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Equine Infectious Anemia Virus (EIAV) is a bovine lentivirus group that creates equine infectious anemia in horses around the globe. In this paper, we propose a basic nonlinear differential equation for EIAV infection. Moreover, we obtain a semianalytic approximate solution by the homotopy analysis method (HAM). The gain of this method allows providing a direct scheme for solving the problem. Furthermore, we find the local and global stability of disease-free and endemic equilibrium using a Lyapunov functional. We use Mathematica to carry out the calculations. Graphical outcomes are carried out, and six terms are sufficient to show the effectiveness and power of the method.

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