Acta mathematica scientia, Series B >
ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES
Received date: 2007-03-27
Online published: 2009-07-20
Supported by
This work is supported in part by NSFC and 973 Project
Under a very general condition (TNC condition) we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization
of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
LA Guo-Lie , MA Zhi-Meng , SUN Su-Yong . ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES[J]. Acta mathematica scientia, Series B, 2009 , 29(4) : 1081 -1094 . DOI: 10.1016/S0252-9602(09)60087-4
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