Some new techniques in compartmental modeling

Abstract

C om partm ental models have been widely used in natural and biomedical sciences for several decades. This dissertation proposes and studies some new techniques in th e theory and applications of stochastic com partm ental analysis. C hapters II and III concentrate on m atching transition tim e moments when th e com partm ental process is non-M arkovian. The well-established theory of gam m a com partm ents is generalized to include com partm ents with phasetype transition tim e distributions. Numerical examples from anim al science are given. C hapters IV and V deal w ith com partm ental models w ith reproducing particles. Specifically, C hapter IV investigates some properties concerning the higher order cum ulants of a tw o-com partm ent model known as the steppingstone model, and C hapter V proposes a finite m ixture m ethod for constructing discrete m ultivariate distributions. D istributions so constructed are applied to approxim ate th e joint distribution of the stepping-stone model by m atching first and second order moments. This technique is illustrated by an example from entomology. C hapter VI proposes two problems for further research w ith some prelim inary results presented: (i) m am m illary systems w ith a birth mechanism; and (ii) random transfer rate coefficients in com partm ental analysis. For (i) the m ean value function is studied and for (ii) th e asym ptotic expansion technique is introduced.