Abstract
A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two-patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, themodel has a unique Patch i-only boundary equilibrium (i = 1, 2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i-only boundary equilibrium is locally asymptotically stablewhenever the invasion reproduction number of Patch 3 - i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi-patch dynamics to a single-patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 349-364 |
| Number of pages | 16 |
| Journal | Mathematical Methods in the Applied Sciences |
| Volume | 38 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 30 2015 |
| Externally published | Yes |
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Keywords
- Equilibria
- Quarantine
- Reproduction number
- Stability
ASJC Scopus subject areas
- Mathematics(all)
- Engineering(all)
Cite this
Dynamics analysis of a quarantine model in two patches. / Safi, Mohammad A.; Gumel, Abba.
In: Mathematical Methods in the Applied Sciences, Vol. 38, No. 2, 30.01.2015, p. 349-364.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dynamics analysis of a quarantine model in two patches
AU - Safi, Mohammad A.
AU - Gumel, Abba
PY - 2015/1/30
Y1 - 2015/1/30
N2 - A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two-patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, themodel has a unique Patch i-only boundary equilibrium (i = 1, 2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i-only boundary equilibrium is locally asymptotically stablewhenever the invasion reproduction number of Patch 3 - i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi-patch dynamics to a single-patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property).
AB - A new deterministic model for assessing the impact of quarantine on the transmission dynamics of a communicable disease in a two-patch community is designed. Rigorous analysis of the model shows that the imperfect nature of quarantine (in the two patches) could induce the phenomenon of backward bifurcation when the associated reproduction number of the model is less than unity. For the case when quarantined susceptible individuals do not acquire infection during quarantine, the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, themodel has a unique Patch i-only boundary equilibrium (i = 1, 2) whenever the associated reproduction number for Patch i is greater than unity. The unique Patch i-only boundary equilibrium is locally asymptotically stablewhenever the invasion reproduction number of Patch 3 - i is less than unity (and the associated reproduction number for Patch i exceeds unity). The model has at least one endemic equilibrium when its reproduction number exceeds unity (and the disease persists in both patches in this case). It is shown that adding multi-patch dynamics to a single-patch quarantine model (which allow the quarantine of susceptible individuals) in a single patch does not alter its quantitative dynamics (with respect to the existence and asymptotic stability of its associated equilibria as well as its backward bifurcation property).
KW - Equilibria
KW - Quarantine
KW - Reproduction number
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84923282096&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84923282096&partnerID=8YFLogxK
U2 - 10.1002/mma.3072
DO - 10.1002/mma.3072
M3 - Article
AN - SCOPUS:84923282096
VL - 38
SP - 349
EP - 364
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
SN - 0170-4214
IS - 2
ER -