AccScience Publishing / IJOCTA / Volume 9 / Issue 1 / DOI: 10.11121/ijocta.01.2019.00423
RESEARCH ARTICLE

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

Shrishail Ramappa Gani1 Shreedevi Veerabhadrappa Halawar1*
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1 Department of Statistics, Karnatak Arts College, Dharwad, India
Received: 29 November 2016 | Accepted: 30 July 2017 | Published online: 1 November 2018
© 2018 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract
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.
Keywords
Epidemic model
Awareness campaigns
Optimal control
Stochastic perturbation
Conflict of interest
The authors declare they have no competing interests.
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