Bulletin of Mathematical Biology

, Volume 43, Issue 6, pp 651–664 | Cite as

Compartmental models with multiple sources of stochastic variability: The one-compartment models with clustering

  • James H. Matis
  • Thomas E. Wehrly


Previous compartmental models have introduced variability either at the particle or at the replicate level. This paper integrates both types of variability through the concept of clustering. The paper develops two different, general clustered models, each with time-dependent hazard rates for the clusters and for the particles within the clusters, and each with random initial number and sizes of clusters. The coefficient of variation of the total number of particles,CV[X(t)], for either model is shown to be bounded below, under very broad conditions, by the coefficient of variation of the initial number of clusters,CV[c(0)]. This high relative variability of the clustered models makes them potentially very useful in kinetic modeling. In many applications, binding and clustering are common phenomena, and two applications of the models to such phenomena are breifly outlined.


Hazard Rate Compartmental Model Probability Generate Function Tracer Molecule Stochastic Compartmental Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Society for Mathematical Biology 1981

Authors and Affiliations

  • James H. Matis
    • 1
  • Thomas E. Wehrly
    • 1
  1. 1.Institute of StatisticsTexas A&M UniversityCollege StationUSA

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