1. ISSN 1749-3889 (print), 1749-3897 (online)
International Journal of Nonlinear Science
Vol.xx(20x) No.xx,pp.??-??
Global asymptotic dynamics of a host-vector model with two delays
Cruz Vargas-De-Le´ n1
o 2 ∗
, Guillermo G´ mez-Alcaraz2
o
1
Unidad Acad´ mica de Matem´ ticas,Universidad Aut´ noma de Guerrero, Chilpancingo, Guerrero, M´ xico
e a o e
2
Facultad de Ciencias, Universidad Nacional Aut´ noma de M´ xico M´ xico, D.F., M´ xico
o e e e
(Received xx , accepted xx, will be set by the editor)
Abstract: Host-vector disease models with discrete time delays or distributed time delays are studied. By
means of Lyapunov’s direct method, we establish the global stability conditions of the equilibrium states. We
proved that the global stability are completely determined by the threshold parameter, R0 . If the threshold
parameter is less than or equal to unity, the disease-free equilibrium state is globally asymptotically stable
for any time delays in the feasible region. If the threshold parameters greater than one, a unique endemic
equilibrium state exists and is globally asymptotically stable for any time delays in the interior of the feasible
region. We extended our analysis to sexually-transmitted diseases models.
Keywords: host-vector model; distributed time-delay; discrete time-delay; global asymptotic stability; method
of Lyapunov functionals.
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∗ Corresponding author. E-mail address: leoncruz82@yahoo.com.mx
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IJNS email for contribution: editor@nonlinearscience.org.uk