Abstract
A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number (Formula presented.) is computed by the next generation matrix method. We prove that if (Formula presented.), then the disease-free equilibrium is globally asymptotically stable. If (Formula presented.), the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for (Formula presented.) in terms of the birds movement rate are performed which show that the impacts could be very complicated.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Bulletin of Mathematical Biology |
| DOIs | |
| State | Accepted/In press - Feb 28 2018 |
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Keywords
- Basic reproduction number
- Birds migration
- Mosquitoes
- Patch model
- Stability
- West Nile virus
ASJC Scopus subject areas
- Neuroscience(all)
- Immunology
- Mathematics(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Pharmacology
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics
Cite this
Two-patch model for the spread of West Nile virus. / Zhang, Juping; Cosner, George; Zhu, Huaiping.
In: Bulletin of Mathematical Biology, 28.02.2018, p. 1-24.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Two-patch model for the spread of West Nile virus
AU - Zhang, Juping
AU - Cosner, George
AU - Zhu, Huaiping
PY - 2018/2/28
Y1 - 2018/2/28
N2 - A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number (Formula presented.) is computed by the next generation matrix method. We prove that if (Formula presented.), then the disease-free equilibrium is globally asymptotically stable. If (Formula presented.), the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for (Formula presented.) in terms of the birds movement rate are performed which show that the impacts could be very complicated.
AB - A two-patch model for the spread of West Nile virus between two discrete geographic regions is established to incorporate a mobility process which describes how contact transmission occurs between individuals from and between two regions. In the mobility process, we assume that the host birds can migrate between regions, but not the mosquitoes. The basic reproduction number (Formula presented.) is computed by the next generation matrix method. We prove that if (Formula presented.), then the disease-free equilibrium is globally asymptotically stable. If (Formula presented.), the endemic equilibrium is globally asymptotically stable for any nonnegative nontrivial initial data. Using the perturbation theory, we obtain the concrete expression of the endemic equilibrium of the model with a mild restriction of the birds movement rate between patches. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between the two regions. Some numerical simulations for (Formula presented.) in terms of the birds movement rate are performed which show that the impacts could be very complicated.
KW - Basic reproduction number
KW - Birds migration
KW - Mosquitoes
KW - Patch model
KW - Stability
KW - West Nile virus
UR - http://www.scopus.com/inward/record.url?scp=85042630048&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042630048&partnerID=8YFLogxK
U2 - 10.1007/s11538-018-0404-8
DO - 10.1007/s11538-018-0404-8
M3 - Article
C2 - 29492829
AN - SCOPUS:85042630048
SP - 1
EP - 24
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
ER -