Optimal Control Model for the Dynamics of Tuberculosis With Control Strategies

The optimal control model with five different control strategies; the control effort on vaccination (u1), the control effort on public health campaigns (u2), the control effort on tuberculosis case detection (u3), the control effort on quarantine (u4) and the control effort on sanitarium (u5) is formulated and analyzed using Pontrayagin’s maximum principle. The numerical simulations of the optimal control model have shown that tuberculosis infection can be effectively controlled in a given population provided that 35.69% control effort on vaccination (u1), 35.69% control effort on public health campaign (u2), 0.0642% control effort on tuberculosis case detection (u3), 28.55% control effort on quarantine (u4), and 0.0021% control effort on sanitarium (u5) are continuously implemented. In this paper, an optimal control model that incorporate five different control effort variables: vaccination (U1), public health campaign (U2), case detection (U3), Quarantine (U4) and sanitarium (U5) as control strategies was proposed. And perform numerical simulation of the model.