Abstract
In this paper, we first establish the theory of principal eigenvalues for a large class of partially degenerate, linear and periodic parabolic cooperative systems with time delay. Then we apply these theoretical results to study the global dynamics of a blacklegged tick Ixodes scapularis population model. To present a threshold-type result in terms of basic reproduction ratio R0 for such a model, we also extend the earlier theory of R0 to abstract functional differential equations with time-delayed internal transition.
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