Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters
Abstract
:1. Introduction
- (i)
- Undetected infections are considered.
- (ii)
- The parameter identification method to estimate the time-varying transmission rate functions in the epidemic model is employed.
- (iii)
- The optimal control measures for different infection peaks are shown.
2. COVID-19 Control System
2.1. Control Reproduction Number
2.2. Parameter Identification
- Step 1°.
- Guess
- Step 2°.
- Divide the interval into m segments: Introduce the following objective functional:
- Step 3°.
- Randomly generate groups of initial valuesLet denote the kth iteration identification variable by the ith initial value Set .
- Step 4°.
- For every use the interior algorithm to solve the problem (NIP), and obtain
- Step 5°.
- From the groups of choose groups which satisfy the constraint conditions and take them as the initial population. Let
- Step 6°.
- Use the genetic algorithm to solve the problem (NIP), and find Judge whether the stop condition is satisfied: if output the optimal solution otherwise, set
3. Optimal Control Problem
4. Numerical Results
4.1. Data Description and Parameter Value
4.2. Parameter Identification
4.3. Optimal Control
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value | Source |
---|---|---|
24,894,300 | [43] | |
0 | Estimated | |
14 | Estimated | |
2 | Estimated | |
10 | [42] | |
1 | [42] | |
1 | [42] | |
0 | Estimated |
Parameter | Value | Source | Parameter | Value | Source |
---|---|---|---|---|---|
[44] | Estimated | ||||
0.0192 | [42] | Estimated | |||
0.4458 | [42] | a | 1 | Estimated | |
Estimated | Estimated | ||||
1 | Estimated | Estimated | |||
0.02693 | [42] | 100 | Estimated | ||
[46] | 0.8 | Estimated | |||
[12] | 0.2 | Estimated | |||
Estimated | Estimated | ||||
Estimated | Estimated |
Case 1 | Case 2 | Case 3 | Case 4 | Case 5 | |
---|---|---|---|---|---|
1 | 28 | 451 | 1158 | 1258 | |
1 | 1 | 1 | 1 | 1 | |
92.7395% | 50.1279% | 10% | 4.9980% | 4.6941% | |
655,816 | 359,886 | 73,119 | 36,700 | 34,466 | |
0.0002 | 0.0440 | 0.5146 | 0.8742 | 0.9116 |
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Li, Y. Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters. Mathematics 2024, 12, 1484. https://doi.org/10.3390/math12101484
Li Y. Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters. Mathematics. 2024; 12(10):1484. https://doi.org/10.3390/math12101484
Chicago/Turabian StyleLi, Yiheng. 2024. "Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters" Mathematics 12, no. 10: 1484. https://doi.org/10.3390/math12101484
APA StyleLi, Y. (2024). Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters. Mathematics, 12(10), 1484. https://doi.org/10.3390/math12101484