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

Abstract

The present study considered the optimal control analysis of both deterministicdifferential equation modeling and stochastic differential equation modeling ofinfectious disease by taking effects of media awareness programs and treatmentof infectives on the epidemic into account. Optimal media awareness strat-egy under the quadratic cost functional using Pontrygin’s Maximum Principleand Hamiltonian-Jacobi-Bellman equation are derived for both deterministicand stochastic optimal problem respectively. The Hamiltonian-Jacobi-Bellmanequation 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 maybe difficult to obtain the numerical results. For the analysis of the stochasticoptimality system, the results of deterministic control problem are used to findan approximate numerical solution for the stochastic control problem. Outputsof the simulations shows that media awareness programs place important rolein the minimization of infectious population with minimum cost.