Abstract
In this paper, a mathematical model of influenza disease with vaccination is formulated to incorporate a spatially homogeneous structure. The explicit formula of the basic reproduction number R0 for the model is obtained. It is shown that the existence and non-existence of the traveling wave solutions for the model are determined completely by the threshold value R0. Here, by introducing an auxiliary system and applying Schauder fixed point theorem, we show that the auxiliary system admits a nontrivial traveling wave solution. And then, by the limit arguments and Arzelà–Ascoli’s theorem, we establish the existence of the traveling wave solutions for the model if R0>1 and c > c*. Furthermore, by the two-sided Laplace transform, we show that the model has no nontrivial traveling wave solutions when R0>1 and c ∈ [0, c*). In addition, we further study the non-existence of the traveling wave solutions for the model when R0<1 and c ≥ 0.
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