Finite-Time Stability of Time-Delay Dynamical System for the Outbreak of COVID-19

Year 2020, Volume: 9 Issue: 3, 25 - 37, 25.12.2020

Gökhan Göksu

https://izlik.org/JA52FD58AB

Abstract

In this study, the finite-time stability of the time-delay system representing the COVID-19 outbreak is analyzed. The infection dynamics is stated with the new kernel function to express the distribution of exposed people in the model. A history-wise Lyapunov functional is used to show the finite-time stability of the proposed system. A condition in terms of linear matrix inequalities is given to ensure finite-time stability. With this condition, it is guaranteed that the norm of the variables which are infected, confirmed, isolated and cured/recovered people do not exceed a certain bound in a fixed finite time interval. The solution of the generalized minimum/maximum parameters is explained and a numerical example is demonstrated to show the validity of the proposed method.

Keywords

Finite-time stability , time-delay systems , infection dynamics , COVID-19

References

• Chen, Y., Cheng, J. Jiang, Y. Liu, K., 2020a. A Time-Delay Dynamical Model for Outbreak of 2019-nCoV and the Parameter Identification. Journal of Inverse and Ill-Posed Problems, 28(2): 243-250.
• Chen, Y., Cheng, J. Jiang, Y. Liu, K., 2020b. A Time-Delay Dynamic System with External Source for the Local Outbreak of 2019-nCoV. Applicable Analysis, In Press.
• Hagood, J. W., Thomson, B.S., 2006. Recovering a Function from a Dini Derivative, The American Mathematical Monthly, 113(1): 34-46.
• Hethcote, H. W., 2000. The Mathematics of Infectious Diseases. SIAM Review, 42(4): 599-653.
• Kermack, W. O., McKendrick, A. G., 1991. Contributions to the Mathematical Theory of Epidemics-I. Bulletin of Mathematical Biology, 53(1-2): 33-55.
• Kermack, W. O., McKendrick, A. G., 1932. Contributions to the Mathematical Theory of Epidemics-II: The Problem of Endemicity. Proceedings of the Royal Society of London Series A, 138(834): 55-83.
• Kermack, W. O., McKendrick, A. G., 1933. Contributions to the Mathematical Theory of Epidemics-III: Further Studies of the Problem of Endemicity. Proceedings of the Royal Society of London Series A, 141(843): 94-122.
• Kermack, W. O., McKendrick, A. G., 1937. Contributions to the Mathematical Theory of Epidemics-IV: Analysis of Experimental Epidemics of the Virus Disease Mouse Ectromelia. Epidemiology & Infection, 37(2): 172-187.
• Kermack, W. O., McKendrick, A. G., 1939. Contributions to the Mathematical Theory of Epidemics-V: Analysis of Experimental Epidemics of Mouse-Typhoid; A Bacterial Disease Conferring Incomplete Immunity. Epidemiology & Infection, 39(3): 271-288.
• Royden, H. L., 1988. Real Analysis, 3rd ed. (pp. 99). Macmillan NewYork.
• World Health Organization, 2020. Novel Coronavirus – China: Disease Outbreak News, 12 January 2020.
• World Health Organization, 2020. Coronavirus Disease 2019 (COVID-19): Situation Reports.