Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay

WANG Xinwei; PENG Haijun; ZHONG Wanxie

doi:10.21656/1000-0887.400048

Volume 40 Issue 7

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WANG Xinwei, PENG Haijun, ZHONG Wanxie. Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay[J]. Applied Mathematics and Mechanics, 2019, 40(7): 701-712. doi: 10.21656/1000-0887.400048

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Optimal Vaccination Strategies for a Time-Varying SEIR Epidemic Model With Latent Delay

doi: 10.21656/1000-0887.400048

State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China

Received Date: 2019-01-28
Rev Recd Date: 2019-05-10
Publish Date: 2019-07-01

Abstract

Abstract

On the basis of the classic SEIR compartmental model, a time-delayed term was introduced to characterize the latent delay. Furthermore, a controlled time-varying SEIR model with delay was established in view of the vaccination, the successfully immune rate and the seasonally varying incidence coefficient. Meanwhile, the optimal vaccination strategy was determined under the frame of the optimal control problem with the vaccination rate taken as the control variable. In the formulated optimal control problem, 3 kinds of constraints (i.e., the constraints on control, the upper limit on the susceptible population and the time-varying upper limit on the vaccination supply) were considered. The optimal control problem was numerically solved with a multi-interval symplectic pseudospectral method. Numerical results demonstrate that the obtained vaccination strategy can effectively suppress the spread of the disease, and the comparison between different cases suggests that omitting time-varying factors may result in unreasonable vaccination strategies.
- SEIR model,
- time delay,
- optimal control,
- vaccination strategy,
- symplectic pseudospectral method

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References

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