A Bovine Babesiosis Model with Dispersion

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, [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.

Models of Bovine Babesiosis Including Juvenile Cattle

“…We assume that all ticks have the same susceptibility to infection with the protozoa responsible for Bovine Babesiosis. In addition, we do not distinguish the different life stages of the ticks, an assumption also made in Friedman and Yakubu (2014), Aranda et al (2012) and Gaff and Gross (2007). However, Hoch et al (2012) state that parasite transmission is mainly by adult ticks.…”

“…Aranda et al (2012) introduced a mathematical model based on ordinary differential equations (ODEs) for Bovine Babesiosis caused by B. bigemina and B. bovis; Friedman and Yakubu (2014) formulated a mathematical model based on partial differential equations for B. bovis, of which the model by Aranda et al (2012) is a special case. Both of these models separate cattle solely based upon their status of infection by Bovine Babesiosis.…”

“…and P.vdD. thank A. Yakubu for sharing with them a preprint of Friedman and Yakubu (2014) and the thesis by D. F. Aranda. The authors thank two anonymous reviewers for helpful comments.…”

A discrete epidemic model for bovine Babesiosis disease and tick populations

“…In [6], we introduced a model based on ordinary differential equations for bovine Babesiosis caused by Babesia bigemina and Babesia bovis for the first time. After that, in view of this previous one, a model of partial differential equations for Babesia bovis was formulated by Friedman and Yakubu [7]. Besides, based on our work in [6], Carvalho et al [8] presented a new version of our classical model changing the ordinary derivative by fractional Caputo derivate.…”

Feedback control variables to restrain the Babesiosis disease

“…One of the well‐recognized constructions and studies is that for Babesiosis disease in bovine and tick populations proposed in Aranda et al Actually, this model has been taken as a fundamental reference for posterior studies on this disease (see previous studies). In Aranda et al, the global stability of the endemic equilibrium point was established but not completely.…”