Existence, stability, and data-driven analysis of a fractional-order avian influenza model in poultry farms

In the present analysis, we consider a chicken disease model in fractional derivatives. The fractional model and its related results are discussed. We present the solution's existence and its uniqueness for the fractional chicken model. Stability at the Disease-free equilibrium is shown, and found that when (Formula presented.), the model is locally asymptotically stable. The existence of an endemic equilibrium when (Formula presented.) shows a unique endemic equilibrium. A numerical scheme to get the solution for the fractional chicken model is presented. Based on the real farm data in Bangladesh, the model is fitted, and the respective values of the parameters are obtained. We present graphical results to show that the disease can be eliminated under various conditions on model parameters. Using real farm data and an 80% vaccine efficacy, we show that the treatment, together with vaccine efficacy, makes the disease controllable.

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