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• W2067241000 abstract "Spectral bounds of quasi-positive matrices are crucial mathematical threshold parameters in population models that are formulated as systems of ordinary differential equations: the sign of the spectral bound of the variational matrix at 0 decides whether, at low density, the population becomes extinct or grows. Another important threshold parameter is the reproduction number $mathcal{R}$, which is the spectral radius of a related positive matrix. As is well known, the spectral bound and $mathcal{R}-1$ have the same sign provided that the matrices have a particular form. The relation between spectral bound and reproduction number extends to models with infinite-dimensional state space and then holds between the spectral bound of a resolvent-positive closed linear operator and the spectral radius of a positive bounded linear operator. We also extend an analogous relation between the spectral radii of two positive linear operators which is relevant for discrete-time models. We illustrate the general theory by applying it to an epidemic model with distributed susceptibility, population models with age structure, and, using evolution semigroups, to time-heterogeneous population models." @default.
• W2067241000 created "2016-06-24" @default.
• W2067241000 creator A5005719484 @default.
• W2067241000 date "2009-01-01" @default.
• W2067241000 modified "2023-10-11" @default.
• W2067241000 title "Spectral Bound and Reproduction Number for Infinite-Dimensional Population Structure and Time Heterogeneity" @default.
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• W2067241000 doi "https://doi.org/10.1137/080732870" @default.
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