Abstract
Modelling the spread of avian influenza by migratory birds between the winter refuge ground and the summer breeding site gives rise to a periodic system of delay differential equations exhibiting both the cooperative dynamics (transition between patches) and the predator-prey interaction (disease transmission within a patch). Such a system has two important basic reproductive ratios, each of which being the spectral radius of a monodromy operator associated with the linearized subsystem (at a certain trivial equilibrium): the (ecological) reproduction ratio R c0 for the birds to survive in the competition between birth and natural death, and the (epidemiological) reproduction ratio R p0 for the disease to persist. We calculate these two ratios by our recently developed finite-dimensional reduction and asymptotic techniques, and we show how these two ratios characterize the nonlinear dynamics of the full system.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 45, Proceedings of the Sixth International Conference on Differential and Functional Differential Equations and International Workshop “Spatio-Temporal Dynamical Systems” (Moscow, Russia, 14–21 August, 2011). Part 1, 2012.
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Wang, XS., Wu, J. Periodic Systems of Delay Differential Equations and Avian Influenza Dynamics. J Math Sci 201, 693–704 (2014). https://doi.org/10.1007/s10958-014-2020-y
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DOI: https://doi.org/10.1007/s10958-014-2020-y