Browsing by Author "Daudi, Salamida"

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    Modelling the optimal control of a large grain borer in a maize farm in the presence of pesticide
    (University of Dar es Salaam, 2013) Daudi, Salamida
    The study is on modelling the optimal control of a large grain borer in a maize farm in the presence of pesticides where by a mathematical model without control to get insight into its dynamical features which give better understanding on the effect brought by LGB as predator over maize density as prey were formulated. The model is well posed and exists in a feasible region where trivial Equilibrium point , the predator free equilibrium point and the Interior equilibrium point were obtained and analysed. The trivial equilibrium point was found to be unstable and it is a saddle point with - axis as its unstable manifold. The predator free equilibrium and the interior equilibrium point were found to be locally asymptotically stable and locally stable respectively under some conditions. In chapter four control variable u was introduced in the proposed model where objective function, langragian of the problem, Hamilitonian, adjoint variables and the optimality condition were presented and studied. Numerical simulations of the model with and without control were carried out to obtain the impact of the embedded parameters in model. Finally we conclude that controlling LGB should be done with great care because more use of pesticides affect both Prey (maize) and predator (LGB) as both go to extinct. To minimise the site effect, the control variable, (i.e. the rate of applying pesticide) should be between 0 and 1 that is .