Abstract
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, \(\mathcal{P}\), a “proliferation index,” which plays the same role as the basic reproduction number \(\mathcal{R}_{0}\) with respect to the stability/instability of the disease-free equilibrium, and observe that \(\mathcal{P}\) decreases as the dispersion coefficients increase. We prove, mathematically, that if \(\mathcal{P}>1\) 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.
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Acknowledgements
This research has been supported in part by the Mathematical Biosciences Institute of The Ohio State University, Department of Homeland Security, DIMACS and CCICADA of Rutgers University and the National Science Foundation under grant DMS 0931642, 0832782, and 1205185.
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Friedman, A., Yakubu, AA. A Bovine Babesiosis Model with Dispersion. Bull Math Biol 76, 98–135 (2014). https://doi.org/10.1007/s11538-013-9912-8
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DOI: https://doi.org/10.1007/s11538-013-9912-8