Friedman Avner, Yakubu Abdul-Aziz
Mathematical Bioscience Institute and Mathematics Department, The Ohio State University, Columbus, OH, 43210, USA,
Bull Math Biol. 2014 Jan;76(1):98-135. doi: 10.1007/s11538-013-9912-8. Epub 2013 Nov 21.
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.
牛巴贝斯虫病（BB）是一种由蜱传播的寄生虫病，全球有超过13亿头牛有被感染的潜在风险。这种疾病也被称为蜱热，牛在接触受感染的蜱后，原生动物感染会导致大量死亡。疾病传播的一个重要因素是牛以及蜱的分散或迁移。在本文中，我们研究了这个因素的影响。我们引入一个数，[公式：见原文]，一个“增殖指数”，它在无病平衡点的稳定性/不稳定性方面与基本再生数[公式：见原文]起着相同的作用，并观察到[公式：见原文]随着扩散系数的增加而减小。我们通过数学证明，如果[公式：见原文]，那么蜱热将保持地方流行。我们还考虑了蜱的出生率经历季节性振荡的情况。基于来自哥伦比亚、南非和巴西的数据，我们使用该模型来确定几种干预方案控制牛巴贝斯虫病进展的有效性。
