A bovine babesiosis model with dispersion.

Bovine Babesiosis (BB) is a tick borne parasitic disease with worldwide over 1.3 billion bovines at potential risk of being infected. The disease, also called tick fever, causes significant mortality from infection by the protozoa upon exposure to infected ticks. An important factor in the spread of the disease is the dispersion or migration of cattle as well as ticks. In this paper, we study the effect of this factor. We introduce a number, [Formula: see text], a "proliferation index," which plays the same role as the basic reproduction number [Formula: see text] with respect to the stability/instability of the disease-free equilibrium, and observe that [Formula: see text] decreases as the dispersion coefficients increase. We prove, mathematically, that if [Formula: see text] then the tick fever will remain endemic. We also consider the case where the birth rate of ticks undergoes seasonal oscillations. Based on data from Colombia, South Africa, and Brazil, we use the model to determine the effectiveness of several intervention schemes to control the progression of BB.