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Spatial‐temporal basic reproduction number and dynamics for a dengue disease diffusion model
Abstract:A reaction‐diffusion system with free boundary is proposed to describe the transmission of the dengue disease from mosquitoes to humans. In addition to the classical basic reproduction number R0, the spatial‐temporal basic reproduction number urn:x-wiley:mma:media:mma5085:mma5085-math-0001 is introduced to determine the persistence and eradication of the disease. Some sufficient conditions for the disease vanishing or spreading are obtained. The disease will go extinct under one of the conditions: the classical basic reproduction number R0 < 1 and the spatial‐temporal basic reproduction number urn:x-wiley:mma:media:mma5085:mma5085-math-0002 with small expanding capability. The spread of the disease in the whole area is possible if urn:x-wiley:mma:media:mma5085:mma5085-math-0003 for some t≥0. Numerical simulations are also given to illustrate the theoretical results.
Keywords:dengue disease  free boundary  reaction‐diffusion system  spatial‐temporal basic reproduction number  spreading and vanishing
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