TY - JOUR
T1 - Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes
AU - Vargas-De-León, Cruz
PY - 2012/1
Y1 - 2012/1
N2 - A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay τ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, ℛ0(τ). If ℛ0(τ) ≤ 1, the disease-free equilibrium is globally asymptotically stable. If ℛ0(τ) > 1 a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).
AB - A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay τ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, ℛ0(τ). If ℛ0(τ) ≤ 1, the disease-free equilibrium is globally asymptotically stable. If ℛ0(τ) > 1 a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).
KW - Global stability
KW - Lyapunov functional
KW - Malaria transmission
KW - Time delay
UR - http://www.scopus.com/inward/record.url?scp=84255192753&partnerID=8YFLogxK
U2 - 10.3934/mbe.2012.9.165
DO - 10.3934/mbe.2012.9.165
M3 - Artículo
SN - 1547-1063
VL - 9
SP - 165
EP - 174
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
IS - 1
ER -