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On the time-dependent reversible stochastic compartmental model—II. A class ofn-compartment systems

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Abstract

This paper discusses the solution of a generaln-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversiblen-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.

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Author notes

  1. M. Cardenas

    Present address: Dept. of Experimental Statistics, New Mexico State University, 88003, Las Cruces, New Mexico

Authors and Affiliations

  1. Institute of Statistics, Texas A & M University, 77840, College Station, Texas

    M. Cardenas & J. H. Matis

Authors
  1. M. Cardenas
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  2. J. H. Matis
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Cardenas, M., Matis, J.H. On the time-dependent reversible stochastic compartmental model—II. A class ofn-compartment systems. Bltn Mathcal Biology 37, 555–564 (1975). https://doi.org/10.1007/BF02459524

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  • DOI: https://doi.org/10.1007/BF02459524

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