OPTIMAL CONTROL ANALYSIS OF SHIGELLA EPIDEMIC MODEL
Keywords:SVGEIAHRB Model, Shigella, Pontryagin’s Maximum Principle, Optimal Control, Vaccination, Treatment, Education Campaign, Screening, Hamiltonian, Numerical Simulation, Transmission.
In this paper, a model for the transmission dynamics of shigella is formulated and five control strategies: vaccination, education campaigns, screening, treatment and sanitation are deployed to minimize the total number of infected individuals, number of bacteria population and the cost associated with the control strategies. Optimal control theory is applied to a system of ordinary differential equations of a shigella epidemic. The Pontryagin’s maximum principle is employed to find the necessary and sufficient conditions for the existence of the optimal controls. Runge-Kutta forward-backward sweep numerical approximation method is used to solve the optimal control system. The results show that for the shigella outbreak to be under control in the community, 49.995% of the vaccine, 49.995%of education campaign, 8.4206 10 % −3 of screening, 3.2323 10 % −12 of treatment and 1.5794 10 % −3 of sanitation should be continually implemented.