Abstract
In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number at the disease free equilibrium , there exists a critical number c ∗ > 0 such that for each c > c ∗, the system admits a nontrivial traveling wave solution with wave speed c, and for c < c ∗, the system admits no nontrivial traveling wave solution. When , we show that there exists no nontrivial traveling wave solution. In addition, for the case and c > c ∗, we also find that the final sizes of susceptible individuals, denoted by , satisfies , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c ∗ on the parameters.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1287-1325 |
| Number of pages | 39 |
| Journal | Nonlinearity |
| Volume | 30 |
| Issue number | 4 |
| DOIs | |
| State | Published - Feb 14 2017 |
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Keywords
- 35B40
- 35K57
- 35R10
- 92D30
- different infectivity
- different susceptibility
- epidemic model
- latent period Mathematics Subject Classification numbers: 35C07
- traveling wave solutions
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
Cite this
Traveling wave solutions in a two-group epidemic model with latent period. / Zhao, Lin; Wang, Zhi Cheng; Ruan, Shigui.
In: Nonlinearity, Vol. 30, No. 4, 14.02.2017, p. 1287-1325.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Traveling wave solutions in a two-group epidemic model with latent period
AU - Zhao, Lin
AU - Wang, Zhi Cheng
AU - Ruan, Shigui
PY - 2017/2/14
Y1 - 2017/2/14
N2 - In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number at the disease free equilibrium , there exists a critical number c ∗ > 0 such that for each c > c ∗, the system admits a nontrivial traveling wave solution with wave speed c, and for c < c ∗, the system admits no nontrivial traveling wave solution. When , we show that there exists no nontrivial traveling wave solution. In addition, for the case and c > c ∗, we also find that the final sizes of susceptible individuals, denoted by , satisfies , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c ∗ on the parameters.
AB - In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number at the disease free equilibrium , there exists a critical number c ∗ > 0 such that for each c > c ∗, the system admits a nontrivial traveling wave solution with wave speed c, and for c < c ∗, the system admits no nontrivial traveling wave solution. When , we show that there exists no nontrivial traveling wave solution. In addition, for the case and c > c ∗, we also find that the final sizes of susceptible individuals, denoted by , satisfies , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c ∗ on the parameters.
KW - 35B40
KW - 35K57
KW - 35R10
KW - 92D30
KW - different infectivity
KW - different susceptibility
KW - epidemic model
KW - latent period Mathematics Subject Classification numbers: 35C07
KW - traveling wave solutions
UR - http://www.scopus.com/inward/record.url?scp=85016152670&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85016152670&partnerID=8YFLogxK
U2 - 10.1088/1361-6544/aa59ae
DO - 10.1088/1361-6544/aa59ae
M3 - Article
VL - 30
SP - 1287
EP - 1325
JO - Nonlinearity
JF - Nonlinearity
SN - 0951-7715
IS - 4
ER -