OPTIMAL CONTROL STRATEGY FOR DENGUE TRANSMISSION MODEL

Advisor: Dr. Temesgen Duressa Keno Abstract In this study, we presented a nonlinear deterministic transmission of dengue dynamics model with cost effectiveness and optimal control strategies. The model consists of six non-linear system of differential equations. First, we have showed that the model’s solution is both positive and bounded. Next, we used the next generation matrix method to determine the basic reproduction number with respect to the disease-free equilibrium point. Then, we demonstrated that disease -free equilibrium is both locally and globally stable using the Routh-Hurwitz criterion and the Lyapunov function. If the basic reproductive number is less than one, the disease -free equilibrium point is both locally and globally asymptotically stable; otherwise, an endemic dengue equilibrium develops. In addition, the model’s parameter sensitivity was examined. Moreover, we extended the model to optimal control model using three controls strategies, namely prevention, treatment and chemical spraying of insecticides. Finally, the combination of treatment and chemical spraying control strategies is the most efficient and least expensive strategy for minimization of the spread of dengue according to numerical prediction of optimality systems. Keywords: Dengue Dynamics; Optimal Control Analysis; Cost Effectiveness Strategies; Sensitivity Analysis