Journal
ACTA APPLICANDAE MATHEMATICAE
Volume 175, Issue 1, Pages -Publisher
SPRINGER
DOI: 10.1007/s10440-021-00432-3
Keywords
Nonlocal dispersal; SIR epidemic model; Nonlinear incidence; Minimal wave speed; Traveling wave solution
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Funding
- Natural Science Foundation of China [11771373, 11861065]
- Natural Science Foundation of Xinjiang Province of China [2016D03022]
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This paper investigates the existence of traveling waves in a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, showing that the presence of traveling waves depends on the minimal wave speed c* and basic reproduction number R-0. Numerical simulations confirm the theoretical findings, which improve and generalize existing results.
In this paper, for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence, we study the existence of traveling waves connecting the disease-free equilibrium with endemic equilibrium. We obtain that the existence of traveling waves depends on the minimal wave speed c* and basic reproduction number R-0. That is, if R-0 > 1 and c > c* then the model has a traveling wave connecting the disease-free equilibrium with endemic equilibrium. Otherwise, if R-0 > 1 and 0 < c < c*, then there does not exist the traveling wave connecting the disease-free equilibrium with endemic equilibrium. The numerical simulations verify the theoretical results. Our results improve and generalize some known results.
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