Global dynamics of a tick ixodes scapularis model

Lyme disease remains the world's most fre-quently recorded vector-borne disease in the temperate zone, with the black-legged tick, Ixodes scapularis Say, as the pri-mary vector in eastern and mid-western United States and Canada. A preliminary to determine the Lyme disease risk is providing detailed information on the tick population. This pa-per establishes the global dynamics of a tick population model developed to capture dynamical temperature in uences on the tick population. It is shown that if the reproduction number for ticks Rtick is less than one, then ticks are doomed to ex-tinction, and it is conrmed that Rtick > 1 implies that ticks can invade into the study region and a positive equilibrium ex-ists. We also use a uctuation argument to establish the global stability of the positive equilibrium.