Optimal Control of Mitigation Strategies for Dengue Virus Transmission

Xue, Ling; Ren, Xue; Magpantay, F. M. G.; Sun, Wei; Zhu, Huaiping

doi:10.1007/s11538-020-00839-3

Cited by 14 publications

(5 citation statements)

References 51 publications

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“…In addition, delay τ 1 is introduced to describe the delay between media reports and infectious disease screening and reporting of cases, and delay τ 2 is given to describe the incubation period of the virus in vectors on disease transmission. Based on the classical vector-borne disease models (see [5][6][7]13,14,19,33] for more detail), the relationship between pathogens, hosts, vectors, and media coverage is shown in Figure 1. Based on the above assumption, a model reads as…”

Section: Model Formulation and Preliminariesmentioning

confidence: 99%

Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

Hu,

Nie

2023

Fractal Fract

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Vector-borne diseases, being one of the most difficult infectious diseases to understand, model, and control, account for a large proportion of human infectious diseases. In the current transmission process of infectious diseases, the latent period of pathogens in vivo, the influence of media coverage, and the presence of awareness on the spread and control of diseases are important factors that cannot be ignored. Based on this, a novel vector-borne disease model with latent delay and media coverage delay is proposed to discuss the impact of these factors. First, the global existence and ultimate boundedness of solutions for this model are obtained. Further, the exact expressions for the basic reproduction number are given, from which the existence and local stability of the disease-free and endemic equilibria are analyzed. Moreover, using the delay as a bifurcation parameter, we also discuss the existence, direction, and stability of the Hopf bifurcation. Finally, some numerical examples are carried out to explain the main theoretical results and discuss the impacts of the main parameters of this model on the transmission of vector-borne disease.

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Section: Model Formulation and Preliminariesmentioning

confidence: 99%

Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

Hu,

Nie

2023

Fractal Fract

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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%

“…With an interest in the optimal control between primary and secondary infection. There are many studies about applying to solve the optimal control problem of dengue fever [28][29][30][31][32].…”

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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“…Xue et al recently investigated the optimal control of dengue virus mitigation measures in ref. [19]. For more information, one can refer to ref.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2024

Progr. Fract. Differ. Appl.

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In this paper, we study the optimal control of the dengue disease model with the vertical transmission in terms of the Caputo fractional derivatives. We apply the control parameters like larvicide, fogging, vaccination, and isolation to stop the spread of the dengue epidemic and explore the influence of the fractional order α (0.6 ≤ α ≤ 1) on the dengue transmission model. We apply a forward-backward sweep scheme using the Adams-type predictor-corrector approach for solving the proposed control problem. Finally, the effects of optimal controls considering three different cases in the given model are discussed.

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Optimal Control of Mitigation Strategies for Dengue Virus Transmission

Cited by 14 publications

References 51 publications

Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

Stability and Hopf Bifurcation Analysis of a Multi-Delay Vector-Borne Disease Model with Presence Awareness and Media Effect

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

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