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Agarwal R, Airan P, Sajid M. Numerical and graphical simulation of the non-linear fractional dynamical system of bone mineralization. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:5138-5163. [PMID: 38872530 DOI: 10.3934/mbe.2024227] [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: 06/15/2024]
Abstract
The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.
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Affiliation(s)
- Ritu Agarwal
- Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India
| | - Pooja Airan
- Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India
| | - Mohammad Sajid
- Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia
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2
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Hassan J, Saeed SM, Deka L, Uddin MJ, Das DB. Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges. Pharmaceutics 2024; 16:260. [PMID: 38399314 PMCID: PMC10892549 DOI: 10.3390/pharmaceutics16020260] [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: 12/08/2023] [Revised: 01/29/2024] [Accepted: 02/07/2024] [Indexed: 02/25/2024] Open
Abstract
The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.
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Affiliation(s)
- Jasmin Hassan
- Drug Delivery & Therapeutics Lab, Dhaka 1212, Bangladesh; (J.H.); (S.M.S.)
| | | | - Lipika Deka
- Faculty of Computing, Engineering and Media, De Montfort University, Leicester LE1 9BH, UK;
| | - Md Jasim Uddin
- Department of Pharmaceutical Technology, Faculty of Pharmacy, Universiti Malaya, Kuala Lumpur 50603, Malaysia
| | - Diganta B. Das
- Department of Chemical Engineering, Loughborough University, Loughborough LE11 3TU, UK
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3
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Stability Analysis of an Extended SEIR COVID-19 Fractional Model with Vaccination Efficiency. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:3754051. [PMID: 36176740 PMCID: PMC9514930 DOI: 10.1155/2022/3754051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/11/2022] [Revised: 08/17/2022] [Accepted: 09/01/2022] [Indexed: 11/18/2022]
Abstract
This work is aimed at presenting a new numerical scheme for COVID-19 epidemic model based on Atangana-Baleanu fractional order derivative in Caputo sense (ABC) to investigate the vaccine efficiency. Our construction of the model is based on the classical SEIR, four compartmental models with an additional compartment V of vaccinated people extending it SEIRV model, for the transmission as well as an effort to cure this infectious disease. The point of disease-free equilibrium is calculated, and the stability analysis of the equilibrium point using the reproduction number is performed. The endemic equilibrium's existence and uniqueness are investigated. For the solution of the nonlinear system presented in the model at different fractional orders, a new numerical scheme based on modified Simpson's 1/3 method is developed. Convergence and stability of the numerical scheme are thoroughly analyzed. We attempted to develop an epidemiological model presenting the COVID-19 dynamics in Italy. The proposed model's dynamics are graphically interpreted to observe the effect of vaccination by altering the vaccination rate.
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Vijayalakshmi G, P RB. A fractal fractional order vaccination model of COVID-19 pandemic using Adam’s moulton analysis. RESULTS IN CONTROL AND OPTIMIZATION 2022. [PMCID: PMC9187878 DOI: 10.1016/j.rico.2022.100144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
The pandemic caused by coronaviruses (SARS-COV-2) is a zoonotic disease targeting the respiratory tract of active humans. Few mild symptoms of fever and tiredness get cured without any medicinal aid, whereas some severe symptoms of dry cough with breathing illness led to perceived risk of secondary transmission. This paper studies the effectiveness of vaccination in Covid-19 pandemic disease by modelling three compartments susceptible, vaccinated and infected (SVI) of Atangana Baleanu of Caputo (ABC) type derivatives in non-integer order. The disease dynamics is analysed and its stability is performed. Numerical approximation is derived using Adam’s Moulton method and simulated to forecast the results for controllability of pandemic spread.
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Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission ☆. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:5083-5095. [PMCID: PMC8502694 DOI: 10.1016/j.aej.2021.10.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2021] [Revised: 09/07/2021] [Accepted: 10/04/2021] [Indexed: 08/23/2023]
Abstract
The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The infection is very destructive to human lives and caused millions of deaths. Various approaches have been made recently to understand the complex dynamics of COVID-19. The mathematical modeling approach is one of the considerable tools to study the disease spreading pattern. In this article, we develop a fractional order epidemic model for COVID-19 in the sense of Caputo operator. The model is based on the effective contacts among the population and environmental impact to analyze the disease dynamics. The fractional models are comparatively better in understanding the disease outbreak and providing deeper insights into the infectious disease dynamics. We first consider the classical integer model studied in recent literature and then we generalize it by introducing the Caputo fractional derivative. Furthermore, we explore some fundamental mathematical analysis of the fractional model, including the basic reproductive number R 0 and equilibria stability utilizing the Routh-Hurwitz and the Lyapunov function approaches. Besides theoretical analysis, we also focused on the numerical solution. To simulate the model, we use the well-known generalized Adams–Bashforth Moulton Scheme. Finally, the influence of some of the model essential parameters on the dynamics of the disease is demonstrated graphically.
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Masandawa L, Mirau SS, Mbalawata IS, Paul JN, Kreppel K, Msamba OM. Modeling nosocomial infection of COVID-19 transmission dynamics. RESULTS IN PHYSICS 2022; 37:105503. [PMID: 35469342 PMCID: PMC9021122 DOI: 10.1016/j.rinp.2022.105503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Revised: 03/03/2022] [Accepted: 04/08/2022] [Indexed: 06/14/2023]
Abstract
COVID-19 epidemic has posed an unprecedented threat to global public health. The disease has alarmed the healthcare system with the harm of nosocomial infection. Nosocomial spread of COVID-19 has been discovered and reported globally in different healthcare facilities. Asymptomatic patients and super-spreaders are sough to be among of the source of these infections. Thus, this study contributes to the subject by formulating a S E I H R mathematical model to gain the insight into nosocomial infection for COVID-19 transmission dynamics. The role of personal protective equipment θ is studied in the proposed model. Benefiting the next generation matrix method, R 0 was computed. Routh-Hurwitz criterion and stable Metzler matrix theory revealed that COVID-19-free equilibrium point is locally and globally asymptotically stable whenever R 0 < 1 . Lyapunov function depicted that the endemic equilibrium point is globally asymptotically stable when R 0 > 1 . Further, the dynamics behavior of R 0 was explored when varying θ . In the absence of θ , the value of R 0 was 8.4584 which implies the expansion of the disease. When θ is introduced in the model, R 0 was 0.4229, indicating the decrease of the disease in the community. Numerical solutions were simulated by using Runge-Kutta fourth-order method. Global sensitivity analysis is performed to present the most significant parameter. The numerical results illustrated mathematically that personal protective equipment can minimizes nosocomial infections of COVID-19.
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Affiliation(s)
- Lemjini Masandawa
- School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania
| | - Silas Steven Mirau
- School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania
| | - Isambi Sailon Mbalawata
- African Institute for Mathematical Sciences, NEI Globla Secretariat, Rue KG590 ST, Kigali, Rwanda
| | - James Nicodemus Paul
- School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania
| | - Katharina Kreppel
- School of Computational and Communication Science and Engineering, The Nelson Mandela African Institution of Science and Technology, P.O. Box 447, Arusha, Tanzania
| | - Oscar M Msamba
- Arusha Technical College, P.O. Box 296, Arusha, Tanzania
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Agarwal P, Ramadan MA, Rageh AAM, Hadhoud AR. A fractional-order mathematical model for analyzing the pandemic trend of COVID-19. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2022; 45:4625-4642. [PMID: 35464830 PMCID: PMC9015554 DOI: 10.1002/mma.8057] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Revised: 10/09/2021] [Accepted: 10/10/2021] [Indexed: 06/14/2023]
Abstract
Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID-19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional-order derivative-based modeling can be beneficial. We propose in this paper a fractional-order mathematical model to examine the COVID-19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID-19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed-point theorem and by helping the Arzela-Ascoli theorem. Using the predictor-corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas.
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Affiliation(s)
- Praveen Agarwal
- Department of MathematicsAnand International College of EngineeringJaipurIndia
| | - Mohamed A. Ramadan
- Department of Mathematics and Computer ScienceFaculty of Science, Menoufia UniversityShebin El‐KomEgypt
| | - Abdulqawi A. M. Rageh
- Department of Mathematics and Computer ScienceFaculty of Science, Menoufia UniversityShebin El‐KomEgypt
- Department of Mathematics and Computer ScienceFaculty of Science, Ibb UniversityIbbYemen
| | - Adel R. Hadhoud
- Department of Mathematics and Computer ScienceFaculty of Science, Menoufia UniversityShebin El‐KomEgypt
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Chhetri B, Vamsi DKK, Sanjeevi CB. Optimal Control Studies on Age Structured Modeling of COVID-19 in Presence of Saturated Medical Treatment of Holling Type III. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 2022:1-40. [PMID: 35194346 PMCID: PMC8855658 DOI: 10.1007/s12591-022-00593-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
COVID-19 pandemic has caused the most severe health problems to adults over 60 years of age, with particularly fatal consequences for those over 80. In this case, age-structured mathematical modeling could be useful to determine the spread of the disease and to develop a better control strategy for different age groups. In this study, we first propose an age-structured model considering two different age groups, the first group with population age below 30 years and the second with population age above 30 years, and discuss the stability of the equilibrium points and the sensitivity of the model parameters. In the second part of the study, we propose an optimal control problem to understand the age-specific role of treatment in controlling the spread of COVID -19 infection. From the stability analysis of the equilibrium points, it was found that the infection-free equilibrium point remains locally asymptotically stable whenR 0 < 1 , and when R 0 is greater than one, the infected equilibrium point remains locally asymptotically stable. The results of the optimal control study show that infection decreases with the implementation of an optimal treatment strategy, and that a combined treatment strategy considering treatment for both age groups is effective in keeping cumulative infection low in severe epidemics. Cumulative infection was found to increase with increasing saturation in medical treatment.
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Affiliation(s)
- Bishal Chhetri
- Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning-SSSIHL, Anantapur, India
| | - D. K. K. Vamsi
- Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning-SSSIHL, Anantapur, India
| | - Carani B Sanjeevi
- Department of Medicine, Karolinska Institute, Stockholm, Sweden
- Sri Sathya Sai Institute of Higher Learning-SSSIHL, Anantapur, India
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Mathematical Modeling and Forecasting of COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo Sense with Power-Law. AXIOMS 2021. [DOI: 10.3390/axioms10030228] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.
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Rahman MU, Ahmad S, Matoog RT, Alshehri NA, Khan T. Study on the mathematical modelling of COVID-19 with Caputo-Fabrizio operator. CHAOS, SOLITONS, AND FRACTALS 2021; 150:111121. [PMID: 34108819 PMCID: PMC8179098 DOI: 10.1016/j.chaos.2021.111121] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Revised: 05/25/2021] [Accepted: 05/26/2021] [Indexed: 05/28/2023]
Abstract
In this article we study a fractional-order mathematical model describing the spread of the new coronavirus (COVID-19) under the Caputo-Fabrizio sense. Exploiting the approach of fixed point theory, we compute existence as well as uniqueness of the related solution. To investigate the exact solution of our model, we use the Laplace Adomian decomposition method (LADM) and obtain results in terms of infinite series. We then present numerical results to illuminate the efficacy of the new derivative. Compared to the classical order derivatives, our obtained results under the new notion show better results concerning the novel coronavirus model.
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Affiliation(s)
- Mati Ur Rahman
- Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road Shanghai P.R. China
| | - Saeed Ahmad
- Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan
| | - R T Matoog
- Department of Mathematics, Faculty of Applied Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
| | - Nawal A Alshehri
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
| | - Tahir Khan
- Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan
- Department of Computing, Muscat College, Oman
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Almalki SJ, Afifi WA, El-Bagoury AAAH, Abd-Elmougod GA. Mathematical search technique for detecting moving novel coronavirus disease (COVID-19) based on minimizing the weight function. RESULTS IN PHYSICS 2021; 26:104455. [PMID: 34155477 PMCID: PMC8205285 DOI: 10.1016/j.rinp.2021.104455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/28/2021] [Revised: 06/10/2021] [Accepted: 06/10/2021] [Indexed: 06/13/2023]
Abstract
The study of search plans has found considerable interest between searchers due to its interesting applications in our real life like searching for located and moving targets. This paper develops a method for detecting moving targets. We propose a novel strategy based on weight function W ( Z ) , W ( Z ) = λ H ( Z ) + ( 1 - λ ) L ( Z ) , where H ( Z ) , L ( Z ) are the total probabilities of un-detecting, and total effort respectively, is searching for moving novel coronavirus disease (COVID-19) cells among finite set of different states. The total search effort will be presented in a more flexible way, so it will be presented as a random variable with a given distribution. The objective is searching for COVID-19 which hidden in one of n cells in each fixed number of time intervals m and the detection functions are supposed to be known to the searcher or robot. We look in depth for the optimal distribution of the total effort which minimizes the probability of undetected the target over the set of possible different states. The effectiveness of this model is illustrated by presenting a numerical example.
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Affiliation(s)
- Saad J Almalki
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
| | - W A Afifi
- Department of Mathematics and Statistics, Faculty of Science, Taibah University, Yanbu, Saudi Arabia
| | | | - Gamal A Abd-Elmougod
- Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
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12
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Ahmed N, Elsonbaty A, Raza A, Rafiq M, Adel W. Numerical simulation and stability analysis of a novel reaction-diffusion COVID-19 model. NONLINEAR DYNAMICS 2021; 106:1293-1310. [PMID: 34219967 PMCID: PMC8236573 DOI: 10.1007/s11071-021-06623-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Accepted: 06/08/2021] [Indexed: 06/13/2023]
Abstract
In this study, a novel reaction-diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19 SEIR model with nonlinear incidence rates by taking into account the effects of random movements of individuals from different compartments in their environments. The equilibrium points of the new system are found for both diffusive and non-diffusive models, where a detailed stability analysis is conducted for them. Moreover, the stability regions in the space of parameters are attained for each equilibrium point for both cases of the model and the effects of parameters are explored. A numerical verification for the proposed model using a finite difference-based method is illustrated along with their consistency, stability and proving the positivity of the acquired solutions. The obtained results reveal that the random motion of individuals has significant impact on the observed dynamics and steady-state stability of the spread of the virus which helps in presenting some strategies for the better control of it.
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Affiliation(s)
- Nauman Ahmed
- Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
| | - Amr Elsonbaty
- Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942 Saudi Arabia
- Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, 35516 Egypt
| | - Ali Raza
- Department of Mathematics, National College of Business Administration and Economics Lahore, Lahore, Pakistan
| | - Muhammad Rafiq
- Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan
| | - Waleed Adel
- Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, 35516 Egypt
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Iddrisu AK, A. Amikiya E, Otoo D. A predictive model for daily cumulative COVID-19 cases in Ghana. F1000Res 2021; 10:343. [PMID: 35464175 PMCID: PMC9005990 DOI: 10.12688/f1000research.52403.2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 03/01/2022] [Indexed: 11/20/2022] Open
Abstract
Background: Coronavirus disease 2019 (COVID-19) is a pandemic that has affected the daily life, governments and economies of many countries all over the globe. Ghana is currently experiencing a surge in the number of cases with a corresponding increase in the cumulative confirmed cases and deaths. The surge in cases and deaths clearly shows that the preventive and management measures are ineffective and that policy makers lack a complete understanding of the dynamics of the disease. Most of the deaths in Ghana are due to lack of adequate health equipment and facilities for managing the disease. Knowledge of the number of cases in advance would aid policy makers in allocating sufficient resources for the effective management of the cases. Methods: A predictive tool is necessary for the effective management and prevention of cases. This study presents a predictive tool that has the ability to accurately forecast the number of cumulative cases. The study applied polynomial and spline models on the COVID-19 data for Ghana, to develop a generalized additive model (GAM) that accurately captures the growth pattern of the cumulative cases. Results: The spline model and the GAM provide accurate forecast values. Conclusion: Cumulative cases of COVID-19 in Ghana are expected to continue to increase if appropriate preventive measures are not enforced. Vaccination against the virus is ongoing in Ghana, thus, future research would consider evaluating the impact of the vaccine.
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Affiliation(s)
- Abdul-Karim Iddrisu
- Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
| | - Emmanuel A. Amikiya
- Department of Management Science, Ghana Institute of Management and Public Administration, Accra, Ghana
| | - Dominic Otoo
- Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
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14
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Iddrisu AK, A. Amikiya E, Otoo D. A predictive model for daily cumulative COVID-19 cases in Ghana. F1000Res 2021; 10:343. [PMID: 35464175 PMCID: PMC9005990 DOI: 10.12688/f1000research.52403.1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Accepted: 04/23/2021] [Indexed: 09/19/2023] Open
Abstract
Background: Coronavirus disease 2019 (COVID-19) is a pandemic that has affected the daily life, governments and economies of many countries all over the globe. Ghana is currently experiencing a surge in the number of cases with a corresponding increase in the cumulative confirmed cases and deaths. The surge in cases and deaths clearly shows that the preventive and management measures are ineffective and that policy makers lack a complete understanding of the dynamics of the disease. Most of the deaths in Ghana are due to lack of adequate health equipment and facilities for managing the disease. Knowledge of the number of cases in advance would aid policy makers in allocating sufficient resources for the effective management of the cases. Methods: A predictive tool is necessary for the effective management and prevention of cases. This study presents a predictive tool that has the ability to accurately forecast the number of cumulative cases. The study applied polynomial and spline models on the COVID-19 data for Ghana, to develop a generalized additive model (GAM) that accurately captures the growth pattern of the cumulative cases. Results: The spline model and the GAM provide accurate forecast values. Conclusion: Cumulative cases of COVID-19 in Ghana are expected to continue to increase if appropriate preventive measures are not enforced. Vaccination against the virus is ongoing in Ghana, thus, future research would consider evaluating the impact of the vaccine.
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Affiliation(s)
- Abdul-Karim Iddrisu
- Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
| | - Emmanuel A. Amikiya
- Department of Management Science, Ghana Institute of Management and Public Administration, Accra, Ghana
| | - Dominic Otoo
- Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana
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15
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Almongy HM, Almetwally EM, Aljohani HM, Alghamdi AS, Hafez EH. A new extended rayleigh distribution with applications of COVID-19 data. RESULTS IN PHYSICS 2021; 23:104012. [PMID: 33728260 PMCID: PMC7952137 DOI: 10.1016/j.rinp.2021.104012] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Revised: 02/16/2021] [Accepted: 02/22/2021] [Indexed: 05/19/2023]
Abstract
This paper aims to model the COVID-19 mortality rates in Italy, Mexico, and the Netherlands, by specifying an optimal statistical model to analyze the mortality rate of COVID-19. A new lifetime distribution with three-parameter is introduced by a combination of Rayleigh distribution and extended odd Weibull family to produce the extended odd Weibull Rayleigh (EOWR) distribution. This new distribution has many excellent properties as simple linear representation, hazard rate function, and moment generating function. Maximum likelihood, maximum product spacing and Bayesian estimation methods are applied to estimate the unknown parameters of EOWR distribution. MCMC method is used for the Bayesian estimation. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. Also, data analysis for the real data of mortality rate is considered.
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Affiliation(s)
- Hisham M Almongy
- Department of Statistics, Faculty of Commerce, Mansoura University, Mansoura, Egypt
| | - Ehab M Almetwally
- Department of Statistics, Faculty of Business Administration, Delta University of Science and Technology, Egypt
| | - Hassan M Aljohani
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
| | - Abdulaziz S Alghamdi
- Department of Mathematics, College of Science & Arts, King Abdulaziz University, P. O. Box 344, Rabigh 21911, Saudi Arabia
| | - E H Hafez
- Mathematics Department, Faculty of Science, Helwan University, Helwan, Egypt
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Ameen IG, Ali HM, Alharthi MR, Abdel-Aty AH, Elshehabey HM. Investigation of the dynamics of COVID-19 with a fractional mathematical model: A comparative study with actual data. RESULTS IN PHYSICS 2021; 23:103976. [PMID: 33623732 PMCID: PMC7892305 DOI: 10.1016/j.rinp.2021.103976] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Revised: 02/07/2021] [Accepted: 02/08/2021] [Indexed: 02/06/2023]
Abstract
One of the greatest challenges facing the humankind nowadays is to confront that emerging virus, which is the Coronavirus (COVID-19), and therefore all organizations have to unite in order to tackle that the transmission risk of this virus. From this standpoint, the scientific researchers have to find good mathematical models that do describe the transmission of such virus and contribute to reducing it in one way or another, where the study of COVID-19 transmission dynamics by mathematical models is very important for analyzing and controlling this disease propagation. Thus, in the current work, we present a new fractional-order mathematical model that describes the dynamics of COVID-19. In the proposed model, the total population is divided into eight classes, in addition to three compartments used to estimate the parameters and initial values. The effective reproduction number ( R 0 ) is derived by next generation matrix (NGM) method and all possible equilibrium points and their stability are investigated in details. We used the reported data (from January 23, 2020, to November 21, 2020) from the National Health Commission (NHC) of China to estimate the parameters and initial conditions (ICs) which suggested for our model. Simulation outcomes demonstrate that the fractional order model (FOM) represents behaviors that follow the real data more accurately than the integer-order model. The current work enhances the recent reported results of Zu et al. published in THE LANCET (doi:10.2139/ssrn.3539669).
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Affiliation(s)
- Ismail Gad Ameen
- Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
| | - Hegagi Mohamed Ali
- Department of Mathematics, Faculty of Science, Aswan University, Aswan 81528, Egypt
| | - M R Alharthi
- Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia
| | - Abdel-Haleem Abdel-Aty
- Department of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia
- Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
| | - Hillal M Elshehabey
- Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
- Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
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Ullah A, Ahmad S, Rahman GU, Alqarni MM, Mahmoud EE. Impact of pangolin bootleg market on the dynamics of COVID-19 model. RESULTS IN PHYSICS 2021; 23:103913. [PMID: 33623730 PMCID: PMC7892304 DOI: 10.1016/j.rinp.2021.103913] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/13/2020] [Revised: 01/27/2021] [Accepted: 01/28/2021] [Indexed: 06/12/2023]
Abstract
In this paper we consider ant-eating pangolin as a possible source of the novel corona virus (COVID-19) and propose a new mathematical model describing the dynamics of COVID-19 pandemic. Our new model is based on the hypotheses that the pangolin and human populations are divided into measurable partitions and also incorporates pangolin bootleg market or reservoir. First we study the important mathematical properties like existence, boundedness and positivity of solution of the proposed model. After finding the threshold quantity for the underlying model, the possible stationary states are explored. We exploit linearization as well as Lyapanuv function theory to exhibit local stability analysis of the model in terms of the threshold quantity. We then discuss the global stability analyses of the newly introduced model and found conditions for its stability in terms of the basic reproduction number. It is also shown that for certain values of R 0 , our model exhibits a backward bifurcation. Numerical simulations are performed to verify and support our analytical findings.
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Affiliation(s)
- Abd Ullah
- Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan
| | - Saeed Ahmad
- Department of Mathematics, University of Malakand Chakdara, Dir (L), Pakhtunkhwa, Pakistan
| | - Ghaus Ur Rahman
- Department of Mathematics and Statistics, University of Swat, District Swat, Pakistan
| | - M M Alqarni
- Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
| | - Emad E Mahmoud
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
- Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
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Thabet STM, Abdo MS, Shah K. Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo-Fabrizio derivative. ADVANCES IN DIFFERENCE EQUATIONS 2021; 2021:184. [PMID: 33777126 PMCID: PMC7988648 DOI: 10.1186/s13662-021-03316-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Accepted: 02/22/2021] [Indexed: 06/12/2023]
Abstract
This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo-Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard's iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian's decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.
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Affiliation(s)
| | | | - Kamal Shah
- Department of Mathematics, University of Malakand, Chakdara, Dir(L), KPK Pakistan
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Sinan M, Ali A, Shah K, Assiri TA, Nofal TA. Stability analysis and optimal control of Covid-19 pandemic SEIQR fractional mathematical model with harmonic mean type incidence rate and treatment. RESULTS IN PHYSICS 2021; 22:103873. [PMID: 33552882 PMCID: PMC7850626 DOI: 10.1016/j.rinp.2021.103873] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/05/2020] [Revised: 01/17/2021] [Accepted: 01/18/2021] [Indexed: 06/12/2023]
Abstract
In the present work, we investigated the transmission dynamics of fractional order SARS-CoV-2 mathematical model with the help of Susceptible S ( t ) , Exposed E ( t ) , Infected I ( t ) , Quarantine Q ( t ) , and Recovered R ( t ) . The aims of this work is to investigate the stability and optimal control of the concerned mathematical model for both local and global stability by third additive compound matrix approach and we also obtained threshold value by the next generation approach. The author's visualized the desired results graphically. We also control each of the population of underlying model with control variables by optimal control strategies with Pontryagin's maximum Principle and obtained the desired numerical results by using the homotopy perturbation method. The proposed model is locally asymptotically unstable, while stable globally asymptotically on endemic equilibrium. We also explored the results graphically in numerical section for better understanding of transmission dynamics.
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Affiliation(s)
- Muhammad Sinan
- Department of Mathematics and Statistics, University of Swat, 18000 Khyber Pakhtunkhwa, Pakistan
| | - Amjad Ali
- Department of Mathematics, Govt P.G Jahanzeb College Swat, 18000 Khyber Pakhtunkhwa, Pakistan
| | - Kamal Shah
- Department of Mathematics, University of Malakand, Chakdara Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
| | - Taghreed A Assiri
- Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia
| | - Taher A Nofal
- Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
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Hussain T, Ozair M, Ali F, Rehman SU, Assiri TA, Mahmoud EE. Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model. RESULTS IN PHYSICS 2021; 22:103956. [PMID: 33623733 PMCID: PMC7889458 DOI: 10.1016/j.rinp.2021.103956] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2021] [Revised: 02/03/2021] [Accepted: 02/04/2021] [Indexed: 05/06/2023]
Abstract
It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.
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Affiliation(s)
- Takasar Hussain
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
| | - Muhammad Ozair
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
| | - Farhad Ali
- Department of Mathematics, Kohat University of Science and Technology, Kohat, Pakistan
| | - Sajid Ur Rehman
- Department of Mathematics, Kohat University of Science and Technology, Kohat, Pakistan
| | - Taghreed A Assiri
- Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia
| | - Emad E Mahmoud
- Department of Mathematics and Statistics, College of Science, Taif University, PO Box 11099, Taif 21944, Saudi Arabia
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