Local and Global Stability Analysis of Dengue Disease with Vaccination and Optimal Control

被引：9

作者：

Chamnan, Anusit ^{[1
]}

Pongsumpun, Puntani ^{[1
]}

Tang, I-Ming ^{[2
]}

Wongvanich, Napasool ^{[3
]}

机构：

[1] King Mongkut's Inst Technol Ladkrabang, Sch Sci, Dept Math, Bangkok 10520, Thailand

[2] Mahidol Univ, Fac Sci, Dept Phys, Bangkok 10400, Thailand

[3] King Mongkuts Inst Technol Ladkrabang, Sch Engn, Dept Instrumentat & Control Engn, Bangkok 10520, Thailand

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 10期

关键词：

dengue fever; global asymptotically stabilities; local asymptotically stabilities; optimal control; vaccination; AEDES-AEGYPTI; MODEL; TRANSMISSION; FEVER; INFECTION; WOLBACHIA; CULICIDAE; EFFICACY; DYNAMICS; COVID-19;

D O I：

10.3390/sym13101917

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV-1, DENV-2, DENV-3, and DENV-4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD-TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.</p>

引用

页数：24

共 53 条

[1] The Impact of the Newly Licensed Dengue Vaccine in Endemic Countries
Aguiar, Maira
Stollenwerk, Nico
Halstead, Scott B.
[J]. PLOS NEGLECTED TROPICAL DISEASES, 2016, 10 (12):
[2] Dynamics of a COVID-19 Model with a Nonlinear Incidence Rate, Quarantine, Media Effects, and Number of Hospital Beds
Ajbar, Abdelhamid
Alqahtani, Rubayyi T.
Boumaza, Mourad
[J]. SYMMETRY-BASEL, 2021, 13 (06):
[3] [Anonymous], 2009, Dengue: guidelines for diagnosis, treatment, prevention and control
[4] Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives
Basti, Bilal
Hammami, Nacereddine
Berrabah, Imadeddine
Nouioua, Farid
Djemiat, Rabah
Benhamidouche, Noureddine
[J]. SYMMETRY-BASEL, 2021, 13 (08):
[5] A PROSPECTIVE-STUDY OF DENGUE INFECTIONS IN BANGKOK
BURKE, DS
NISALAK, A
JOHNSON, DE
SCOTT, RM
[J]. AMERICAN JOURNAL OF TROPICAL MEDICINE AND HYGIENE, 1988, 38 (01) : 172 - 180
[6] Optimal Control of Dengue Transmission with Vaccination
Chamnan, Anusit
Pongsumpun, Puntani
Tang, I-Ming
Wongvanich, Napasool
[J]. MATHEMATICS, 2021, 9 (15)
[7] SIR Model for Dengue Disease with Effect of Dengue Vaccination
Chanprasopchai, Pratchaya
Tang, I. Ming
Pongsumpun, Puntani
[J]. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE, 2018, 2018
[8] Volterra-Lyapunov Stability Analysis of the Solutions of Babesiosis Disease Model
Chien, Fengsheng
Shateyi, Stanford
[J]. SYMMETRY-BASEL, 2021, 13 (07):
[9] Dengue fever: Mathematical modelling and computer simulation
Derouich, M.
Boutayeb, A.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 177 (02) : 528 - 544
[10] Edelstein-Keshet L., 2005, MATH MODELS BIOL

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