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Qualitative Study of Trypanosomiasis Dynamics with Optional Control

Sangotola Adekunle Oluseye, O. O. Ugbebor


A mathematics model for trypanosomiasis is presented with multiple control strategies. Conditions were derived for existence of disease free and endemic equilibria and their stabilities were analysed. A threshold parameter R_0 exists and the disease can persist if and only if R_0 exceeds 1. We used linear and non-linear Lyapunov function together with La Salle’s invariant principle to show that the disease free and endemic equilibria are globally asymptotically stable. The existence of an optionality system is discussed. The characterization of the optional control via adjoint variable is established. The impact of using combinations of the three controls either one at a time or two at a time or three at a time on the spread of the disease is also examined.


Lyapunov function; Optimal control; Stability; Basic reproduction number.

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