TY - JOUR
T1 - Traveling wave solutions in a two-group SIR epidemic model with constant recruitment
AU - Zhao, Lin
AU - Wang, Zhi Cheng
AU - Ruan, Shigui
N1 - Funding Information:
Zhi-Cheng Wang: Research was partially supported by NNSF of China (11371179). Shigui Ruan: Research was partially supported by NSF (DMS-1412454).
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number R0. More specifically, we prove that (i) when the basic reproduction number R0> 1 , there exists a minimal wave speed c∗> 0 , such that for each c≥ c∗ the system admits a nontrivial traveling wave solution with wave speed c and for c< c∗ there exists no nontrivial traveling wave satisfying the system; (ii) when R0≤ 1 , the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.
AB - Host heterogeneity can be modeled by using multi-group structures in the population. In this paper we investigate the existence and nonexistence of traveling waves of a two-group SIR epidemic model with time delay and constant recruitment and show that the existence of traveling waves is determined by the basic reproduction number R0. More specifically, we prove that (i) when the basic reproduction number R0> 1 , there exists a minimal wave speed c∗> 0 , such that for each c≥ c∗ the system admits a nontrivial traveling wave solution with wave speed c and for c< c∗ there exists no nontrivial traveling wave satisfying the system; (ii) when R0≤ 1 , the system admits no nontrivial traveling waves. Finally, we present some numerical simulations to show the existence of traveling waves of the system.
KW - Basic reproduction number
KW - Constant recruitment
KW - Time delay
KW - Traveling wave solutions
KW - Two-group epidemic model
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U2 - 10.1007/s00285-018-1227-9
DO - 10.1007/s00285-018-1227-9
M3 - Article
C2 - 29564532
AN - SCOPUS:85044221093
VL - 77
SP - 1871
EP - 1915
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
SN - 0303-6812
IS - 6-7
ER -