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Volume 11,     Number 1,     Spring 2003

 

GLOBAL STABILITY IN A MODEL FOR DISEASES TRANSMITTED BY IXODID TICKS
HORACIO GÓMEZ-ACEVEDO

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.

 

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