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Abstract
A novel coronavirus infection system is established for the analytical and computational aspects of this study, using a fuzzy fractional evolution equation (FFEE) stated in Caputo’s sense for order (1,2). It is constructed using the FFEE formulated in Caputo’s meaning. The model consist of six components illustrating the coronavirus outbreak, involving the susceptible people Kℓ(ω), the exposed population Lℓ(ω), total infected strength Cℓ(ω), asymptotically infected population Mℓ(ω), total number of humans recovered Eℓ(ω), and reservoir Qℓ(ω). Numerical results using the fuzzy Laplace approach in combination with the Adomian decomposition transform are developed to better understand the dynamical structures of the physical behavior of COVID-19. For the controlling model, such behavior on the generic characteristics of RNA in COVID-19 is also examined. The findings show that the proposed technique of addressing the uncertainty issue in a pandemic situation is effective.
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Padmapriya V, Kaliyappan M. Fuzzy fractional mathematical model of COVID-19 epidemic. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-211173] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In this paper, we develop a mathematical model with a Caputo fractional derivative under fuzzy sense for the prediction of COVID-19. We present numerical results of the mathematical model for COVID-19 of most three infected countries such as the USA, India and Italy. Using the proposed model, we estimate predicting future outbreaks, the effectiveness of preventive measures and potential control strategies of the infection. We provide a comparative study of the proposed model with Ahmadian’s fuzzy fractional mathematical model. The results demonstrate that our proposed fuzzy fractional model gives a nearer forecast to the actual data. The present study can confirm the efficiency and applicability of the fractional derivative under uncertainty conditions to mathematical epidemiology.
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Affiliation(s)
- V. Padmapriya
- Research Scholar, Vellore Institute of Technology, Chennai Campus, India
- New Prince Shri Bhavani Arts and Sciences College, Chennai, India
| | - M. Kaliyappan
- Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai Campus, India
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Fotsa-Mbogne DJ, Tchoumi SY, Kouakep-Tchaptchie Y, Kamla VC, Kamgang JC, Houpa-Danga DE, Bowong-Tsakou S, Bekolle D. Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon. NONLINEAR DYNAMICS 2021; 106:2703-2738. [PMID: 34697521 PMCID: PMC8528969 DOI: 10.1007/s11071-021-06920-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 09/18/2021] [Indexed: 05/31/2023]
Abstract
This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold T 0 is less or equal to 1 and the basic reproduction number R 0 is calculated. A convergence index T 1 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of R 0 , T 0 and T 1 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.
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Affiliation(s)
- David Jaurès Fotsa-Mbogne
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Stéphane Yanick Tchoumi
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Yannick Kouakep-Tchaptchie
- Department of Fundamental Science and Engineering, EGCIM, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
| | - Vivient Corneille Kamla
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Jean-Claude Kamgang
- Department of Mathematics and Computer Science, ENSAI, The University of Ngaoundere, P.O. Box 455, Ngaoundere, Cameroon
| | - Duplex Elvis Houpa-Danga
- Department of Mathematics and Computer Science, FS, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
| | - Samuel Bowong-Tsakou
- Department of Mathematics and Computer Science, FS, The University of Douala, P.O. Box 24157, Douala, Cameroon
| | - David Bekolle
- Department of Mathematics and Computer Science, FS, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
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Ahmad S, Ullah A, Ullah A, Akgül A, Abdeljawad T. Computational analysis of fuzzy fractional order non-dimensional Fisher equation. PHYSICA SCRIPTA 2021; 96:084004. [DOI: 10.1088/1402-4896/abface] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
Abstract
In recent decades, fuzzy differential equations of integer and arbitrary order are extensively used for analyzing the dynamics of a mathematical model of the physical process because crisp operators of integer and arbitrary order are not able to study the model being studied when there is uncertainty in values used in modeling. In this article, we have considered the time-fractional Fisher equation in a fuzzy environment. The basic aim of this article is to deduce a semi-analytical solution to the fuzzy fractional-order non-dimensional model of the Fisher equation. Since the Laplace-Adomian method has a good convergence rate. We use the Laplace- Adomian decomposition method (LADM) to determine a solution under a fuzzy concept in parametric form. We discuss the convergence and error analysis of the proposed method. For the validity of the proposed scheme, we provide few examples with detailed solutions. We provide comparisons between exact and approximate solutions through graphs. In the end, the conclusion of the paper is provided.
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Askar SS, Ghosh D, Santra PK, Elsadany AA, Mahapatra GS. A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect. RESULTS IN PHYSICS 2021; 24:104067. [PMID: 33777667 PMCID: PMC7985659 DOI: 10.1016/j.rinp.2021.104067] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Revised: 03/07/2021] [Accepted: 03/08/2021] [Indexed: 05/07/2023]
Abstract
In this paper, we consider a mathematical model to explain, understanding, and to forecast the outbreaks of COVID-19 in India. The model has four components leading to a system of fractional order differential equations incorporating the refuge concept to study the lockdown effect in controlling COVID-19 spread in India. We investigate the model using the concept of Caputo fractional-order derivative. The goal of this model is to estimate the number of total infected, active cases, deaths, as well as recoveries from COVID-19 to control or minimize the above issues in India. The existence, uniqueness, non-negativity, and boundedness of the solutions are established. In addition, the local and global asymptotic stability of the equilibrium points of the fractional-order system and the basic reproduction number are studied for understanding and prediction of the transmission of COVID-19 in India. The next step is to carry out sensitivity analysis to find out which parameter is the most dominant to affect the disease's endemicity. The results reveal that the parameters η , μ and ρ are the most dominant sensitivity indices towards the basic reproductive number. A numerical illustration is presented via computer simulations using MATLAB to show a realistic point of view.
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Affiliation(s)
- S S Askar
- Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
| | - Dipankar Ghosh
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
| | - P K Santra
- Abada Nsup School, Howrah, West Bengal, India
| | - Abdelalim A Elsadany
- Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt
| | - G S Mahapatra
- Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India
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Arfan M, Alrabaiah H, Rahman MU, Sun YL, Hashim AS, Pansera BA, Ahmadian A, Salahshour S. Investigation of fractal-fractional order model of COVID-19 in Pakistan under Atangana-Baleanu Caputo (ABC) derivative. RESULTS IN PHYSICS 2021; 24:104046. [PMID: 33868907 PMCID: PMC8044634 DOI: 10.1016/j.rinp.2021.104046] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2021] [Revised: 03/01/2021] [Accepted: 03/03/2021] [Indexed: 05/20/2023]
Abstract
This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.
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Affiliation(s)
- Muhammad Arfan
- Department of Mathematics, University of Malakand, Chakdara Dir (L), KPK, Pakistan
| | - Hussam Alrabaiah
- Al Ain University, Al Ain, United Arab Emirates
- Mathematics Department, Tafila Technical University, Tafila, Jordan
| | - Mati Ur Rahman
- Department of Mathematics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, PR China
| | - Yu-Liang Sun
- School of Science, Huzhou University, Huzhou 313000, PR China
| | - Ahmad Sobri Hashim
- Computer & Information Sciences Department, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Perak, Malaysia
| | - Bruno A Pansera
- Department of Law, Economics and Human Sciences & Decisions Lab, Mediterranea University of Reggio Calabria, Reggio Calabria 89125, Italy
| | - Ali Ahmadian
- Institute of IR 4.0, The National University of Malaysia, Bangi, 43600 UKM, Selangor, Malaysia
- School of Mathematical Sciences, College of Science and Technology Wenzhou-Kean University, Wenzhou, PR China
| | - Soheil Salahshour
- Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
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Verma P, Kumar M. On the existence and stability of fuzzy CF variable fractional differential equation for COVID-19 epidemic. ENGINEERING WITH COMPUTERS 2021; 38:1053-1064. [PMID: 33583985 PMCID: PMC7870457 DOI: 10.1007/s00366-021-01296-9] [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: 12/12/2020] [Accepted: 01/10/2021] [Indexed: 05/24/2023]
Abstract
In this paper, we convert the recent COVID-19 model with the use of the most influential theories, such as variable fractional calculus and fuzzy theory. We propose the fuzzy variable fractional differential equation for the COVID-19 model in which the variable fractional-order derivative is described using the Caputo-Fabrizio in the Caputo sense. Furthermore, we provide the results on the existence and uniqueness using Lipschitz conditions. Also, discuss the stability analysis of the present new COVID-19 model by employing Hyers-Ulam stability.
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Affiliation(s)
- Pratibha Verma
- Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004 Uttar Pradesh India
| | - Manoj Kumar
- Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004 Uttar Pradesh India
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Ahmad N, Ullah A, Ullah A, Ahmad S, Shah K, Ahmad I. On analysis of the fuzzy fractional order Volterra-Fredholm integro-differential equation. ALEXANDRIA ENGINEERING JOURNAL 2021; 60:1827-1838. [DOI: 10.1016/j.aej.2020.11.031] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Hanif A, Butt AIK, Ahmad S, Din RU, Inc M. A new fuzzy fractional order model of transmission of Covid-19 with quarantine class. EUROPEAN PHYSICAL JOURNAL PLUS 2021; 136:1179. [PMID: 34849324 PMCID: PMC8612626 DOI: 10.1140/epjp/s13360-021-02178-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 11/13/2021] [Indexed: 05/02/2023]
Abstract
This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo's sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.
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Affiliation(s)
- Asma Hanif
- Department of Mathematics, Government College University Lahore, Lahore, Pakistan
| | - A. I. K. Butt
- Department of Mathematics, Government College University Lahore, Lahore, Pakistan
| | - Shabir Ahmad
- Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa Pakistan
| | - Rahim Ud Din
- Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa Pakistan
| | - Mustafa Inc
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
- Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey
- Department of Medical Research, China Medical University, Taichung, Taiwan
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