Control of malaria outbreak using a non-linear robust strategy with adaptive gains

摘要

The aim of this study is to develop a non-linear robust controller with adaptive gains in order to prevent malaria epidemic as a positive system with an uncertain model. The malaria outbreak is modelled by seven non-linear coupled differential equations for the population variables: susceptible, exposed, symptomatic infected and recovered humans and the susceptible, exposed and infected mosquitoes. The non-linear robust adaptive integral-sliding-mode controller is developed in order to appropriately adjust the use of treated bednets, treatment rate of infected individuals and the use of insecticide spray to control malaria epidemic. Accordingly, the numbers of exposed and infected humans and infected mosquitoes are decreased to zero by employing the designed control scheme. However, the numbers of susceptible individuals and mosquitoes are increased due to their birth rates and loss of malaria immunity in recovered individuals. The Lyapunov stability theorem is used to prove the stability, robustness and tracking convergence of the closed-loop system in the presence of modelling uncertainties. The simulation results demonstrate that by increasing the therapy time interval, the use of treated bednets and insecticide spray is decreased; however, a higher treatment rate is required for the infected population.