Compartmental System
Posted: Fri Apr 02, 1999 12:02 am
I should like to post preliminary responses to those that have answered to my plea for help with developing matrix models of compartmental systems.
Andy,
Thank you very much for your reply. Judging from the table of contents your new book seems to be very interesting and the appendix on spatial dynamics is certainly relevant. I shall try to get my hands on the book as soon as possible.
Colin,
Thank you very much for the Powersim equations for a compartmental matrix model. I would be thankful if you could send me the model so that I can see its structure.
I have not yet digested your comments on constraining the content of compartments with minimum and/or maximum values, but it does seem to be difficult to implement this feature in a Powersim model. Bob Eberlein has mentioned the possibility of doing this in Vensim. He says
"Now you need to figure out how to override the inflow
equation to prevent capacities from overflowing - that
requires allocation logic (Vensim has a function to do this
that might work)".
j-d,
You are right when you say that the problem is not well defined. I wanted to keep the model on a general level and use it as a kernel or module for more specific models. Your comments made me realise that it may be necessary to be more specific about the content of the compartments.
My point of departure was a system of compartments all of which contained various categories or kinds of the same "stuff". Let me take as an example a health service system, such as a hospital, which may be said to consist of a number of compartments, some of which may be physical while others may be conceptual. We may have patients waiting to be admitted, patients under treatment in various wards, patients waiting for discharge in various wards, patients that have been discharged, etc. Patients may "flow" through the system by being admitted, transferred between wards, transferred from the state of being under treatment to the state of waiting for discharge, and by being discharged. This could perhaps be an example of what you call case 1.1. It might be of importance to be able to assign maximum values to compartments in such a system, for example because a hospital ward has a finite size or a finite number of beds.
Each compartment in this system might contain different categories of patients, for example patients with schizophrenia, affective disorders, personality disorders, etc. The rate of flow through the system might be different for these different categories of patients. This could be an example of case 1.2.
I am in point of fact chief of just such a system - a fairly large acute psychiatric hospital with six wards.
Another example might be an epidemiologic system with people in various states of health or disease, and with various categories of people within each state. The rate of transfer between states might be different for different categories of people.
Thank your for the reference.
Kinds regards to all of you,
Oddur
From: "bjobj" <bjobj@online.no>
Andy,
Thank you very much for your reply. Judging from the table of contents your new book seems to be very interesting and the appendix on spatial dynamics is certainly relevant. I shall try to get my hands on the book as soon as possible.
Colin,
Thank you very much for the Powersim equations for a compartmental matrix model. I would be thankful if you could send me the model so that I can see its structure.
I have not yet digested your comments on constraining the content of compartments with minimum and/or maximum values, but it does seem to be difficult to implement this feature in a Powersim model. Bob Eberlein has mentioned the possibility of doing this in Vensim. He says
"Now you need to figure out how to override the inflow
equation to prevent capacities from overflowing - that
requires allocation logic (Vensim has a function to do this
that might work)".
j-d,
You are right when you say that the problem is not well defined. I wanted to keep the model on a general level and use it as a kernel or module for more specific models. Your comments made me realise that it may be necessary to be more specific about the content of the compartments.
My point of departure was a system of compartments all of which contained various categories or kinds of the same "stuff". Let me take as an example a health service system, such as a hospital, which may be said to consist of a number of compartments, some of which may be physical while others may be conceptual. We may have patients waiting to be admitted, patients under treatment in various wards, patients waiting for discharge in various wards, patients that have been discharged, etc. Patients may "flow" through the system by being admitted, transferred between wards, transferred from the state of being under treatment to the state of waiting for discharge, and by being discharged. This could perhaps be an example of what you call case 1.1. It might be of importance to be able to assign maximum values to compartments in such a system, for example because a hospital ward has a finite size or a finite number of beds.
Each compartment in this system might contain different categories of patients, for example patients with schizophrenia, affective disorders, personality disorders, etc. The rate of flow through the system might be different for these different categories of patients. This could be an example of case 1.2.
I am in point of fact chief of just such a system - a fairly large acute psychiatric hospital with six wards.
Another example might be an epidemiologic system with people in various states of health or disease, and with various categories of people within each state. The rate of transfer between states might be different for different categories of people.
Thank your for the reference.
Kinds regards to all of you,
Oddur
From: "bjobj" <bjobj@online.no>