No abstract

An (n+1) dimensional compartmental model is studied. It is an n dimensional model sits in (n+1) dimensional space, consists of (n+1) variables and (n+1) equations. The model is a generalization of well-known SIR model. Reduced dimensional model is introduced. The reduced model consists of n variables and n equations. The equilibrium points of the original model and reduced model are discussed. The stability of the equilibrium points are analyzed and compared. Numerical simulation is applied for n = 5. The numerical result which is the evolution of the variables is presented.

In this chapter, the authors develop an optimal control model of knowledge dissemination among people in the society. The knowledge transfer system is formulated in term of compartmental model, where the society members are categorized into four classes based on knowledge acquisition and their willingness to disseminate. The model is equipped with a set of control variables for process intervening, namely technical training for ignorant-immigrants, information dissemination through social media for solitariants and enthusiants, and technical training for solitariants. Optimality conditions in terms of differential equations system was derived by using Pontryagin minimum principle leading to the characterization of optimal control strategies that minimizing the number of solitariants, enthusiants, and ignorants simultaneously with the control efforts. The sweep method and the fourth order Runge-Kutta algorithm was implemented to numerically solve the equation systems. The effectiveness of the control strategies toward a set of control scenarios was evaluated through examples.