Abstract
Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector–host disease transmission dynamics. In this paper, we propose vector–host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models. The analytic results reveal that the global dynamics of such vector–host disease models with time delays are completely determined by the basic reproduction number. Some specific cases with discrete delay are studied and the corresponding results are improved.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-27 |
| Number of pages | 27 |
| Journal | Journal of Mathematical Biology |
| DOIs | |
| State | Accepted/In press - Sep 22 2016 |
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Keywords
- Basic reproduction number
- Global stability
- Liapunov functional
- Time delay
- Vector–host disease model
ASJC Scopus subject areas
- Modeling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
Cite this
Global properties of vector–host disease models with time delays. / Cai, Li Ming; Li, Xue Zhi; Fang, Bin; Ruan, Shigui.
In: Journal of Mathematical Biology, 22.09.2016, p. 1-27.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Global properties of vector–host disease models with time delays
AU - Cai, Li Ming
AU - Li, Xue Zhi
AU - Fang, Bin
AU - Ruan, Shigui
PY - 2016/9/22
Y1 - 2016/9/22
N2 - Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector–host disease transmission dynamics. In this paper, we propose vector–host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models. The analytic results reveal that the global dynamics of such vector–host disease models with time delays are completely determined by the basic reproduction number. Some specific cases with discrete delay are studied and the corresponding results are improved.
AB - Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector–host disease transmission dynamics. In this paper, we propose vector–host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models. The analytic results reveal that the global dynamics of such vector–host disease models with time delays are completely determined by the basic reproduction number. Some specific cases with discrete delay are studied and the corresponding results are improved.
KW - Basic reproduction number
KW - Global stability
KW - Liapunov functional
KW - Time delay
KW - Vector–host disease model
UR - http://www.scopus.com/inward/record.url?scp=84988697823&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84988697823&partnerID=8YFLogxK
U2 - 10.1007/s00285-016-1047-8
DO - 10.1007/s00285-016-1047-8
M3 - Article
C2 - 27659303
AN - SCOPUS:84988697823
SP - 1
EP - 27
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
SN - 0303-6812
ER -