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| Forced Epidemic Waves in a Nonlocal Dispersal SIR Model with Shifting Transmission and Time Delay |
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| KeyWord:Forced waves, shifting transmission, nonlocal dispersal, SIR mod-el, time delay |
| Author Name | Affiliation | | Yilun Han | School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China | | Yan Li | School of Mathematics and Statistics, Xidian University, Xi'an 710071, Shaanxi, China | | Jiabing Wang | School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China
Chongqing CUG Industrial Technology Research Institute, Chongqing 401336, China
Shenzhen Research Institute, China University of Geosciences, Shenzhen 518000, China |
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| Abstract: |
| This paper is concerned with the forced epidemic waves of a nonlocal dispersal SIR model with shifting transmission and time delay. We first demonstrate that the existence of forced waves can be reduced to a fixed point problem. Then by constructing different pairs of upper and lower solutions and using Schauder's fixed point theorem, we establish two types of forced epidemic waves that reveal different state conversions of the disease. Moreover, we prove the nonexistence of forced epidemic waves when the basic reproduction number is less than unity. Finally, some biological explanations for the theoretical results are given in the discussion. |
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