On the probability of extinction in a periodic environment

摘要: For a certain class of multi-type branching processes in continuous-time periodic environment, we show that the extinction probability is equal to (resp. less than) 1 if basic reproduction number $$R_0$$ less than (resp. bigger 1. The proof uses results concerning asymptotic behavior cooperative systems differential equations. In epidemiology may be used as time-periodic measure epidemic risk. As an example consider linearized SEIR model and data from recent measles France. Discrete-time models with potential applications conservation biology are also discussed.