TY - JOUR
T1 - Effect of pathogen-resistant vectors on the transmission dynamics of a vector-borne disease
AU - Arino, Julien
AU - Bowman, Chris
AU - Gumel, Abba
AU - Portet, Stéphanie
N1 - Funding Information:
We are greatly indebted to Claudio Struchiner for introducing us to the subject of Transposable Elements, and for comments on earlier versions of the manuscript. We acknowledge expert help for the proof of the existence part of Theorem 4.1 from Bernard Gibert, and discussions with P. van den Driessche and James Watmough about the next generation technique. Four anonymous referees of two different versions of this paper provided helpful comments. The work of JA, AB and SP is supported in part by NSERC. JA and AB are also supported in part by MITACS.
PY - 2007/10
Y1 - 2007/10
N2 - A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector–host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.
AB - A model is introduced for the transmission dynamics of a vector-borne disease with two vector strains, one wild and one pathogen-resistant; resistance comes at the cost of reduced reproductive fitness. The model, which assumes that vector reproduction can lead to the transmission or loss of resistance (reversion), is analyzed in a particular case with specified forms for the birth and force of infection functions. The vector component can have, in the absence of disease, a coexistence equilibrium where both strains survive. In the case where reversion is possible, this coexistence equilibrium is globally asymptotically stable when it exists. This equilibrium is still present in the full vector–host system, leading to a reduction of the associated reproduction number, thereby making elimination of the disease more feasible. When reversion is not possible, there can exist an additional equilibrium with only resistant vectors.
KW - Multiple disease-free equilibria
KW - Pair formation
KW - Vector–host disease
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U2 - 10.1080/17513750701605614
DO - 10.1080/17513750701605614
M3 - Article
C2 - 22876820
AN - SCOPUS:84873708581
SN - 1751-3758
VL - 1
SP - 320
EP - 346
JO - Journal of biological dynamics
JF - Journal of biological dynamics
IS - 4
ER -