Optimal control analysis of deterministic and stochastic epidemic model with media awareness programs

The present study considered the optimal control analysis of  both deterministic differential equation modeling and stochastic differential equation modeling of infectious disease by taking effects of media awareness programs  and treatment of infectives on the epidemic into account. Optimal media awareness strategy under the quadratic cost functional using Pontrygin's Maximum Principle  and Hamiltonian-Jacobi-Bellman equation are derived for both deterministic and stochastic optimal problem respectively. The Hamiltonian-Jacobi-Bellman equation is used to solve stochastic system, which is fully non-linear equation, however it ought to be pointed out that for stochastic optimality system it may be difficult to obtain the numerical results. For the analysis of the stochastic optimality system, the results of deterministic control problem are used to find an approximate numerical solution for the stochastic control problem.  Outputs of the simulations shows that media awareness programs place important role in the minimization of infectious population with minimum cost.