Abstract: In
host macroparasite model there exists time delay between entry to the definitive
host and the point when the parasite begins the production of eggs or larvae for
transmission to the other hosts. In the case without delay if and
increasing
and tends asymptotically to zero otherwise, we show that every positive solution
of oscillates
about the endemic equilibrium point due to the delay time and prove that every
non-oscillatory solution tends to the endemic equilibrium point as t
tends to infinity. Here, we focus on the dynamics of the adult worms assuming
that the dynamics of the infective stages move on a much faster time-scale so as
to be effectively adjusted to its equilibrium.
Keywords and phrases: oscillation, delay time, host parasite model.
