Study of the Optimal Integrated Control of a Dengue Transmission Model

LI Yazhi; LIU Lili

doi:10.21656/1000-0887.420258

Volume 43 Issue 4

Apr. 2022

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LI Yazhi, LIU Lili. Study of the Optimal Integrated Control of a Dengue Transmission Model[J]. Applied Mathematics and Mechanics, 2022, 43(4): 445-452. doi: 10.21656/1000-0887.420258

Citation:

LI Yazhi, LIU Lili. Study of the Optimal Integrated Control of a Dengue Transmission Model[J]. Applied Mathematics and Mechanics, 2022, 43(4): 445-452. doi: 10.21656/1000-0887.420258

Citation:

LI Yazhi, LIU Lili. Study of the Optimal Integrated Control of a Dengue Transmission Model[J]. Applied Mathematics and Mechanics, 2022, 43(4): 445-452. doi: 10.21656/1000-0887.420258

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Study of the Optimal Integrated Control of a Dengue Transmission Model

doi: 10.21656/1000-0887.420258

LI Yazhi^{1, 2
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LIU Lili^{3
,
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1.
School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, Guizhou 558000, P.R.China
2.
Key Laboratory of Complex Systems and Intelligent Optimization of Qiannan,Duyun, Guizhou 558000, P.R.China
3.
Complex Systems Research Center, Shanxi University, Taiyuan 030006, P.R.China

Received Date: 2021-08-30
Accepted Date: 2021-09-15
Rev Recd Date: 2021-09-15

Available Online: 2022-03-16

Publish Date: 2022-04-01

Abstract

Abstract

A transmission model for dengue fever between mosquitoes and human beings was established. Three control measures: Wolbachia, self-protection and insecticide were introduced. The constant control and the time-varying control were discussed respectively. Firstly, the influences of the constant control on the basic regeneration number of the model were analyzed. It is shown that Wolbachia helps reduce the basic regeneration number, and the basic regeneration number is negatively correlated with self-protection and insecticide. Secondly, in order to minimize the number of infections and the implementation cost, the optimal control was discussed with Pontryagin’s extreme value principle. Finally, the effects of the optimal control was demonstrated through numerical simulation.
- dengue,
- transmission model,
- optimal control,
- numerical simulation

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References(13)

References

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