| Abstract: |
| In the previous paper (JMB 65, 309-348, 2012), I proposed a new general definition of the basic reproduction number R0 for structured populations in general time-heterogeneous environments. Using the idea of cone spectral radius, we show that our R0 is the spectral radius of the generation evolution operator (GEO) in the time-state space. Next we show that the sign relation holds between R0 and the growth bound of the evolutionary family associated with the linearized population evolution equation, which implies that this R0 is the invasion threshold. We also discuss that this R0 can work as a threshold value for existence of periodic endemic solution for epidemic models in periodic environments. |
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