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Iqbal MS, Shahzad M, Ahmed N, Akgül A, Ghafoor M, Hassani MK. Optimum study of fractional polio model with exponential decay kernel. Sci Rep 2024; 14:17237. [PMID: 39060276 PMCID: PMC11282190 DOI: 10.1038/s41598-024-64611-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Accepted: 06/11/2024] [Indexed: 07/28/2024] Open
Abstract
This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease's stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.
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Affiliation(s)
- Muhammad Sajid Iqbal
- School of Foundation Studies and Mathematics, OUC with Liverpool John Moores University (UK), Qatar Campus, 12253, Doha, Qatar
- Department of Humanities & Basic Science, Military College of Signals, NUST, Islamabad, Pakistan
- MEU Research Unit, Faculty of Information Technology, Middle East University, Amman, 11831, Jordan
| | - Muhammad Shahzad
- Department of Mathematics and statistics, The University of Lahore, Lahore, Pakistan
| | - Nauman Ahmed
- Department of Mathematics and statistics, The University of Lahore, Lahore, Pakistan.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
| | - Ali Akgül
- Department of Mathematics, Art and Science Faculty, Siirt University, 56100, Siirt, Turkey.
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.
| | - Madiha Ghafoor
- Department of Mathematics and statistics, The University of Lahore, Lahore, Pakistan
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Bozkurt F, Baleanu D, Bilgil H. A mathematical model of mobility-related infection and vaccination in an epidemiological case. Comput Methods Biomech Biomed Engin 2024:1-21. [PMID: 38982901 DOI: 10.1080/10255842.2024.2371035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2024] [Accepted: 06/16/2024] [Indexed: 07/11/2024]
Abstract
In this study, we established a system of differential equations with piecewise constant arguments to explain the impact of epidemiological transmission between different locations. Our main goal is to look into the need for vaccines as well as the necessity of the lockdown period. We proved that keeping social distance was necessary during the pandemic spread to stop transmissions between different locations and that re-vaccinations, including screening tests, were crucial to avoid reinfections. Using the Routh-Hurwitz Criterion, we examined the model's local stability and demonstrated that the system could experience Stationary and Neimark-Sacker bifurcations depending on certain circumstances.
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Affiliation(s)
- Fatma Bozkurt
- Department of Mathematics, Erciyes University, Kayseri, Turkiye
| | - Dumitru Baleanu
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
- Institute of Space Science, Bucharest-Magurele, Romania
| | - Halis Bilgil
- Department of Basic Engineering Sciences, Kayseri University, Kayseri, Turkiye
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Mohammadaliee B, Roomi V, Samei ME. [Formula: see text] model for analyzing [Formula: see text]-19 pandemic process via [Formula: see text]-Caputo fractional derivative and numerical simulation. Sci Rep 2024; 14:723. [PMID: 38184696 PMCID: PMC10771536 DOI: 10.1038/s41598-024-51415-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/04/2024] [Indexed: 01/08/2024] Open
Abstract
The objective of this study is to develop the [Formula: see text] epidemic model for [Formula: see text]-[Formula: see text] utilizing the [Formula: see text]-Caputo fractional derivative. The reproduction number ([Formula: see text]) is calculated utilizing the next generation matrix method. The equilibrium points of the model are computed, and both the local and global stability of the disease-free equilibrium point are demonstrated. Sensitivity analysis is discussed to describe the importance of the parameters and to demonstrate the existence of a unique solution for the model by applying a fixed point theorem. Utilizing the fractional Euler procedure, an approximate solution to the model is obtained. To study the transmission dynamics of infection, numerical simulations are conducted by using MatLab. Both numerical methods and simulations can provide valuable insights into the behavior of the system and help in understanding the existence and properties of solutions. By placing the values [Formula: see text], [Formula: see text] and [Formula: see text] instead of [Formula: see text], the derivatives of the Caputo and Caputo-Hadamard and Katugampola appear, respectively, to compare the results of each with real data. Besides, these simulations specifically with different fractional orders to examine the transmission dynamics. At the end, we come to the conclusion that the simulation utilizing Caputo derivative with the order of 0.95 shows the prevalence of the disease better. Our results are new which provide a good contribution to the current research on this field of research.
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Affiliation(s)
| | - Vahid Roomi
- Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
- Insurance Research Center, Tehran, Iran
| | - Mohammad Esmael Samei
- Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan, 65178-38695, Iran.
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Kuddus MA, Paul AK, Theparod T. Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach. Sci Rep 2024; 14:494. [PMID: 38177230 PMCID: PMC10766655 DOI: 10.1038/s41598-023-50799-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2023] [Accepted: 12/26/2023] [Indexed: 01/06/2024] Open
Abstract
COVID-19 is an infectious disease that causes millions of deaths worldwide, and it is the principal leading cause of morbidity and mortality in all nations. Although the governments of developed and developing countries are enforcing their universal control strategies, more precise and cost-effective single or combination interventions are required to control COVID-19 outbreaks. Using proper optimal control strategies with appropriate cost-effectiveness analysis is important to simulate, examine, and forecast the COVID-19 transmission phase. In this study, we developed a COVID-19 mathematical model and considered two important features including direct link between vaccination and latently population, and practical healthcare cost by separation of infections into Mild and Critical cases. We derived basic reproduction numbers and performed mesh and contour plots to explore the impact of different parameters on COVID-19 dynamics. Our model fitted and calibrated with number of cases of the COVID-19 data in Bangladesh as a case study to determine the optimal combinations of interventions for particular scenarios. We evaluated the cost-effectiveness of varying single and combinations of three intervention strategies, including transmission control, treatment, and vaccination, all within the optimal control framework of the single-intervention policies; enhanced transmission control is the most cost-effective and prompt in declining the COVID-19 cases in Bangladesh. Our finding recommends that a three-intervention strategy that integrates transmission control, treatment, and vaccination is the most cost-effective compared to single and double intervention techniques and potentially reduce the overall infections. Other policies can be implemented to control COVID-19 depending on the accessibility of funds and policymakers' judgments.
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Affiliation(s)
- Md Abdul Kuddus
- Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh
| | - Anip Kumar Paul
- Department of Mathematics, University of Rajshahi, Rajshahi, 6205, Bangladesh
| | - Thitiya Theparod
- Department of Mathematics, Mahasarakham University, Maha Sarakham, 44150, Thailand.
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Maamar MH, Ehrhardt M, Tabharit L. A nonstandard finite difference scheme for a time-fractional model of Zika virus transmission. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:924-962. [PMID: 38303449 DOI: 10.3934/mbe.2024039] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
In this work, we investigate the transmission dynamics of the Zika virus, considering both a compartmental model involving humans and mosquitoes and an extended model that introduces a non-human primate (monkey) as a second reservoir host. The novelty of our approach lies in the later generalization of the model using a fractional time derivative. The significance of this study is underscored by its contribution to understanding the complex dynamics of Zika virus transmission. Unlike previous studies, we incorporate a non-human primate reservoir host into the model, providing a more comprehensive representation of the disease spread. Our results reveal the importance of utilizing a nonstandard finite difference (NSFD) scheme to simulate the disease's dynamics accurately. This NSFD scheme ensures the positivity of the solution and captures the correct asymptotic behavior, addressing a crucial limitation of standard solvers like the Runge-Kutta Fehlberg method (ode45). The numerical simulations vividly demonstrate the advantages of our approach, particularly in terms of positivity preservation, offering a more reliable depiction of Zika virus transmission dynamics. From these findings, we draw the conclusion that considering a non-human primate reservoir host and employing an NSFD scheme significantly enhances the accuracy and reliability of modeling Zika virus transmission. Researchers and policymakers can use these insights to develop more effective strategies for disease control and prevention.
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Affiliation(s)
- Maghnia Hamou Maamar
- Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University, Algeria
| | - Matthias Ehrhardt
- Chair of Applied and Computational Mathematics, University of Wuppertal, Germany
| | - Louiza Tabharit
- Department of Mathematics and Computer Science, Abdelhamid Ibn Badis University, Algeria
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Intarapanya T, Suratanee A, Pattaradilokrat S, Plaimas K. Modeling the Spread of COVID-19 with the Control of Mixed Vaccine Types during the Pandemic in Thailand. Trop Med Infect Dis 2023; 8:tropicalmed8030175. [PMID: 36977177 PMCID: PMC10056006 DOI: 10.3390/tropicalmed8030175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Revised: 03/11/2023] [Accepted: 03/14/2023] [Indexed: 03/19/2023] Open
Abstract
COVID-19 is a respiratory disease that can spread rapidly. Controlling the spread through vaccination is one of the measures for activating immunization that helps to reduce the number of infected people. Different types of vaccines are effective in preventing and alleviating the symptoms of the disease in different ways. In this study, a mathematical model, SVIHR, was developed to assess the behavior of disease transmission in Thailand by considering the vaccine efficacy of different vaccine types and the vaccination rate. The equilibrium points were investigated and the basic reproduction number R0 was calculated using a next-generation matrix to determine the stability of the equilibrium. We found that the disease-free equilibrium point was asymptotically stable if, and only if, R0<1, and the endemic equilibrium was asymptotically stable if, and only if, R0>1. The simulation results and the estimation of the parameters applied to the actual data in Thailand are reported. The sensitivity of parameters related to the basic reproduction number was compared with estimates of the effectiveness of pandemic controls. The simulations of different vaccine efficacies for different vaccine types were compared and the average mixing of vaccine types was reported to assess the vaccination policies. Finally, the trade-off between the vaccine efficacy and the vaccination rate was investigated, resulting in the essentiality of vaccine efficacy to restrict the spread of COVID-19.
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Affiliation(s)
- Tanatorn Intarapanya
- Advanced Virtual and Intelligence Computing (AVIC) Center, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand;
| | - Apichat Suratanee
- Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;
- Intelligent and Nonlinear Dynamic Innovations Research Center, Science and Technology Research Institute, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
| | | | - Kitiporn Plaimas
- Advanced Virtual and Intelligence Computing (AVIC) Center, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand;
- Correspondence:
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