In this paper, a
controlled SIWR model was considered which was an extension of the simple SIR
model by adjoining a compartment (W) that tracks the pathogen concentration in
the water. New infections arise both through exposure to contaminated water, as
well as by the classical SIR person-person transmission pathway. The objective
of optimal control is to effectively manage and minimize the transmission of
waterborne diseases through strategic interventions and management strategies.
The two controls were employed which represent immune boosting and pathogen
suppressing drugs. The objective function is based on a combination of
minimizing the number of infected individuals and the cost of the drug dose.
Pontryagin's maximum principle has been used to characterize the optimal levels
of the two controls. The optimal control is obtained by solving the optimality
system which was composed of four nonlinear ODEs with initial conditions and
four nonlinear adjoint ODEs with transversality conditions. The results show
that the optimal combination of immune-boosting and pathogen-suppressing drugs
required to achieve the set objective will depend on the relative cost of each
of the control measures. The results were analysed and interpreted numerically
using MATLAB.
Author(s) Details
G. Devipriya
Sri Krishna Adithya College of Arts
& Science, Kovaipudur Coimbatore – 641042, India.
Please see the book here:- https://doi.org/10.9734/bpi/strufp/v10/1518
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