Feedback control variables to restrain the Babesiosis disease. (20th August 2019)

• Record Type: Journal Article
• Authors: Dang, Quang A.; Hoang, Manh T.; Trejos, Deccy Y.; Valverde, Jose C.
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 18(2020)
• Page Start: 7517
• Page End: 7527
• Publication Date: 2019-08-20
• Subjects: attractors -- Babesiosis disease -- feedback control -- global stability -- Lyapunov functions and stability -- numerical treatment of dynamical systems; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5877
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we complete the study of the dynamics of a recognized continuous‐time model for the Babesiosis disease. The local and global asymptotic stability of the endemic state are established theoretically and experimentally. In addition, to restrain the disease in the original model when the endemic state exists, we propose and study the continuous model with feedback controls. The global stability of the boundary‐equilibrium point of this model is analyzed by means of rigorous mathematical methods. As an important consequence of this result, we propose a strategy to select feedback control variables in order to restrain the disease in the original model. This strategy allows us to make the disease vanish completely. In other words, the feedback controls are specially effective for restraining disease in the model. The validity of the established theoretical result is supported by a set of numerical simulations.