Feedback control variables to restrain the Babesiosis disease

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. KEYWORDS attractors, Babesiosis disease, feedback control, global stability, Lyapunov functions and stability, numerical treatment of dynamical systems MSC CLASSIFICATION 34D23; 37B25; 93B52 Math Meth Appl Sci. 2019;42:7517-7527.wileyonlinelibrary.com/journal/mma

Global Dynamics of a Computer Virus Propagation Model With Feedback Controls

“…Then, we desire L * + B * to be as small as possible. The estimate (6) shows that it is possible to make L * + B * arbitrarily small by making K sufficiently large. This may be achieved because K depends on the control variables (see Table 1 in Section 4.)…”

“…In this situation one of the effective approaches is to consider the model with feedback control variables. For models with feedback controls see [3,4,6,7,11,12] and the references therein. If it is possible to prove that the feedback control variables do not affect the global stability of the original differential model but only change the position of the viral equilibrium, then the feedback control variables can be used to limit the number of computers infected with viruses in the system.…”

Volterra–Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model

“…Babesiosis has an important economic impact in the livestock sector of tropical regions [9][10][11][12]. The mathematical models of bovine Babesiosis have recently attracted an increasing amount of attention from researchers [13][14][15][16][17]. Aranda et al [14] investigated the dynamical behavior of the tick-borne diseases.…”

“…Recently, the global stability of the endemic equilibrium has received considerable attention and several techniques were discussed [18][19][20]. Dang et al [16] investigated the model of Babesiosis disease in more detail. They also examined the local stability of the disease-free equilibrium (DFE) by calculating eigenvalues.…”

“…They also examined the local stability of the disease-free equilibrium (DFE) by calculating eigenvalues. The authors in [16] stated "Since it is difficult to study the global stability property of this equilibrium point by analytical methods, we will do it by means of numerical simulations, as in Examples 1 and 2". Consequently, it is necessary to apply an analytical method to confirm that point E * is asymptotically stable.…”