Stochastic compartment models with Prendville growth rates

The Prendville growth mechanism, which assumes a linearly decreasing population growth rate, was generalized to a multicompartment system by Parthasarathy and Kumar. This article shows that their solution is only an approximate one. A diagnostic test is presented to indicate parameter vectors for which this first approximation is not very accurate. A second approximation, which overcomes some limitations of the first one, is developed and illustrated.