2019/01/18 by Primitivo B. Acosta-Humánez, Acosta-Humanez, Primitivo B., José A. Capitán +3
Computer Science · Mathematics · Medicine · #12H05 #35A22 #35C05 #92D25 #FOS: Biological sciences #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models #Polynomial and algebraic computation #Populations and Evolution (q-bio.PE) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1901.06266
openalex publication_date 2019/01/18 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Stochastic birth-death processes are described as continuous-time Markov\nprocesses in models of population dynamics. A system of infinite, coupled\nordinary differential equations (the so-called master equation) describes the\ntime-dependence of the probability of each system state. Using a generating\nfunction, the master equation can be transformed into a partial differential\nequation. In this contribution we analyze the integrability of two types of\nstochastic birth-death processes (with polynomial birth and death rates) using\nstandard differential Galois theory. We discuss the integrability of the PDE\nvia a Laplace transform acting over the temporal variable. We show that the PDE\nis not integrable except for the (trivial) case in which rates are linear\nfunctions of the number of individuals.\n