Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Liu, Guiyun; Chen, Jieyong; Liang, Zhongwei; Peng, Zhimin; Li, Junqiang

doi:10.3390/math9090929

Cited by 16 publications

(10 citation statements)

References 38 publications

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“…It is obvious that all the terms appearing in Equation ( 41) are always nonpositive. Now, using LaSalle's extension to Lyapunov's theorem [21,[25][26][27][28][29], we have dθ dt ≤ 0 and so the function dθ dt is to be negative definite. The limit set of each solution is contained in the largest invariant set for which S H ia = S * H ia , S H ia V = S * H ia V and R H ia = 0 which is the singleton {E 1 * }.…”

Section: Local and Global Stabilitiesmentioning

confidence: 99%

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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: Local and Global Stabilitiesmentioning

confidence: 99%

“…, I H ia = 0, and I H ia V = 0. Therefore, by LaSalle's extension to Lyapunov's function theorem [21,[25][26][27][28][29], the endemic steady state E 2…”

Section: Local and Global Stabilitiesmentioning

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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“…As a result, the two factors are used as control variables to mitigate the spread of false information [ 43 ]. It can generally use network control strategies such as forced silence, information labeling, administrator control, and controlling the relative density of individual nodes to suppress online information transmission [ 4 , 44 – 46 ].…”

Section: Introductionmentioning

confidence: 99%

“…Few scholars consider the transmission individuals’ attributes. Generally, most scholars primarily focus on controlling and transmitting negative information in networks [ 44 , 46 ]. On the other hand, confidential information must be transmitted via the contact for information that must be taught in person, such as high technology or practical skills.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal control of the developed information transmission model

Kang

Hou

et al. 2022

PLoS ONE

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Information transmission significantly impacts social stability and technological advancement. This paper compares the phenomenon of “Super transmission” and “Asymptomatic infection” in COVID-19 transmission to information transmission. The former is similar to authoritative information transmission individuals, whereas the latter is similar to individuals with low acceptance in information transmission. It then constructs an S2EIR model with transmitter authority and individual acceptance levels. Then, it analyzes the asymptotic stability of information-free and information-existence equilibrium on a local and global scale, as well as the model’s basic reproduction number, R0. Distinguished with traditional studies, the population density function and Hamiltonian function are constructed by taking proportion of “Super transmitter” and proportion of hesitant group turning into transmitters as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively facilitate information transmission. The numerical simulation corroborates the theoretical analysis results and the system’s sensitivity to control parameter changes. The research results indicate that the authoritative “Super transmitter” has a beneficial effect on information transmission. In contrast, the “Asymptomatic infected individual” with poor individual acceptance level negatively affects information transmission.

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“…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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Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Cited by 16 publications

References 38 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

Dynamical analysis and optimal control of the developed information transmission model

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

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