Multiple control strategies for prevention of rotavirus disease with saturated incidence rate

Rotavirus is a leading cause of severe diarrhea in children in both developed and developing countries and is estimated to cause over half a million deaths worldwide with much of this mortality burden concentrated in developing countries. Rotavirus spreads easily especially among infants. In this paper, we consider the SVI-B rotavirus model with saturated incidence rate function. Here, S, V, I and B refer to the susceptible individuals, vaccinated individuals, infected individuals, and the pathogen population at time t, respectively. Optimal control is conducted by using three control variables i.e. health education campaigns, effort to restrict direct contact S-I and pathogens eradication during the outbreak of an epidemic. Some results concerning the existence and the characterization of the optimal control will be given. The optimality is taken to be to minimize the total number of infected by the end of the epidemic outbreak. The technical tool is used to determine the optimal strategy by using the Pontryagin Minimum Principle. Numerical simulations are also presented using fourth order Runge-Kutta scheme. Results show that multiple control strategies are more effective than a single control strategy.