Abstract
This paper studies the global stability analysis of a mathematical model on Babesiosis transmission dynamics on bovines and ticks populations as proposed by Dang et al. First, the global stability analysis of disease-free equilibrium (DFE) is presented. Furthermore, using the properties of Volterra–Lyapunov matrices, we show that it is possible to prove the global stability of the endemic equilibrium. The property of symmetry in the structure of Volterra–Lyapunov matrices plays an important role in achieving this goal. Furthermore, numerical simulations are used to verify the result presented.
Highlights
The study of epidemiology plays an essential role in understanding the pattern of disease transmission and prevention
Aranda et al [14] investigated the dynamical behavior of the tick-borne diseases. They determined the system’s equilibria and performed stability analysis. In this model the total population of bovine NB(t) divides into three classes, namely bovines who may become infected (SB(t)-susceptible), bovine infected by the Babesia parasite (IB(t)-infected) and bovine who have been treated for Babesiosis (CB(t)-controlled) and the population of ticks NT(t) is divided into two categories, namely, ticks who may become infected (SB(t)-susceptible) and ticks infected by the Babesia parasite (SB(t)-infected)
We consider the mathematical model of Babesiosis disease for bovine and tick populations that was formulated by the following system of differential equations: dS1(t) dt α1 )C (t)
Summary
The study of epidemiology plays an essential role in understanding the pattern of disease transmission and prevention. Bovine Babesia species are principally maintained by subclinically infected cattle that have recovered from disease and by tick vectors via transovarial transmission. Aranda et al [14] investigated the dynamical behavior of the tick-borne diseases They determined the system’s equilibria and performed stability analysis. Liao and Wang [21] proposed a combination of the Lyapunov function method and Volterra–Lyapunov matrix properties and proved the global asymptotic stability of the endemic equilibria. In the process of proving the stability of equilibrium points in the present work, the symmetry of the matrices is one of the main conditions This is mentioned in the definition of a positive (negative) definite matrix.
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