Stochastic Dynamics of Optimal Pandemic Control

We develop an evolutionary SIR model with a stochastic information layer to analyze how uncertainty affects infection dynamics at the onset of a pandemic. The framework incorporates two forms of uncertainty: (i) uncertainty in health indicators, including unknown initial infection rates, and (ii) uncertainty in the information-updating process arising from interactions between individuals exposed to competing information types. We characterize the stability properties of the stochastic system and compare the resulting evolutionary dynamics with those of the corresponding deterministic model. We then formulate and solve the associated optimal control problem, deriving the optimal trajectory of the planner's information-control effort. Numerical simulations illustrate how parameter variations influence infection dynamics and the optimal level of the social planner's intervention aimed at improving information reliability in the population.

Keywords

control system analysis; optimal control; sir model; epidemic process; misinformation spreading.

References

1. Capasso V. Mathematical Structures of Epidemic Systems. Heidelberg, Springer, 1993, 283 p. DOI: 10.1007/978-3-540-70514-7
2. Starnini M., Aleta A., Tizzoni M., Moreno Y. Impact of Data Accuracy on the Evaluation of COVID-19 Mitigation Policies. Data & Policy, 2021, vol. 3, no. e28, 10 p. DOI: 10.1017/dap.2021.25
3. Cramer E.Y., Yuxin Huang, Yijin Wang et al. The United States Covid-19 Forecast Hub Dataset. Scientific Data, 2022, vol. 9, article ID: 462, 15 p. DOI: 10.1038/s41597-022-01517-w
4. Hethcote H.W., Van Ark J.W. Epidemiological Models for Heterogeneous Populations: Proportionate Mixing, Parameter Estimation, and Immunization Programs. Mathematical Biosciences, 1987, vol. 84, no. 1, pp. 85-118. DOI: 10.1016/0025-5564(87)90044-7
5. Kermack W.O., McKendrick A.G. Contributions to the Mathematical Theory of Epidemics-I. 1927. Bulletin of Mathematical Biology, 1991, vol. 53, no. 1-2, pp. 33-55. DOI: 10.1007/BF02464423
6. Nowzari C., Preciado V.M., Pappas G.J.: Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks. IEEE Control Systems Magazine, 2016, vol. 36, no. 1, pp. 26-46. DOI: 10.1109/MCS.2015.2495000
7. Pastor-Satorras R., Castellano C., Mieghem V.M., Vespignani A. Epidemic Processes in Complex Networks. Reviews of Modern Physics, 2015, vol. 87, no. 3, pp. 925-979. DOI: 10.1103/RevModPhys.87.925
8. Gubar E., Taynitskiy V., Dahmouni I. The Impact of Fake News on Infection Dynamics in Pandemic Control: An Evolutionary SIR Model. IFAC-PapersOnLine, 2023, vol. 56, no. 2, pp. 1778-1783. DOI: 10.1016/j.ifacol.2023.10.1889
9. Paarporn K., Eksin C., Weitz J.S., Wardi Y. Optimal Control Policies for Evolutionary Dynamics with Environmental Feedback. IEEE Conference on Decision and Control, 2018, pp. 1905-1910. DOI: 10.1109/CDC.2018.8619604
10. Rocha Y. M., de Moura G.A., Desiderio G.A. et al. The Impact of Fake News on Social Media and Its Influence on Health During the COVID-19 Pandemic: A Systematic Review. Journal of Public Health, 2023, vol. 31, pp. 1007-1016. DOI: 10.1007/s10389-021-01658-z
11. Rowthorn R., Flavio T. The Optimal Control of Infectious Diseases Via Prevention and Treatment. Technical Report 2013, Cambridge-INET Working Paper, Cambridge, 2020, 57 p.
12. Modgil S., Singh R.K., Gupta S., Dennehy D. A Confirmation Bias View on Social Media Induced Polarisation During Covid-19. Information Systems Frontiers, 2021, vol. 26, pp. 417-441. DOI: 10.1007/s10796-021-10222-9
13. Khouzani M., Sarkar S, Altman E. Optimal Control of Epidemic Evolution. Proceedings IEEE INFOCOM, Shanghai, 2011, pp. 1683-1691. DOI: 10.1109/INFCOM.2011.5934963
14. Dahmouni I., Kuchesfehani E.K. Necessity of Social Distancing in Pandemic Control: A Dynamic Game Theory Approach. Dynamic Games and Applications, 2022, vol. 12, no. 1, pp. 237-257. DOI: 10.1007/s13235-021-00409-9
15. Gubar E., Policardo L., Sanchez Carrera E.J., Taynitskiy V. On Optimal Lockdown Policies While Facing Socioeconomic Costs. Annals of Operations Research, 2023, vol. 337, pp. 959-992. DOI: 10.1007/s10479-023-05454-8
16. Yunhan Huang, Quanyan Zhu. Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review. Dynamic Games and Applications, 2022, vol. 12, no. 1, pp. 7-48. DOI: 10.1007/s13235-022-00428-0
17. Sethi S.P., Thompson G.L. Optimal Control Theory: Applications to Management Science and Economics. Springer, Berlin, 2005. DOI: 10.1007/0-387-29903-3
18. Taynitskiy V., Gubar E., Fedyanin D. et al. Optimal Control of Joint Multi-Virus Infection and Information Spreading. IFAC-PapersOnLine, 2020, vol. 53, no. 2, pp. 6650-6655. DOI: 10.1016/j.ifacol.2020.12.086
19. Weibull J.W. Evolutionary Game Theory. Cambridge, The MIT Press, 1995, 265 p.
20. Pontryagin L., Boltyanskii V., Gamkrelidze R., Mishchenko E. The Mathematical Theory of Optimal Processes. New York, Interscience Publishers, 1962.
21. Gubar E., Taynitskiy V., Quanyan Zhu. Optimal Control of Heterogeneous Mutating Viruses. Games, 2018, vol. 9, no. 4, 18 p. DOI: 10.3390/g9040103
22. Feng Fu, Rosenbloom D.I., Long Wang, Nowak M.A. Imitation Dynamics of Vaccination Behaviour on Social Networks. Proceedings of the Royal Society B: Biological Sciences, 2011, vol. 278, pp. 42-49. DOI: 10.1098/rspb.2010.1107
23. Sandholm W.H. Population Games and Evolutionary Dynamics. Cambridge, The MIT Press, 2010, 616 p.
24. Asadzadeh A., Samad-Soltani T., Rezaei-Hachesu P. Applications of Virtual and Augmented Reality in Infectious Disease Epidemics with a Focus on the COVID-19 Outbreak. Informatics in Medicine Unlocked, 2021, vol. 24, article ID: 100579, 8 p. DOI: 10.1016/j.imu.2021.100579
25. Erhu Du, Eddie Chen, Ji Liu, Chunmiao Zheng. How do Social Media and Individual Behaviors Affect Epidemic Transmission and Control? Science of the Total Environment, 2021, vol. 761, article ID: 144114, 10 p. DOI: 10.1016/j.scitotenv.2020.144114