ON THE BASIC REPRODUCTION NUMBER OF GENERAL BRANCHING PROCESSES

doi:10.1016/S0252-9602(09)60087-4

Abstract

Abstract:

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.

Key words: general branching process, extinction probability, reproduction kernel, spec-tral radius, TNC condition, basic reproduction number, SIR model

CLC Number:

60J80

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.

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