TY - JOUR
T1 - The basic reproduction number in epidemic models with periodic demographics
AU - Wesley, Curtis L.
AU - Allen, Linda J.S.
PY - 2009
Y1 - 2009
N2 - Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.
AB - Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains.
KW - Basic reproduction number
KW - Differential equations
KW - Epidemic models
KW - Periodic coefficients
UR - http://www.scopus.com/inward/record.url?scp=77950631940&partnerID=8YFLogxK
U2 - 10.1080/17513750802304893
DO - 10.1080/17513750802304893
M3 - Article
C2 - 22880824
AN - SCOPUS:77950631940
SN - 1751-3758
VL - 3
SP - 116
EP - 129
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
IS - 2-3
ER -