Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

Sweilam, N. H.; Saad, Omar M.; Mohamed, D. G.

doi:10.1186/s13662-019-2147-8

Cited by 13 publications

(9 citation statements)

References 61 publications

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“…Consider the state presented (1.2), in R 5 , with control functions admissible [28][29][30][31][32]:…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

“…From (3.5) and (3.7), the conditions, necessary and sufficient for OPC are We construct a theorem similar to that presented in [28][29][30][31][32], [44][45][46][47].…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

“…For more on optimal controls for solving models, see [29][30][31][32]44,47]. Polynomials have rectangular with rating to the products indoor…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

“…In 1766, Islamic scholars presented for the first time what was considered the beginning of modern epidemiology discovery to be since followed. Model smoking is one of the most famous and important model commonly used by researchers [8][9][10][11][12][13][14], [18][19][20][21], [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. According to the World Health Organization [14], the global tobacco pandemic killed several million people.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Mahdy¹,

Mohamed²,

Amiri³

et al. 2022

Intelligent Automation &Amp; Soft Computing

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In this manuscript, we solve the ordinary model of nonlinear smoking mathematically by using the second kind of shifted Chebyshev polynomials. The stability of the equilibrium point is calculated. The schematic of the model illustrates our proposition. We discuss the optimal control of this model, and formularize the optimal control smoking work through the necessary optimality cases. A numerical technique for the simulation of the control problem is adopted. Moreover, a numerical method is presented, and its stability analysis discussed. Numerical simulation then demonstrates our idea. Optimal control for the model is further discussed by clarifying the optimal control through drawing before and after control. Fractional request differential equations (FDEs) are usually used to display frameworks that have memory and exist in a few thermoelasticity models and organic standards. FDEs show the realistic biphasic decline of infection of diseases but at a slower rate. FDEs are more suitable than integer order ones in modeling complex systems, such as biological systems.

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“…Consider the state presented (1.2), in R 5 , with control functions admissible [28][29][30][31][32]:…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

“…From (3.5) and (3.7), the conditions, necessary and sufficient for OPC are We construct a theorem similar to that presented in [28][29][30][31][32], [44][45][46][47].…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

“…For more on optimal controls for solving models, see [29][30][31][32]44,47]. Polynomials have rectangular with rating to the products indoor…”

Section: Optimal Control For Smoking Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Mahdy¹,

Mohamed²,

Amiri³

et al. 2022

Intelligent Automation &Amp; Soft Computing

View full text Add to dashboard Cite

show abstract

“…Based on the fractional order, the ABC operator is to model the actual systems of communicable diseases along with its numerous characteristics [31][32][33][34][35][36][37]. The spreading diseases of numerous vector-host designs form a mathematical model, like dengue [38], schistosomiasis [39], zoonotic instinctive leptospirosis [40], Zika [41], and West Nile virus [42]. Furthermore, the authors considered the linear care function on the disease of vector-host communications, which is physiologically unsuitable in circumstances, where the infected grow, and the society lacks adequate health resources.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Botmart¹,

Hiader²,

Sabir³

et al. 2023

Computers, Materials &Amp; Continua

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The goal of this research is to introduce the simulation studies of the vector-host disease nonlinear system (VHDNS) along with the numerical treatment of artificial neural networks (ANNs) techniques supported by Levenberg-Marquardt backpropagation (LMQBP), known as ANNs-LMQBP. This mechanism is physically appropriate, where the number of infected people is increasing along with the limited health services. Furthermore, the biological effects have fading memories and exhibit transition behavior. Initially, the model is developed by considering the two and three categories for the humans and the vector species. The VHDNS is constructed with five classes, susceptible humans S h (t), infected humans I h (t), recovered humans R h (t), infected vectors I v (t) , and susceptible vector S v (t) based system of the fractional-order nonlinear ordinary differential equations. To solve the number of variations of the VHDNS, the numerical simulations are performed using the stochastic ANNs-LMQBP. The achieved numerical solutions for solving the VHDNS using the stochastic ANNs-LMQBP have been described for training, verifying, and testing data to decrease the mean square error (MSE). An extensive analysis is provided using the correlation studies, MSE, error histograms (EHs), state transitions (STs), and regression to observe the accuracy, efficiency, expertise, and aptitude of the computing ANNs-LMQBP.

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Necessary and sufficient conditions for near‐optimal controls of a stochastic West Nile virus system with spatial diffusion

Min-na

Zhang

Zhao

2022

Math Methods in App Sciences

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Near‐optimal controls are as meaningful as optimal controls given both theory and applications; however, they are usually much easier to be obtained than optimal ones, which are simply impossible to be obtained in many complicated systems. Therefore, this paper focuses on the near‐optimal control problems of a stochastic West Nile virus system with spatial diffusion describing the virus transmission among the bird, mosquito, and human populations. First, we introduce two control variables, namely, antimosquito and the treatment of the infected humans, into the system and prove the existence and uniqueness of the global positive solution of the system. Second, the necessary and sufficient conditions for two controls to be near‐optimal are acquired in terms of a Hamiltonian function and a small parameter ε$$ \varepsilon $$ based on the Ekeland principle, the adjoint equation, and some prior estimates. Finally, we use numerical simulations to illustrate the theoretical results and conclude that mosquito control is the most critical factor preventing West Nile virus.

show abstract

Fractional optimal control in transmission dynamics of West Nile virus model with state and control time delay: a numerical approach

Cited by 13 publications

References 61 publications

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Optimal Control and Spectral Collocation Method for Solving Smoking Models

Stochastic Investigations for the Fractional Vector-Host Diseased Based Saturated Function of Treatment Model

Necessary and sufficient conditions for near‐optimal controls of a stochastic West Nile virus system with spatial diffusion

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