A Discrete Study on Stochastic Epidemic Models with the Optimal Control Policies and Its Analysis

Mohammad Chand Jamali, Mohammed Abushohada, Samar Abdulkhalek, Shahla Shafique, Rehab Jamali


The article aims to assess the stochastic model's control variant and study the effect of time on the epidemic's behavior. A single population must have strong immunity as it recovers from the epidemic. Lower the infected and susceptible individuals and maximize the absolute amount of recovered individuals by using possible minimal control variables. We have demonstrated whether we should implement a treatment policy to minimize the number of death cases by examining three different examples from various perspectives. We have also proved that the best policy in the event of a fatality is to avoid it. The epidemic model will be a bang policy with only one switch if the cost function depicted in the illustration is utilized. Furthermore, a switch can only be activated if criteria are satisfied. As a result, we investigate the approaches for preventing the HBV model. Finally, we will develop a more realistic model-building strategy that integrates the emergence of treatment effect on the infectives during their incubation period for a fatal epidemic. A fatal epidemic is expected to be more severe than a general epidemic, and more realistic model-building approaches are developed. The same mathematical methods and conclusions may be used nearly immediately to a wide range of spreading processes, which should be stressed.


Keywords: discrete study, stochastic epidemic model, optimal control.




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TRAN K., & YIN G. Optimal Control and Numerical Methods for Hybrid Stochastic SIS Models. Nonlinear Analysis: Hybrid Systems, 2021, 41: 101051. https://doi.org/10.1016/j.nahs.2021.101051

HALAWAR S., GANI S., and HALAWAR S. Optimal Control Analysis of Deterministic and Stochastic SIS Epidemic Model with Vaccination. International Journal of Solids and Structures, 2021, 12: 251-263. https://www.ripublication.com/ijss17/ijssv12n2_08.pdf

BOUTAYEB H., SARA B., ZAKARY O., and RACHIK M. A New Simple Epidemic Discrete-Time Model Describing the Dissemination of Information with Optimal Control Strategy. Discrete Dynamics in Nature and Society, 2020: 7465761. https://doi.org/10.1155/2020/7465761

KOVACEVIC R., VELIOV V., and GRANDITS P. Optimal Control and the Value of Information for a Stochastic Epidemiological SIS-Model. Journal of Mathematical Analysis and Applications, 2019, 476(2): 665-695. https://doi.org/10.1016/j.jmaa.2019.04.005

LORCH L., DE A., BHATT S., TROULEAU W., UPADHYAY U., and GOMEZ-RODRIGUEZ M. Stochastic Optimal Control of Epidemic Processes in Networks. arXiv, 2018: 1810.13043v4. https://doi.org/10.48550/arXiv.1810.13043

BOLZONI L., BONACINI E., SORESINA C., and GROPPI M. Time-optimal control strategies in SIR epidemic models. Mathematical Biosciences, 2017, 292: 86-96. https://doi.org/10.1016/j.mbs.2017.07.011

NASIR A., & REHMAN H. Optimal control for stochastic model of epidemic infections. Proceedings of the 14th International Bhurban Conference on Applied Sciences and Technology, Islamabad, 2017, pp. 278-284. https://doi.org/10.1109/IBCAST.2017.7868065

GANI S. R., & HALAWAR S. V. Deterministic and Stochastic Optimal Control Analysis of an SIR Epidemic model. Global Journal of Pure and Applied Mathematics, 2017, 13(9): 5761-5778. https://www.semanticscholar.org/paper/Deterministic-and-Stochastic-Optimal-Control-of-an/d99196b1efaafadf2bb952369359c5e1bca1a61c

MALIK T., & SHAROM O. Optimal control in epidemiology. Annals of Operations Research, 2017, 251: 55-71. https://doi.org/10.1007/s10479-015-1834-4

LEE H., LEE S., and LEE C. Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea. Applied Mathematics and Computation, 2016, 286: 232-249. https://doi.org/10.1016/j.amc.2016.04.019

DING W., & LENHART S. Introduction to Optimal Control for Discrete Time Models with an Application to Disease Modeling. DIMACS: Series in Discrete Mathematics & Theoretical Computer Science, 2010, 75: 109-119. https://doi.org/10.1090/dimacs/075/05


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