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

[1] Misra, A.K., Sharma, A. & Shukla, J.B. (2015). Sta- bility analysis and optimal control of an epidemic model with awareness program by media. J Bio Sys., 138, 53-62.
[2] Liu, W. & Zheng, O. (2015). A stochastic SIS epi- demic model incorporating media coverage in a two patch setting. Applied Mathematics and Computation, 262, 160-168.
[3] Durrett, R. & Levin, S.A. (1994). Stochastic spa- tial models:The users guide to ecological application. Philosophical Transactions: Biological Sciences, 343, 329 - 350.
[4] Tchunche,J.M., Khamis, S.A., Agusto, F.B. &Mpeshe, S.C. (2010). Optimal control and sensitiv- ity analysis of an in丑uenza model with treatment and vaccination. Acta Biotheoretica, 59, 1-28.
[5] Okosun, K.O., Makide, O. D. & Takaidza, I. (2013). The impact of optimal control on the treatment of HIV/AIDS and screening of unaware infective. Ap- plied Mathematical Modeling, 37, 3802 - 3820.
[6] Ishikawa, M. (2012). Optimal strategies for vaccina- tion using the stochastic SIRV model. Transactions of the Institute of the Systems, Control and Information Engineers, 25, 343 - 348.
[7] Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. & Mishchenko, E.F. (1962). The mathematical theory of optimal processes, Wiley, New York.
[8] Fleming, W.H. & Rishel, R.W. (1975). Deterministic and stochastic optimal control, Springer Verlag, New York.
[9] Zhao, Y., Jiang, D. & O’Regan, D. (2013). The ex- tinction and persistance of the stochastic SIS epidemic model with vaccination, Physica A, 392, 4916-4927.
[10] Carletti, M. (2002). On stability properties of stochas- tic model for phase-bacteria interaction in open ma- rine environment, Math. Biosci., 175, 117-131.
[11] Sulem, A., & Tapiero, C.S. (1994). Computational aspects in applied stochastic control, Computational Economics, 7, 109146.
[12] Tornatore, E., Buccellato, S.M., & Vetro, P. (2006). On a stochastic disease model with vaccination, Ren- diconti del Circolo Matematicodi Palermo. Serie II, 55, 223240.
[13] Tornatore, E., Vetro, P. & Buccellato, S. M. (2014). SIVR epidemic model with stochastic perturbation, Neural Computing and Applications, 24, 309315.
[14] Witbooi, P.J., Muller, G.E. & Van Schallkwyk, G.J.(2015). Vaccination Control in a Stochastic SVIR Epi- demic Model, Computational and Mathematical Meth- ods in Medicine, Article ID 271654, 9 pages.
[15] Lukes, D.L. (1982). Diferential equations: classical to control, Academic press.
[16] Dalal, N., Greenhalgh, D. & Mao, X. (2007). A sto- chastic Model of AIDS and Condom use, J. Math. Anal. Appl. 325, 36-53.
[17] Gray,A., Greenhalgh, D., Hu, L., Mao, X. & Pan, J.(2011). A stochastic diferential equation SIS epidemic model, SIAM J.Appl. Math., 71, 876-902.
[18] Mao, X. (1997). Stochastic diferential equations and applications. Horwood.
[19] Oksendal,B. (1998). Stochastic diferential equa- tions: an introduction with applications, Universitext, Springer, Berlin, Germany, 5th edition.
[20] Higham, D. (2001). An algorithmic introduction to nu- merical simulation of stochastic diferential equations, SIAM Rev., 43, 525546.