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Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism

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Abstract

We are concerned with a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism in a one dimensional bounded domain. We first prove the existence of endemic equilibrium (EE) whenever the basic reproduction number is greater than unity. We then focus on the asymptotic behavior of EE in three cases: large advection; small diffusion of the susceptible population; small diffusion of the infected population. Our main results show that the asymptotic profiles of the susceptible and infected populations obtained here are very different from that of the corresponding system without advection and that of the system with standard incidence infection mechanism. Thus, the effects of advection and different infection mechanisms are substantial on the spatial distribution of infectious disease; our findings bring novel insight into the disease control strategy.

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Authors and Affiliations

  1. Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, Heilongjiang Province, China

    Renhao Cui

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong Province, China

    Huicong Li

  3. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China

    Rui Peng

  4. Chern Institute of Mathematics & LPMC, Nankai University, Tianjin, 300071, China

    Maolin Zhou

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  1. Renhao Cui
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  2. Huicong Li
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  3. Rui Peng
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  4. Maolin Zhou
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Correspondence to Maolin Zhou.

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Communicated by P. Rabinowitz.

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M. Zhou was partially supported by National Key R&D Program of China (2020YFA0713300) and Nankai Zhide Foundation. R. Cui was supported by Natural Science Foundation of Heilongjiang Province (No. LH2020A012). H. Li was supported by NSF of China (Nos. 11701180, 11971498). R. Peng was supported by NSF of China (No. 11671175), the Priority Academic Program Development of Jiangsu Higher Education Institutions, Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (No. PPZY2015A013) and Qing Lan Project of Jiangsu Province.

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Cui, R., Li, H., Peng, R. et al. Concentration behavior of endemic equilibrium for a reaction–diffusion–advection SIS epidemic model with mass action infection mechanism. Calc. Var. 60, 184 (2021). https://doi.org/10.1007/s00526-021-01992-w

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