Maths - Integrals

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JoseG
Junior Member
Posts: 4
Joined: Mon Jul 06, 2020 8:19 am
Vensim version: PLE

Maths - Integrals

Hi all,

I am trying to represent this mathematical expression into a SD-Vensim 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+(1-Yo/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 stock-and-flows diagram model in Vensim?

Posts: 3975
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.
http://www.ventanasystems.co.uk/forum/v ... f=2&t=4391

Units are important!
http://www.bbc.co.uk/news/magazine-27509559
JoseG
Junior Member
Posts: 4
Joined: Mon Jul 06, 2020 8:19 am
Vensim version: PLE

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