Jocirei D. Ferreira . Diego F. Aranda . Deccy Y. Trejos . V. Sree Hari Rao

Institute of Exact and Earth Science, Federal University of Mato Grosso, Barra do Garc¸as , MT, Brazil E-mail:jocireiufmt@gmail.com Universidad Nacional Abierta y a Distancia-UNAD, Escuela de Ciencias de la Educaci´on-ECEDU E-mails:arandalozanodiego@gmail.com, diego.aranda@unad.edu.co Faculty of Sciences, Universida Francisco Jose de Caldas, Santa Fe de Bogot´a, Colombia E-mail:deccyangel@gmail.com Foundation for Scientific Research and Technological Innovation, Hyderabad 500 102, India E-mails: vshrao@researchfoundation.in; vshrao@gmail.com

Received in final form on June 06, 2023

Abstract
In a recent research, a five dimensional ordinary differential equation model describing the transmission of babesiosis disease between bovine and tick populations has been studied. Self-diffusion, modeling the spatial dynamics of the babesiosis disease, is incorporated in the ordinary differential equation model. The normalized version of the proposed model, where the unknown functions are the proportions of the susceptible, infected, and controlled individuals in the total population is analyzed. The main results presented in this work are the local linear stability analysis for the spatially homogeneous equilibrium points, and the global stability of both, the disease-free and endemic equilibria when the proposed model is restricted to inside of the first octant. Finally, numerical simulations presented in this research support our theoretical results and help one to predict some scenarios on the spread of the disease.

Keywords
Population Dynamics, Babesiosis Model, Reaction Diffusion Model, Local Stability, Global Stability.

Cite This Article
Jocirei D. Ferreira . Diego F. Aranda . Deccy Y. Trejos . V. Sree Hari Rao, Reaction Diffusion Babesiosis Model Involving Bovine and Tick Populations, J. Innovation Sciences and Sustainable Technologies, 3(3)(2023), 139 - 160. https://doie.org/10.0904/JISST.2023705141

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