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Mathematical Model, Optimal Control and Transmission Dynamics of Avian Spirochaetosis

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Document pages: 24 pages

Abstract: Avian Spirochaetosis is an acute endemic tick-borne disease of birds, caused by Borrelia anserins, a species of Borrelia bacteria. In this paper, we present a compartmental mathematical model of the disease for the bird population and Tick population. The disease steady-state and the conditions for reaching a stable disease-free steady state are determined. The analysis by Lyapunov method shows both local and global stability. Further investigation involves the introduction of controls to the model; the existence and uniqueness of optimal control are established. Finally, the effect of the controls is investigated using numerical solutions.

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