Summary: MATHEMATICAL BIOSCIENCES http://www.mbejournal.org/
AND ENGINEERING
Volume 4, Number 4, October 2007 pp. 567­572
GLOBAL STABILITY OF EQUILIBRIA IN A TICK-BORNE
DISEASE MODEL
Shangbing Ai
Department of Mathematical Sciences
University of Alabama in Huntsville, Huntsville, AL 35899, USA
(Communicated by Philip Maini)
Abstract. In this short note we establish global stability results for a four-
dimensional nonlinear system that was developed in modeling a tick-borne
disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265­288)
where local stability results were obtained. These results provide the parameter
ranges for controlling long-term population and disease dynamics.
1. Introduction. In the United States, ticks are the most common vectors of
vector-borne diseases. Ticks can carry and transmit a remarkable array of pathogens,
such as bacteria, spirochetes, rickettsiae, protozoa, viruses, nematodes, and toxins,
and cause several human diseases including Lyme disease, Rocky Mountain spotted
fever, human babesiosis, ehrlichiosis, tick-borne relapsing fever, Colorado tick fever
and tick paralysis. The spatial and temporal patterns of outbreaks of these diseases

Source: Ai, Shangbing - Department of Mathematical Sciences, University of Alabama in Huntsville

Collections: Mathematics