Volume 11, Number 1, Spring 2003
GLOBAL STABILITY IN A MODEL FOR
DISEASES TRANSMITTED BY IXODID TICKS
Abstract. Ixodid (hard) ticks act as a vector for several
diseases. We consider a compartmental model for the interaction between host and ixodid ticks. Our mathematical
analysis establishes that the global dynamics of the infection is completely determined by a basic reproductive number R0. If
R0 > 1, the disease becomes endemic, and a unique endemic
equilibrium exists and is globally stable in the interior of a feasible region. If R0≤1, the disease dies out.