Based On The Optimal Impulse Control Problem In Mosquito Control And Management Under The Background Of Dengue Fever

For centuries,Dengue fever,have been big fears for the public health in the world?An actual way to prevent diseases spread due to mosquito is to control mosquitoes.We proposed two different state pulse control models for fertile mosquitoes by two risk thresholds in the second section.By the geometrical theory,the successor function and the Poincare standard,the existence,uniqueness and stability of order-one periodic solutions(OOPSs)are proved.In the third chapter,two optimal state control problem-s determined by impulse and phase sets on a period are formulated respectively.By rescaled time and constrain violation functions,the optimal problems are translated to a control parametrization ones.From the gradients of the cost functionals on parameters,simulations are conducted to select the suitable parameters and period to minimize the cost functions.Correspondingly,the optimal control strategies are obtained.Results indicate that optimal strategies are more environmentally friendly and economical than the primary ones.In the fourth part,we consider the optimal feedback control problem of mosquitoes,where its dynamic systems is described by stochastic non-linear sys-tems subjected to winer process and state jumps.Thus,the nonlinear system is treated by means of the complete linearization method.We show that the stochastic impulsive optimal parameter selection problem is equivalent to a deterministic impulsive optimal parameter selection problem.Afterwards,the rescaled time and a constrain violation function are introduced to translate the above optimal problem to a parameter selection problem in a specified time with the unconstraint.Then,gradients of the objective func-tion on all parameters are given to compute the optimal value of cost function for the numerical computation.This result implies that the optimal control problem assures to obtain better result than the non-control situation.Numerical illustrations are provided in support of the theoretical results.