Applications of Legendre spectral collocation method for solving system of time delay differential equations

The Zika virus model (ZIKV) is mathematically modeled to create the perfect control strategies. The main characteristics of the model without control strategies, in particular reproduction number, are specified. Based on the basic reproduction number, if R0<0, then ZIKV satisfies the disease-free equilibrium. If R0>1, then ZIKV satisfies the endemic equilibrium. We use the maximum principle from Pontryagin’s. This describes the critical conditions for optimal control of ZIKV. Notwithstanding, due to the prevention and treatment of mosquito populations without spraying, people infected with the disease have decreased dramatically. Be that as it may, there has been no critical decline in mosquitoes contaminated with the disease. The usage of preventive treatments and insecticide procedures to mitigate the spread of the proposed virus showed a more noticeable centrality in the decrease in contaminated people and mosquitoes. The application of preventive measures including treatment and insecticides has emerged as the most ideal way to reduce the spread of ZIKV. Best of all, to decrease the spread of ZIKV is to use avoidance, treatment and bug spraying simultaneously as control methods. Moreover, for the numerical solution of such stochastic models, we apply the spectral technique. The stochastic or random phenomenons are more realistic and make the model more informative with the additive information. Throughout this paper, the additive term is assumed as additive white noise. The Legendre polynomials and applications are implemented to transform the proposed system into a nonlinear algebraic system.

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“…The Legendre-Gauss (LG) quadrature together with weight function refer [29][30][31][32][33][34] is given by…”

Section: Methods Descriptionmentioning

confidence: 99%

Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method

Algehyne

Khan

et al. 2022

Symmetry

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“…LSCM is also used for the numerical approach of stochastic DDEs. [36][37][38] The main advantage of our proposed scheme over other available method for the model under consideration is that our method has exponential order of convergence which is the best possible rate of convergence for any numerical scheme. This means that one can get a spectral accuracy using a few collocation points.…”

Section: 𝛼mentioning

confidence: 99%

“…The spectral element method was first introduced by Lehotzky et al 35 for the stability analysis of delay differential equations (DDEs) with time‐periodic delay. LSCM is also used for the numerical approach of stochastic DDEs 36–38 . The main advantage of our proposed scheme over other available method for the model under consideration is that our method has exponential order of convergence which is the best possible rate of convergence for any numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

On dynamics of stochastic avian influenza model with asymptomatic carrier using spectral method

Ali

Khan

Ali

et al. 2022

Math Methods in App Sciences

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Avian influenza is an acute viral epidemic disease induced by influenza virus. In human beings, the influenza disease is one of the serious health issue caused by infection. This further motivates some other infections as well and may cause a death among the high risk community. According to the global observation by the World Health Organization (WHO), avian influenza attacks 5% to 15% of the people, which means it affects around five million people worldwide and

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“…These methods leverage the spectral decomposition of operators to approximate solutions in terms of basis functions, often leading to accurate and efficient computational strategies. Spectral methods have been widely applied to standard differential equations and partial differential equations (PDEs), but their adaptation to FSDDEs represents a compelling avenue of research and application 30 – 32 .…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis

Li,

Khan,

Riaz

et al. 2024

Sci Rep

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The fractional stochastic delay differential equation (FSDDE) is a powerful mathematical tool for modeling complex systems that exhibit both fractional order dynamics and stochasticity with time delays. The purpose of this study is to explore the stability analysis of a system of FSDDEs. Our study emphasizes the interaction between fractional calculus, stochasticity, and time delays in understanding the stability of such systems. Analyzing the moments of the system’s solutions, we investigate stochasticity’s influence on FSDDS. The article provides practical insight into solving FSDDS efficiently using various numerical techniques. Additionally, this research focuses both on asymptotic as well as Lyapunov stability of FSDDS. The local stability conditions are clearly presented and also the effects of a fractional orders with delay on the stability properties are examine. Through a comprehensive test of a stability criteria, practical examples and numerical simulations we demonstrate the complexity and challenges concern with the analyzing FSDDEs.

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Applications of Legendre spectral collocation method for solving system of time delay differential equations

Cited by 22 publications

References 29 publications

Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method

Dynamics of Stochastic Zika Virus with Treatment Class in Human Population via Spectral Method

On dynamics of stochastic avian influenza model with asymptomatic carrier using spectral method

Numerical simulation of a fractional stochastic delay differential equations using spectral scheme: a comprehensive stability analysis

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