Abstract
For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 205-227 |
| Number of pages | 23 |
| Journal | Mathematical Biosciences |
| Volume | 75 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1985 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics
Cite this
Stability of the endemic equilibrium in epidemic models with subpopulations. / Hethcote, Herbert W.; Thieme, Horst.
In: Mathematical Biosciences, Vol. 75, No. 2, 1985, p. 205-227.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stability of the endemic equilibrium in epidemic models with subpopulations
AU - Hethcote, Herbert W.
AU - Thieme, Horst
PY - 1985
Y1 - 1985
N2 - For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.
AB - For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.
UR - http://www.scopus.com/inward/record.url?scp=0021984692&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0021984692&partnerID=8YFLogxK
U2 - 10.1016/0025-5564(85)90038-0
DO - 10.1016/0025-5564(85)90038-0
M3 - Article
AN - SCOPUS:0021984692
VL - 75
SP - 205
EP - 227
JO - Mathematical Biosciences
JF - Mathematical Biosciences
SN - 0025-5564
IS - 2
ER -