Hi all,
I am trying to represent this mathematical expression into a SDVensim model:
X(t)=∫X(t,r)f(r)dr
The integral is defined between zero and R=2 (for example)
X(t,r) represent a variable (disease incidence) at time t with a rate r, and is defined by the logistic equation X(t)=1/(1+(1Yo/Yo)*EXP(r*t)).
Yo is a parameter constant.
f(r) is a density function, specifically, the exponential distribution: f(r)=EXP(r/d)/d.
d is a parameter constant
Is it possible to translate this into a stockandflows diagram model in Vensim?
Thanks in advance
Maths  Integrals

 Super Administrator
 Posts: 3920
 Joined: Wed Mar 05, 2003 3:10 am
Re: Maths  Integrals
Have you tried implementing this yourself? If yes, feel free to upload the model and explain why you think it's not correct.
1. What is "disease incidence" measured in?
2. What is the rate "r" measured in?
You would usually calculate the rate at which disease occurs, then put this into a level which would be the number of people/animals/whatever that have the disease at a point in time.
1. What is "disease incidence" measured in?
2. What is the rate "r" measured in?
You would usually calculate the rate at which disease occurs, then put this into a level which would be the number of people/animals/whatever that have the disease at a point in time.
Advice to posters seeking help (it really helps us to help you)
http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391
Units are important!
http://www.bbc.co.uk/news/magazine27509559
http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391
Units are important!
http://www.bbc.co.uk/news/magazine27509559
Re: Maths  Integrals
Disease incidence represents the proportion of plants diseased out of the total of a plot, and therefore is dimensionless.
the rate of disease, r, is 1/time (e.g., 1/day)
I create a model with a stock (level) for disease incidence, but I have problems in including the exponential distribution of r on it
the rate of disease, r, is 1/time (e.g., 1/day)
I create a model with a stock (level) for disease incidence, but I have problems in including the exponential distribution of r on it