TY - JOUR
T1 - Stability and permanence in gender- and stage-structured models for the boreal toad
AU - Mallawaarachchi, D. K.
AU - Allen, Linda J.S.
AU - Carey, Cynthia
N1 - Funding Information:
Financial support was provided by the National Science Foundation DMS-0718302. We thank Keith Emmert, for the help with the initial formulation of this model. In addition, we thank two anonymous referees for their helpful suggestions.
PY - 2011/1
Y1 - 2011/1
N2 - The boreal toad Bufo boreas boreas, once common in the western USA, is listed as an endangered species in Colorado and New Mexico, and protected inWyoming. Populations have dramatically declined due to the presence of the fungal pathogen Batrachochytrium dendrobatidis (Bd).A gender- and stage-structured model for the boreal toad is formulated which depends on its life cycle and breeding strategies. In addition, an epizootic model for the spread of Bd is formulated.Analysis of these models provides two thresholds. The first threshold, the basic reproduction number for the population, R0, determines whether the population persists and the second threshold, the basic reproduction number for the fungal disease, RF, determines whether the disease persists. If R0 > 1 and RF < 1, then the population becomes disease-free. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen.
AB - The boreal toad Bufo boreas boreas, once common in the western USA, is listed as an endangered species in Colorado and New Mexico, and protected inWyoming. Populations have dramatically declined due to the presence of the fungal pathogen Batrachochytrium dendrobatidis (Bd).A gender- and stage-structured model for the boreal toad is formulated which depends on its life cycle and breeding strategies. In addition, an epizootic model for the spread of Bd is formulated.Analysis of these models provides two thresholds. The first threshold, the basic reproduction number for the population, R0, determines whether the population persists and the second threshold, the basic reproduction number for the fungal disease, RF, determines whether the disease persists. If R0 > 1 and RF < 1, then the population becomes disease-free. However, if both thresholds are greater than one, the population levels are severely reduced by the fungal pathogen.
KW - Boreal toad
KW - Chytridiomycosis
KW - Difference equations
KW - Permanence
UR - http://www.scopus.com/inward/record.url?scp=79955382591&partnerID=8YFLogxK
U2 - 10.1080/17513751003777515
DO - 10.1080/17513751003777515
M3 - Article
C2 - 22877227
AN - SCOPUS:79955382591
SN - 1751-3758
VL - 5
SP - 1
EP - 26
JO - Journal of Biological Dynamics
JF - Journal of Biological Dynamics
IS - 1
ER -