Keywords
Complex networks
Epidemic model
Numerical simulation
Submitted : 2025-05-07
Accepted : 2025-05-22
Published : 2025-06-06
Abstract
Infectious diseases pose a significant threat to human life, health, and safety. Therefore, it is crucial to develop effective control strategies. This paper aims to address this concern through the construction of an SEIQRS model on complex networks. This model focuses on viruses that have an incubation period and are infectious during this period. In order to minimize the costs, optimal control theory is used to solve the time-varying control problem of vaccination, quarantine, and treatment. Subsequently, numerical simulations are performed to analyze the pros and cons of different control combinations, as well as the impact of parameters on the effectiveness of control. By doing so, better control strategies can be developed, and the relationship between parameters, contagion, and control can be revealed.
References
Kermack WO, McKendrick AG, 1927, A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London, The Royal Society, 115(772): 700–721.
Kermack WO, McKendrick AG, 1932, Contribution to the Mathematical Theory of Epidemics II: The Problem of Endemicity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences,1932(138A): 55–83.
Watts D, Strogatz S, 1998, Collective Dynamics of “Small-world” Networks. Nature, 393(6684): 440–442.
Pastor-Satorras R, Castellano C, Van Mieghem P, et al., 2015, Epidemic Processes in Complex Networks. Reviews of Modern Physics, 87(3): 925–986.
Liu G, Liu L, Jin Z, 2018, Dynamics Analysis of Epidemic and Information Spreading in Overlay Networks. Journal of Theoretical Biology, 2018(444): 28–37.
Holme P, Saramaki J, 2012, Temporal Networks. Physics Reports, 2012(519): 97–125.
Xia CY, Wang ZS, Zheng CY, et al., 2019, A New Coupled Disease-awareness Spreading Model with Mass Media on Multiplex Networks. Information Sciences, 2019(471): 185–120.
Jia N, Ding L, Liu YJ, et al., 2018, Global Stability and Optimal Control of Epidemic Spreading on Multiplex Networks with Nonlinear Mutual Interaction. Physica A, 2018(502): 93–105.
Fleming WH, Rishel RW, 1975, Deterministic and Stochastic Optimal Control. Springer Verlag, New York, 26–99.