On a class of nonlocal SIR models

  • Li Guan
  • Dong Li
  • Ke Wang
  • Kun ZhaoEmail author


We revisit the classic susceptible–infected–recovered (SIR) epidemic model and one of its recently developed nonlocal variations. We introduce several new approaches to derive exact analytical solutions in the classical situation and analyze the corresponding effective approximations in the nonlocal setting. An interesting new feature of the nonlocal models, compared with the classic SIR model, is the appearance of multiple peak solutions for the infected population. We provide several rigorous results on the existence and non-existence of peak solutions with sharp asymptotics.


Susceptible–infected–recovered model Analytical solution Peak solution 

Mathematics Subject Classification




The authors would like to thank the anonymous referee(s) for careful reading and thoughtful comments to improve the quality of the paper. DL is partially supported by Hong Kong RGC Grant GRF 16307317 and 16309518, KW is partially supported by HKUST Initiation Grant IGN16SC05, KZ is partially supported by Simons Foundation Collaboration Grant for Mathematicians 413028.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsTulane UniversityNew OrleansUSA
  2. 2.Department of MathematicsThe Hong Kong University of Science and TechnologyKowloonHong Kong

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