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

Butt, Azhar Iqbal Kashif; Chamaleen, D.B.D.; Imran, Muhammad; Batool, Saira; Nuwairan, Muneerah Al

doi:10.1002/mma.9482

Cited by 5 publications

(3 citation statements)

References 58 publications

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“…Therefore, while developing mathematical models for infectious diseases, it is very important to focus on procedures needed in formulating the epidemiology of the disease and to identify the most important and controllable parameters for disease control. A variety of epidemiological models have been developed based on disease transmission mechanisms and are available in literature, see [44][45][46][47][48][49][50][51][52][53]. These models have played a significant role in formulating and designing control strategies for different diseases.…”

Section: Model Formulationmentioning

confidence: 99%

Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis

Butt

2023

Symmetry

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Whooping cough, or pertussis, is an infectious disease that causes serious threats to people of all ages, specifically to infant and young children, all over the world. Due to the severe impact on health, it is necessary to construct a mathematical model that can be used to predict future dynamics of the disease, as well as to suggest strategies to eliminate the disease in an optimal way. For this, we constructed a new Atangana–Baleanu fractional model for whooping cough disease to predict the future dynamics of the disease, as well as to suggest strategies to eliminate the disease in an optimal way. We prove that the proposed model has a unique solution that is positive and bounded. To measure the contagiousness of the disease, we determined the reproduction number R0 and used it to examine the local and global stability at equilibrium points that have symmetry. Through sensitivity analysis, we determined parameters of the model that are most sensitive to R0. The ultimate aim of this research was to analyze different disease prevention approaches in order to find the most suitable one. For this, we included the vaccination and quarantine compartments in the proposed model and formulated an optimal control problem to assess the effect of vaccination and quarantine rates on disease control in three distinct scenarios. Firstly, we study the impact of vaccination strategy and conclude the findings with a graphical presentation of the results. Secondly, we examine the impact of quarantine strategy on whooping cough infection and its possible elimination from society. Lastly, we implement vaccination and quarantine strategies together to visualize their combined effect on infection control. In addition to the study of the optimal control problem, we examine the effect of the fractional order on disease dynamics, as well as the impact of constant vaccination and quarantine rates on disease transmission and control. The numerical results reveal that the optimal control strategy with vaccination and quarantine together would be more effective in reducing the spread of whooping cough infection. The implementation of the Toufik–Atangana-type numerical scheme for the solution of the fractional optimal control problem is another contribution of this article.

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Section: Model Formulationmentioning

confidence: 99%

Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis

Butt

2023

Symmetry

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“…For instance, the authors of [ 20 ] examined the SIR model to manage the spread of disease. The authors in [ 21 – 23 ] employed optimal control techniques to investigate strategies for preventing and managing various infections. Mathematical modeling is a powerful method for researching the spread of diseases and population dynamics to understand the complex system.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and computational modeling for analyzing and controlling Hepatitis B: A novel epidemic approach

Farhan,

Shah,

Ling

et al. 2024

PLoS ONE

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Hepatitis B virus (HBV) infection is a global public health issue. We offer a comprehensive analysis of the dynamics of HBV, which can be successfully controlled with vaccine and treatment. Hepatitis B virus (HBV) causes a significantly more severe and protracted disease compared to hepatitis A. While it initially presents as an acute disease, in approximately 5 to 10% of cases, it can develop into a chronic disease that causes permanent damage to the liver. The hepatitis B virus can remain active outside the body for at least seven days. If the virus penetrates an individual’s body without immunization, it may still result in infection. Upon exposure to HBV, the symptoms often last for a duration ranging from 10 days to 6 months. In this study, we developed a new model for Hepatitis B Virus (HBV) that includes asymptomatic carriers, vaccination, and treatment classes to gain a comprehensive knowledge of HBV dynamics. The basic reproduction number R 0 is calculated to identify future recurrence. The local and global stabilities of the proposed model are evaluated for values of R 0 that are both below and above 1. The Lyapunov function is employed to ensure the global stability of the HBV model. Further, the existence and uniqueness of the proposed model are demonstrated. To look at the solution of the proposed model graphically, we used a useful numerical strategy, such as the non-standard finite difference method, to obtain more thorough numerical findings for the parameters that have a significant impact on disease elimination. In addition, the study of treatment class in the population, we may assess the effectiveness of alternative medicines to treat infected populations can be determined. Numerical simulations and graphical representations are employed to illustrate the implications of our theoretical conclusions.

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“…The foundation of epidemiological models can be traced back to Kermack and McKendrick [36], who developed the deterministic SIR epidemic model in 1927 and later expanded it to SEIR. Over time, numerous mathematical models have been proposed in the literature for various diseases, e.g., coronavirus, tuberculous, whooping cough, and lumpy skin disease [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies

Butt,

Imran,

McKinney

et al. 2023

Mathematics

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Historically, humans have been infected by mosquito-borne diseases, including dengue fever and malaria fever. There is an urgent need for comprehensive methods in the prevention, control, and awareness of the hazards posed by dengue and malaria fever to public health. We propose a new mathematical model for dengue and malaria co-infection with the aim of comprehending disease dynamics better and developing more efficient control strategies in light of the threat posed to public health by co-infection. The proposed mathematical model comprises four time-dependent vector population classes (SEIdIm) and seven host population classes (SEIdImIdmTR). First, we show that the proposed model is well defined by proving that it is bounded and positive in a feasible region. We further identify the equilibrium states of the model, including disease-free and endemic equilibrium points, where we perform stability analysis at equilibrium points. Then, we determine the reproduction number R0 to measure the level of disease containment. We perform a sensitivity analysis of the model’s parameters to identify the most critical ones for potential control strategies. We also prove that the proposed model is well posed. Finally, the article examines three distinct co-infection control measures, including spraying or killing vectors, taking precautions for one’s own safety, and reducing the infectious contact between the host and vector populations. The control analysis of the proposed model reveals that all control parameters are effective in disease control. However, self-precaution is the most effective and accessible method, and the reduction of the vector population through spraying is the second most effective strategy to implement. Disease eradication is attainable as the vector population decreases. The effectiveness of the implemented strategies is also illustrated with the help of graphs.

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

Cited by 5 publications

References 58 publications

Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis

Atangana-Baleanu Fractional Dynamics of Predictive Whooping Cough Model with Optimal Control Analysis

Global dynamics and computational modeling for analyzing and controlling Hepatitis B: A novel epidemic approach

Mathematical and Stability Analysis of Dengue–Malaria Co-Infection with Disease Control Strategies

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