Q: How can I solve a differential equation that cannot be written in compartmental form?

A: Generate a compartment with an exogenous input:

The corresponding differential equation is then:

q1' = + ex1

The exogenous input ex1  can now be defined equal to any function of the parameters or of q1,or of other compartmental masses or parameters.

For example, the following system of equations can be written using two compartments and two inputs:

q1' = + ex1 = r*q1    -g*q1*q2

q2' = + ex2 = h*q1*q2 - m*q2

These equations describe the well-known Lotka-Volterra model for predator-prey interaction, independently developed by Lotka in 1925 and Volterra in 1926 (see e.g. R. E. Keen and J. D. Spain. Computer Simulation in Biology: A BASIC Introduction. Wiley-Liss, New York, 1992, pp. 113-122, or G. E. Hutchinson. An Introduction to Population Ecology. Yale University Press, New Haven, Connecticut, USA, 1978). 

See also the links:

• How can I solve a compartmental model where the rate constants are time-varying?
• How can I solve a second-order differential equation?

for more information about entering user-defined differential equations in SAAM II.

<< Back to Support Page