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Periodic Matrix Population Models: Growth Rate, Basic Reproduction Number, and Entropy

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Abstract

This article considers three different aspects of periodic matrix population models. First, a formula for the sensitivity analysis of the growth rate λ is obtained that is simpler than the one obtained by Caswell and Trevisan. Secondly, the formula for the basic reproduction number ℛ0 in a constant environment is generalized to the case of a periodic environment. Some inequalities between λ and ℛ0 proved by Cushing and Zhou are also generalized to the periodic case. Finally, we add some remarks on Demetrius’ notion of evolutionary entropy H and its relationship to the growth rate λ in the periodic case.

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  1. IRD—Institut de Recherche pour le Développement, 32 avenue Henri Varagnat, 93143, Bondy, France

    Nicolas Bacaër

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  1. Nicolas Bacaër
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Correspondence to Nicolas Bacaër.

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Bacaër, N. Periodic Matrix Population Models: Growth Rate, Basic Reproduction Number, and Entropy. Bull. Math. Biol. 71, 1781–1792 (2009). https://doi.org/10.1007/s11538-009-9426-6

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  • DOI: https://doi.org/10.1007/s11538-009-9426-6

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