Numerical approach to solve Caputo‐Fabrizio‐fractional model of corona pandemic with optimal control design and analysis

Hanif, Asma; Butt, Azhar Iqbal Kashif; Ahmad, Waheed

doi:10.1002/mma.9085

Cited by 23 publications

(17 citation statements)

References 65 publications

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“…The most effective measure for protecting humans against Rubella virus disease is the administration of the MMR (Measles, Mumps, and Rubella) vaccine. Vaccination is an essential measure to protect individuals from the disease and contribute to the overall control and prevention efforts [17,18,[51][52][53]. To incorporate this vaccination aspect, we extend the SEITR model (1) by introducing an additional compartment for vaccination denoted by V. We assume that susceptible individuals are being fully vaccinated at the rate ρ 1 .…”

Section: Modified Rubella Epidemic Modelmentioning

confidence: 99%

Developing computationally efficient optimal control strategies to eradicate Rubella disease

Ahmad,

Butt,

Akhtar

et al. 2024

Phys. Scr.

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The threat of Rubella virus disease looms large, posing signiﬁcant risks to public health and emphasizing the urgent need for comprehensive prevention, control, and awareness strategies. We conducted an extensive analysis of a newly developed SEITR deterministic model for the lethal Rubella virus disease. The main objective of our study is to gain deep insights into the disease dynamics and devise an optimal control strategy for the model, utilizing vaccination and treatment as preventive measures. We employed various mathematical techniques to establish the positivity and bounded nature of solutions. The value of threshold parameter is computed using the next-generation method to anticipate future dynamical behavior of the epidemic. The local and global stability of the equilibrium points was successfully assessed. Additionally, we utilized the well-known Non-Standard Finite Diﬀerence (NSFD) method to obtain numerical solutions for the Rubella model. A numerical analysis is carried out to assess the eﬃcacy of a constant treatment strategy, and the results are presented through graphical illustrations. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identiﬁed. In addition, the bifurcation nature of the model is examined. Subsequently, an optimal control problem is introduced for the model, aiming to determine the best time-dependent strategies for treatment and vaccination. The main goal is to reduce the number of individuals infected within the human population and the cost of controls. Designed optimal control problem and its corresponding optimality conditions of Pontryagin type have been derived. An important aspect of this study is the utilization of the NSFD method, implemented backward in time, to solve the optimal control problem, as opposed to other conventional methods. Numerical simulations were carried out to assess the impact of the applied controls on the dynamics of all classes, both before and after optimization.

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Section: Modified Rubella Epidemic Modelmentioning

confidence: 99%

Developing computationally efficient optimal control strategies to eradicate Rubella disease

Ahmad,

Butt,

Akhtar

et al. 2024

Phys. Scr.

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“…A well‐designed mathematical model could help us in understanding the disease's transmission mechanism and it may be useful to study disease patterns for eradication of disease effectively. There exist several mathematical models [1–29] designed by researchers with different assumptions to study flow dynamics and to control of corona virus disease. In this section, we design a new mathematical model for the corona virus disease that will explain the disease transmission dynamics reliably.…”

Section: Covid‐19 Model Formulationmentioning

confidence: 99%

“…If the infection becomes more acute, the infected human may face pneumonia, kidney failure, respiratory syndrome, and even death due to infection. The fatality rate of infectious disease can be decreased by using face masks, washing hands, avoiding social gatherings, and isolating infected individuals along with proper medication [3][4][5]. The people in the age group of 60 or more and the people of any age with severe health issues such as obesity, diabetes, and heart problems are at high risk of developing acute symptoms of corona virus [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…The fatality rate of infectious disease can be decreased by using face masks, washing hands, avoiding social gatherings, and isolating infected individuals along with proper medication [3][4][5]. The people in the age group of 60 or more and the people of any age with severe health issues such as obesity, diabetes, and heart problems are at high risk of developing acute symptoms of corona virus [1][2][3][4][5]. The main reason of transmission of virus to others is due to the droplets ejected from the nose when a COVID-19 infected person coughs or sneezes.…”

Section: Introductionmentioning

confidence: 99%

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A new design and analysis of optimal control problems arising from COVID‐19 outbreak

Butt

Chamaleen

Imran

et al. 2023

Math Methods in App Sciences

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In this manuscript, we append the hospitalization, diagnosed and isolation compartments to the classic SEIR model to design a new COVID‐19 epidemic model. We further subdivide the isolation compartment into asymptomatic infected and symptomatic infected compartments. For validity of the purposed model, we prove the existence of a unique solution and prove the positivity and boundedness of the solution. To study disease dynamics, we compute equilibrium points and the reproduction number . We also investigate the local and global stabilities at both of the equilibrium points. Sensitivity analysis will be performed to observe the effect of transmission parameters on . For optimal control analysis, we design two different optimal control problems by taking different optimal control approaches. Firstly, we add an isolation compartment in the newly designed model, and secondly, three parameters describing non‐pharmaceutical behaviors such as educating people to take precautionary measures, providing intensive medical care with medication, and utilizing resources by government are added in the model. We set up optimality conditions by using Pontryagin's maximum principle and develop computing algorithms to solve the conditions numerically. At the end, numerical solutions will be displayed graphically with discussion.

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“…In addition, predictive studies of disease transmission have also been conducted (Ahmad et al., 2021; Ge et al., 2020; Shringi et al., 2021). Several studies introduced preventive measures and control strategies to discuss the spread of COVID‐19, and mathematical analysis confirmed the rationality of the solution (Butt et al., 2023; Hanif et al., 2023).…”

Section: Introductionmentioning

confidence: 95%

Epidemic propagation risk study with effective fractal dimension

Nian

2023

Risk Analysis

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In this article, the risk of epidemic transmission on complex networks is studied from the perspective of effective fractal dimension. First, we introduce the method of calculating the effective fractal dimension of the network by taking a scale‐free network as an example. Second, we propose the construction method of administrative fractal network and calculate the . using the classical susceptible exposed infectious removed (SEIR) infectious disease model, we simulate the virus propagation process on the administrative fractal network. The results show that the larger the is, the higher the risk of virus transmission is. Later, we proposed five parameters P, M, B, F, and D, where P denotes population mobility, M denotes geographical distance, B denotes GDP, F denotes , and D denotes population density. The new epidemic growth index formula was obtained by combining these five parameters, and the validity of I in epidemic transmission risk assessment was demonstrated by parameter sensitivity analysis and reliability analysis. Finally, we also confirmed the reliability of the SEIR dynamic transmission model in simulating early COVID‐19 transmission trends and the ability of timely quarantine measures to effectively control the spread of the epidemic.

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Numerical approach to solve Caputo‐Fabrizio‐fractional model of corona pandemic with optimal control design and analysis

Cited by 23 publications

References 65 publications

Developing computationally efficient optimal control strategies to eradicate Rubella disease

Developing computationally efficient optimal control strategies to eradicate Rubella disease

A new design and analysis of optimal control problems arising from COVID‐19 outbreak

Epidemic propagation risk study with effective fractal dimension

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