them died. so already in 1 first 5 people catched it and 3 of them died. so my S = 139995, I = 5, R = 3.

I don't know how to set this up and I'm supposed to do this in Excel but I have no clue.. Hope there is someone in here who really can help me i would appreciate it a lot and it would mean everything for me..

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/10859444_10205478304547955_1562106692_n.jpg?
oh=354d778b99697123c7aa952ea416346c&oe=54989C4C&__gda__=1419290845_e120699950fbccc54094cfd91c999db1

The link is an example on how to do it in excel but i don't know what my "dt" is or a or c or d on that example.

 

[HallsofIvy]

It sounds like you are saying that you are required to solve a differential equation using "Euler's method" but do not know what Euler's method is. Euler's method is a numerical method for approximating the solution to a differential equation. Given the equation $\displaystyle \frac{dx}{dt}= f(x, t)$ with initial value x(0), write the equation as $\displaystyle dx= f(x, y)dt$. Now, instead of treating dt as an "infinitesimal", choose some time change step, say one day, one week, or one month, whatever you think is reasonable. You have to choose dt yourself. Given the initial value, calculate dx= f(x(0), 0)dt and then $\displaystyle x_1(t_1)$ is x(0) plus that step: $\displaystyle x_1(t_1)= x(0)+ f(x(0), 0)dt$, $\displaystyle t_1= 0+ dt$. Now calculate a new dx: $\displaystyle dx= f(x_1(t_1), t_1)dt$ and add that dx to $\displaystyle x_1(t_1)$ to find the next value of x, $\displaystyle x_2(t_2)= x_1(t_1)+ f(x_1(t_1), t_1)dt$, $\displaystyle t_2= t_1+ dt$ and continue.

No one here can tell you what the values of "a", "c", and "d" are in Excel= those values depend not only on the problem but how you choose to set it up in Excel.

 

[krisjoergensen]

It sounds like you are saying that you are required to solve a differential equation using "Euler's method" but do not know what Euler's method is. Euler's method is a numerical method for approximating the solution to a differential equation. Given the equation $\displaystyle \frac{dx}{dt}= f(x, t)$ with initial value x(0), write the equation as $\displaystyle dx= f(x, y)dt$. Now, instead of treating dt as an "infinitesimal", choose some time change step, say one day, one week, or one month, whatever you think is reasonable. You have to choose dt yourself. Given the initial value, calculate dx= f(x(0), 0)dt and then $\displaystyle x_1(t_1)$ is x(0) plus that step: $\displaystyle x_1(t_1)= x(0)+ f(x(0), 0)dt$, $\displaystyle t_1= 0+ dt$. Now calculate a new dx: $\displaystyle dx= f(x_1(t_1), t_1)dt$ and add that dx to $\displaystyle x_1(t_1)$ to find the next value of x, $\displaystyle x_2(t_2)= x_1(t_1)+ f(x_1(t_1), t_1)dt$, $\displaystyle t_2= t_1+ dt$ and continue.

No one here can tell you what the values of "a", "c", and "d" are in Excel= those values depend not only on the problem but how you choose to set it up in Excel.

Can you give me an example with theoretical values? I have to prove that SIR can be used on epidemics like cholera but i have to choose my own values for S(t), I(t) and R(t).. I been trying to change the values for S, I, R, a, c, d but i can't make it look like the numbers i have from the cholera

 

[stapel]

Can you give me an example with theoretical values?

Can somebody give you an example of what with theoretical values? Are you wanting someone to take your data (?), take the model (?) you're supposed to use, apply the method(s) they told you to use, plug in some other sort of data into something somewhere, and provide you with a completed Excel spreadsheet and full report?

Please be specific. Thank you.