TY - JOUR
T1 - The basic reproduction number in some discrete-time epidemic models
AU - Allen, Linda J.S.
AU - Van Den Driessche, P.
N1 - Funding Information:
Financial support was provided by the National Science Foundation, DMS-0201105 and DMS-0718302 (LJSA), the Fogarty International Centre, #R01TW006986-02 under the NIH NSF Ecology of Infectious Diseases initiative (LJSA), the National Sciences and Engineering Council of Canada (PvdD), and the Mathematics of Information Technology and Complex Systems (PvdD). We thank the reviewer for helpful suggestions.
PY - 2008/10
Y1 - 2008/10
N2 - The next generation matrix approach for calculating the basic reproduction number [image omitted] is summarized for discrete-time epidemic models. This approach is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians. Two of the models include discrete spatial patches. For each model, [image omitted] is calculated in terms of the model parameters. For [image omitted], if a small number of infectives is introduced, then the wildlife disease dies out. Global stability of the disease-free equilibrium is verified for a special case of the SI hantavirus model when [image omitted]. In addition, a numerical example indicates that there is a transcritical bifurcation at [image omitted], with the disease dying out if [image omitted] but tending to an endemic level if [image omitted].
AB - The next generation matrix approach for calculating the basic reproduction number [image omitted] is summarized for discrete-time epidemic models. This approach is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians. Two of the models include discrete spatial patches. For each model, [image omitted] is calculated in terms of the model parameters. For [image omitted], if a small number of infectives is introduced, then the wildlife disease dies out. Global stability of the disease-free equilibrium is verified for a special case of the SI hantavirus model when [image omitted]. In addition, a numerical example indicates that there is a transcritical bifurcation at [image omitted], with the disease dying out if [image omitted] but tending to an endemic level if [image omitted].
KW - Basic reproduction number
KW - Chytridiomycosis
KW - Discrete-time epidemic model
KW - Epidemic model on patches
KW - Hantavirus
KW - Next generation matrix
UR - http://www.scopus.com/inward/record.url?scp=53349151865&partnerID=8YFLogxK
U2 - 10.1080/10236190802332308
DO - 10.1080/10236190802332308
M3 - Article
AN - SCOPUS:53349151865
SN - 1023-6198
VL - 14
SP - 1127
EP - 1147
JO - Journal of Difference Equations and Applications
JF - Journal of Difference Equations and Applications
IS - 10-11
ER -