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Spatial‐temporal basic reproduction number and dynamics for a dengue disease diffusion model
Author(s) -
Zhu Dandan,
Ren Jingli,
Zhu Huaiping
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5085
Subject(s) - basic reproduction number , reproduction , mathematics , dengue fever , boundary (topology) , transmission (telecommunications) , diffusion , disease transmission , biology , computer science , mathematical analysis , ecology , virology , demography , physics , population , telecommunications , sociology , thermodynamics
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 R 0 , the spatial‐temporal basic reproduction numberR 0 F ( t ) 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 R 0 < 1 and the spatial‐temporal basic reproduction numberR 0 F ( 0 ) < 1 < R 0 with small expanding capability. The spread of the disease in the whole area is possible ifR 0 F ( t ) > 1 for some t ≥0. Numerical simulations are also given to illustrate the theoretical results.