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

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.

Inspec keywords: closed loop systems; uncertain systems; differential equations; control system synthesis; epidemics; variable structure systems; medical control systems; stability; nonlinear control systems; diseases; Lyapunov methods; adaptive control; robust control

Other keywords: infected population; robustness; adaptive integral-sliding-mode controller; nonlinear robust strategy; nonlinear robust controller; nonlinear coupled differential equations; adaptive gains; positive system; infected mosquitoes; closed-loop system; infected humans; malaria epidemic control; population variables; tracking convergence; treatment rate; malaria outbreak; susceptible individuals; insecticide spray; malaria immunity

Subjects: Control system analysis and synthesis methods; Self-adjusting control systems; Biological and medical control systems; Stability in control theory; Multivariable control systems; Mathematical analysis; Nonlinear control systems

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