TY - JOUR
T1 - Stability and bifurcation analysis of a vector-bias model of malaria transmission
AU - Buonomo, Bruno
AU - Vargas-De-León, Cruz
N1 - Funding Information:
One of the authors (B. B.) has been partially supported by University of Naples Federico II, FARO 2010 Research Program (Finanziamento per l’Avvio di Ricerche Originali) . We would like to thank the anonymous referees for their valuable comments and suggestions.
PY - 2013/3
Y1 - 2013/3
N2 - The vector-bias model of malaria transmission, recently proposed by Chamchod and Britton, is considered. Nonlinear stability analysis is performed by means of the Lyapunov theory and the LaSalle Invariance Principle. The classical threshold for the basic reproductive number, R0, is obtained: if R0>1, then the disease will spread and persist within its host population. If R0<1, then the disease will die out. Then, the model has been extended to incorporate both immigration and disease-induced death of humans. This modification has been shown to strongly affect the system dynamics. In particular, by using the theory of center manifold, the occurrence of a backward bifurcation at R0=1 is shown possible. This implies that a stable endemic equilibrium may also exists for R0<1. When R0>1, the endemic persistence of the disease has been proved to hold also for the extended model. This last result is obtained by means of the geometric approach to global stability.
AB - The vector-bias model of malaria transmission, recently proposed by Chamchod and Britton, is considered. Nonlinear stability analysis is performed by means of the Lyapunov theory and the LaSalle Invariance Principle. The classical threshold for the basic reproductive number, R0, is obtained: if R0>1, then the disease will spread and persist within its host population. If R0<1, then the disease will die out. Then, the model has been extended to incorporate both immigration and disease-induced death of humans. This modification has been shown to strongly affect the system dynamics. In particular, by using the theory of center manifold, the occurrence of a backward bifurcation at R0=1 is shown possible. This implies that a stable endemic equilibrium may also exists for R0<1. When R0>1, the endemic persistence of the disease has been proved to hold also for the extended model. This last result is obtained by means of the geometric approach to global stability.
KW - Bifurcations
KW - Lyapunov function
KW - Malaria
KW - Mathematical model
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84873258483&partnerID=8YFLogxK
U2 - 10.1016/j.mbs.2012.12.001
DO - 10.1016/j.mbs.2012.12.001
M3 - Artículo
SN - 0025-5564
VL - 242
SP - 59
EP - 67
JO - Mathematical Biosciences
JF - Mathematical Biosciences
IS - 1
ER -