1. On a class of nonlocal SIR models
- Author
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Li Guan, Dong Li, Ke Wang, and Kun Zhao
- Subjects
0303 health sciences ,Class (set theory) ,Applied Mathematics ,01 natural sciences ,Agricultural and Biological Sciences (miscellaneous) ,Communicable Diseases ,Models, Biological ,010305 fluids & plasmas ,03 medical and health sciences ,Feature (computer vision) ,Modeling and Simulation ,0103 physical sciences ,Quantitative Biology::Populations and Evolution ,Applied mathematics ,Humans ,Computer Simulation ,Disease Susceptibility ,Infected population ,Epidemic model ,Epidemics ,030304 developmental biology ,Mathematics - Abstract
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.
- Published
- 2018