Optimal Control of Dengue Transmission with Vaccination

Chamnan, Anusit; Pongsumpun, Puntani; Tang, I‐Ming; Wongvanich, Napasool

doi:10.3390/math9151833

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…In this section, we carried out a sensitivity analysis [31,32] test of the effect of the parameters on the basic reproduction number R 0 to ascertain the impact of these parameters on dengue transmission.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

et al. 2022

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The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.

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Section: Sensitivity Analysismentioning

confidence: 99%

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

et al. 2022

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“…Then in paper [53] using Optimal Control on the Dengue Hemorrhagic Fever (DHF) Disease Model by providing herbal medicine treatment with the research location on the Martapura Riverbank. Optimal control is also used when only individuals with a recorded history of past dengue infection for which the individual has been given are vaccinated, this is the case in some parts of Thailand [54], while in Johor Malaysia in 2012, control with a combination of optimal personal protection, larvicidal and adult control involving eight mutually exclusive compartments with the introduction of personal protection, the model was also adapted to data related to DHF outbreaks using the least squares method [47]. Likewise, the discussion of optimal control in the model of the spread of dengue fever using the Pontryagin minimum principle can be prevented by administering a vaccine called Chimeric Yellow Fever 17D-Tetravalent Dengue Vaccine (CYD-TDV) [55].…”

Section: Optimal Control On Dhf Problemsmentioning

confidence: 99%

Sistematic Review: Mathematics Model Epidemiology of Dengue Fever

Affandi¹,

K.²,

Suhartono³

et al. 2022

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Dengue Hemorrhagic Fever (DHF) is a disease caused by an arbovirus that enters the human body through the Aedes aegypti mosquito. Dengue Hemorrhagic Fever is characterized by symptoms, headache; reddish skin that looks like measles; and muscle and joint pain. The spread of dengue hemorrhagic fever (DHF) globally has tended to be higher in the last 50 years, thus giving rise to ideas for systematic prevention. Many factors cause this dengue fever, climate factors, weather, residential density, and other factors. The Epidemiological Model of DHF can provide a pattern of prevention against dengue outbreaks so that this problem can be modeled mathematically and through the stability of the equilibrium point, the dynamics or behavior of the model can be determined. The spread of DHF can be suppressed by providing control in the form of vaccines, eradication with insecticides and treatment. This review article aims to provide a systematic description of the causative factors, a mathematical model of DHF with an epidemiological approach. To get the right model related to the SIR epidemiological mathematical model and its modifications which can be an alternative solution to describe and analyze the model mathematically. The methodology used is to systematically search for journals and articles from August 2021 to April 2022. This is done by accessing electronic journal portals such as: Elsevier, Springer, ResearchGate, google scholar, Scient direct and so on. Other references also use national journals and information on the Ministry of Health's website. The results of a review of factors that cause dengue fever are physical environmental factors that have a significant influence on rainfall and air temperature. Mathematical models with Optimal Control can be used as an alternative to mathematical analysis which is expected to help solutions to reduce the spread of dengue fever. The recommendation given is to investigate the disease-causing factors from the chemical aspect related to the chemical effect in water that influences the growth of mosquito larvae in water which can indirectly affect DHF disease and involves these parameters in mathematical models and optimal control.

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“…where m 1 , m 2 , C 1 , C 2 , D 1 , D 2 > 0, and ψ > 1. Therefore, there exists an optimal control for the system of Equations ( 33)- (36) satisfying the Pontryagin's minimum principle [25][26][27][28][29]51,52]. Theorem 6.…”

Section: Optimal Control Strategiesmentioning

confidence: 99%

“…The two policy control models were insecticide and vaccinations which simulated the parameters affecting this model control. The authors [27] study a dynamic basic mathematical model for dengue transmission in Thailand, by including infection of different serotypes to analyze the effects of different vaccination strategies. With an interest in the optimal control between primary and secondary infection.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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Optimal Control of Dengue Transmission with Vaccination

Cited by 11 publications

References 30 publications

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis

Sistematic Review: Mathematics Model Epidemiology of Dengue Fever

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

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