Author(s)

Joy I. Uwakwe^1*, Blessing O. Emerenini², Simeon C. Inyama¹

¹Deapartment of Mathematics, Federal University of Technology, Owerri, Nigeria.
²Department of Mathematics, Oregon State University, Corvallis, USA.

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.

Avian Spirochaetosis, Tick Fever, Mathematical Model, Control Measure, Transmission Dynamics

Uwakwe, J. , Emerenini, B. and Inyama, S. (2020) Mathematical Model, Optimal Control and Transmission Dynamics of Avian Spirochaetosis. Journal of Applied Mathematics and Physics, 8, 270-293. doi: 10.4236/jamp.2020.82022.