TY - JOUR
T1 - Uniform weak implies uniform strong persistence for non-autonomous semiflows
AU - Thieme, Horst
PY - 1999
Y1 - 1999
N2 - It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are also uniformly strongly persistent even if they are non-autonomous. This result is applied to a time-heterogeneous model of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are almost periodic, an almost sharp threshold result is obtained for uniform strong endemicity versus extinction.
AB - It is shown that, under two additional assumptions, uniformly weakly persistent semiflows are also uniformly strongly persistent even if they are non-autonomous. This result is applied to a time-heterogeneous model of S-I-R-S type for the spread of infectious childhood diseases. If some of the parameter functions are almost periodic, an almost sharp threshold result is obtained for uniform strong endemicity versus extinction.
UR - http://www.scopus.com/inward/record.url?scp=22644452774&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=22644452774&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-99-05034-0
DO - 10.1090/s0002-9939-99-05034-0
M3 - Article
AN - SCOPUS:22644452774
SN - 0002-9939
VL - 127
SP - 2395
EP - 2403
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -