TY - JOUR
T1 - Approximation of epidemics by inhomogeneous birth-and-death processes
AU - Clancy, Damian
AU - O'Neill, Philip D.
PY - 1998
Y1 - 1998
N2 - This paper is concerned with the approximation of a class of open population epidemic models by time-inhomogeneous birth-and-death processes. In particular, we consider models in which the population of susceptibles behaves in the absence of infection as a general branching process. It is shown that for a large initial number of susceptibles, the process of infectives behaves approximately as a time-inhomogeneous birth-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0,tN], where N is the initial number of susceptibles and tN→∞ as N→∞.
AB - This paper is concerned with the approximation of a class of open population epidemic models by time-inhomogeneous birth-and-death processes. In particular, we consider models in which the population of susceptibles behaves in the absence of infection as a general branching process. It is shown that for a large initial number of susceptibles, the process of infectives behaves approximately as a time-inhomogeneous birth-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0,tN], where N is the initial number of susceptibles and tN→∞ as N→∞.
U2 - 10.1016/S0304-4149(97)00092-6
DO - 10.1016/S0304-4149(97)00092-6
M3 - Article
SN - 0304-4149
VL - 73
SP - 233
EP - 245
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -