Chemical and Biological Control of Parasite-Borne Disease Schistosomiasis: an Impulsive Optimal Control Approach

This article deals in a continuous Schistosomiasis transmission model involving hosts human and freshwater snail, and two free living Schistosoma larva forms Miracidia and Cercariae. Along with derivation of basic reproduction number and standard equilibrium analysis, Hopf bifurcation phenomenon is demonstrated analytically and numerically. Parameter sensitivity analysis of system solution has been used to identify significant parameters for the change of disease dynamics. Impulsive optimal control of the same system, adding combined biological and chemical control of snail population to minimize human infection is undertaken. Snail natural predator crayfish is used for biological control and molluscicide is used for chemical control, where both controls are released in water periodically for finite number of times. Mathematically, the continuous system is converted to a discrete-continuous hybrid control problem applying Pontryagin’s Maximum Principle. The optimum solution revealed the quantity of each control to be released at each time point. The control analysis identified parameters crucial to success of combined control.