51
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Rizvi STR, Seadawy AR, Ali K, Younis M, Ashraf MA. Multiple lump and rogue wave for time fractional resonant nonlinear Schrödinger equation under parabolic law with weak nonlocal nonlinearity. OPTICAL AND QUANTUM ELECTRONICS 2022; 54:212. [PMID: 35308635 PMCID: PMC8918080 DOI: 10.1007/s11082-022-03606-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 02/05/2022] [Indexed: 06/14/2023]
Abstract
This article retrieve lump, lump with one kink and rogue wave soliton for the time fractional resonant nonlinear Schrödinger equation with parabolic law having weak nonlocal nonlinearity. According to theory of dynamical systems, Schrödinger equation may be converted into plane systems. We use Hirota bilinear method to obtained these solutions. At the end, we present graphical representation of our results in various dimensions.
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Affiliation(s)
- Syed T. R. Rizvi
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
| | - Aly R. Seadawy
- Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
| | - K. Ali
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
| | - M. Younis
- PUCIT, University of the Punjab, Lahore, Pakistan
| | - M. A. Ashraf
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
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52
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Poonia A, Chakrabarty SP. Two strains and drug adherence: An HIV model in the paradigm of community transmission. NONLINEAR DYNAMICS 2022; 108:2767-2792. [PMID: 35310019 PMCID: PMC8916704 DOI: 10.1007/s11071-022-07323-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 01/31/2022] [Indexed: 06/14/2023]
Abstract
A two-strain model, comprising of drug-sensitive and drug-resistant strains, is proposed for the dynamics of Human Immunodeficiency Virus (HIV) spread in a community. A treatment model is introduced by taking drug adherence into account. The treatment-free model is analyzed for the effect of treatment availability and drug adherence on disease dynamics. The analysis revealed that for the treatment-free model, at least one strain faces competitive exclusion, and co-existence of both strains is not possible. On the contrary, both strains may co-exist in presence of treatment. The analysis carried out was both local, as well as global. A comprehensive bifurcation analysis showed periodic behaviour and all solutions approached a stable limit cycle for a wide range of parametric values. Overall, we concluded that the treatment availability and drug adherence play a significant role in determining the dynamics of HIV spread. Numerical simulations are performed to validate the analytical results using MATLAB.
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Affiliation(s)
- Ashish Poonia
- Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, India
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53
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Kumar S, Chauhan RP, Aly AA, Momani S, Hadid S. A study on fractional HBV model through singular and non-singular derivatives. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2022; 231:1885-1904. [PMID: 35251498 PMCID: PMC8889534 DOI: 10.1140/epjs/s11734-022-00460-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
The current study's aim is to evaluate the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers using two different numerical algorithms and various values of the fractional-order parameter. We considered the model with two different fractional-order derivatives, namely the Caputo derivative and Atangana-Baleanu derivative in the Caputo sense (ABC). The considered derivatives are the most widely used fractional operators in modeling. We present some mathematical analysis of the fractional ABC model. The fixed-point theory is used to determine the existence and uniqueness of the solutions to the considered fractional model. For numerical results, we show a generalized Adams-Bashforth-Moulton (ABM) method for Caputo derivative and an Adams type predictor-corrector (PC) algorithm for Atangana-Baleanu derivatives. Finally, the models are numerically solved using computational techniques and obtained results graphically illustrated with a wide range of fractional-order values. We compare the numerical results for Caputo and ABC derivatives graphically. In addition, a new variable-order fractional network of the HBV model is proposed. Considering the fact that most communities interact with each other, and the rate of disease spread is affected by this factor, the proposed network can provide more accurate insight for the modeling of the disease.
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Affiliation(s)
- Sunil Kumar
- Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 831014 India
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
- Department of Mathematics, College of Science, King Saud University, P.O.box 2455, Riyadh 1141, Saudi Arabia
- Department of Mathematics, University Center for Research and Development, Chandigarh University, Grauhan, Mohali, Punjab India
| | - R. P. Chauhan
- Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 831014 India
| | - Ayman A. Aly
- Department of Mechanical Engineering, College of Engineering, Taif University, PO Box 11099, Taif, 21944 Saudi Arabia
| | - Shaher Momani
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
- Department of Mathematics, Faculty of Science, University of Jordan, Amman, 11942 Jordan
| | - Samir Hadid
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
- Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman, UAE
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54
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Fu Z, He X, Liu P, Palizban A, Liao W. Distributed Neural Network and Particle Swarm Optimization for Micro-grid Adaptive Power Allocation. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10760-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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55
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Zeb A, Kumar P, Erturk VS, Sitthiwirattham T. A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms. JOURNAL OF KING SAUD UNIVERSITY. SCIENCE 2022; 34:101914. [PMID: 35194351 PMCID: PMC8851876 DOI: 10.1016/j.jksus.2022.101914] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 09/27/2021] [Accepted: 02/14/2022] [Indexed: 05/24/2023]
Abstract
The main purpose of this paper is to provide new vaccinated models of COVID-19 in the sense of Caputo-Fabrizio and new generalized Caputo-type fractional derivatives. The formulation of the given models is presented including an exhaustive study of the model dynamics such as positivity, boundedness of the solutions and local stability analysis. Furthermore, the unique solution existence for the proposed fractional order models is discussed via fixed point theory. Numerical solutions are also derived by using two-steps Adams-Bashforth algorithm for Caputo-Fabrizio operator, and modified Predictor-Corrector method for generalised Caputo fractional derivative. Our analysis allow to show that the given fractional-order models exemplify the dynamics of COVID-19 much better than the classical ones. Also, the analysis on the convergence and stability for the proposed methods are performed. By this study, we see that how the vaccine availability plays an important role in the control of COVID-19 infection.
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Affiliation(s)
- Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad 22060, K.P.K, Pakistan
| | - Pushpendra Kumar
- Department of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab, 151001, India
| | - Vedat Suat Erturk
- Department of Mathematics, Ondokuz Mayis University, Atakum-55200, Samsun, Turkey
| | - Thanin Sitthiwirattham
- Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
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56
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The Complex Systems for Conflict Interaction Modelling to Describe a Non-Trivial Epidemiological Situation. MATHEMATICS 2022. [DOI: 10.3390/math10040537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
This study investigates a complex system that describes a non-trivial epidemiological model with integrated internal conflict (interregional migration) on the example of cyclic migration using the software. JetBrains PyCharm Community Edition 2020.3.3, a free and open-source integrated development environment (IDE) in the Python programming language, was chosen as the software development tool. The Matplotlib 3.5 library was used to display the modelling results graphically. The integration of internal conflict into the model revealed significant and notable changes in its behavior. This study’s results prove that not only the characteristics of the interaction factors but also the size of the values determine the direction of migration concerning relation to competitors.
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Subramanian M, Manigandan M, Tunç C, Gopal TN, Alzabut J. On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2022. [DOI: 10.1080/16583655.2021.2010984] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- M. Subramanian
- Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, India
| | - M. Manigandan
- Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India
| | - C. Tunç
- Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, Turkey
| | - T. N. Gopal
- Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore, India
| | - J. Alzabut
- Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
- Department of Industrial Engineering, OSTİM Technical University, Ankara, Turkey
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58
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Anwar N, Ahmad I, Raja MAZ, Naz S, Shoaib M, Kiani AK. Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays. EUROPEAN PHYSICAL JOURNAL PLUS 2022; 137:144. [PMID: 35079560 PMCID: PMC8775172 DOI: 10.1140/epjp/s13360-021-02248-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2021] [Accepted: 12/02/2021] [Indexed: 05/10/2023]
Abstract
The presented study deals with the exploitation of the artificial intelligence knacks-based stochastic paradigm for the numerical treatment of the nonlinear delay differential system for dynamics of plant virus propagation with the impact of seasonality and delays (PVP-SD) model by implementing neural networks backpropagation with Bayesian regularization scheme (NNs-BBRS). The PVP-SD model is represented with five classes-based ODEs systems for the interaction between insects and plants. The nonlinear PVP-SD model governs with five populations: S(t) susceptible plants, I(t) infected plants, X(t) susceptible insect vectors, Y(t) infected insect vectors and P(t) predators. Adams numerical procedure is adopted to generate the reference solutions of the nonlinear PVP-SD model based on the variety of cases by varying the plants bite rate due to vectors, vector bite rate due to plants, plant's recovery rate, predator contact rate with healthy insects, predator contact rate with infected insects and death rate caused by insecticides. The approximate solutions of the nonlinear PVP-SD model are determined by executing the designed NNs-BBRS through different target and inputs arbitrary selected samples for the training and testing data. Validation of the consistent precision and convergence of the designed NNs-BBRS is efficaciously substantiated through exhaustive simulations and analyses on mean square error-based merit function, index of regression and error histogram illustrations.
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Affiliation(s)
- Nabeela Anwar
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Iftikhar Ahmad
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002 Yunlin Taiwan, R.O.C
| | - Shafaq Naz
- Department of Mathematics, University of Gujrat, Gujrat, 50700 Pakistan
| | - Muhammad Shoaib
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600 Pakistan
| | - Adiqa Kausar Kiani
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002 Yunlin Taiwan, R.O.C
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59
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Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-021-00061-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractIn this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described.
By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.
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60
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Raja MAZ, Naz H, Shoaib M, Mehmood A. Design of backpropagated neurocomputing paradigm for Stuxnet virus dynamics in control infrastructure. Neural Comput Appl 2022. [DOI: 10.1007/s00521-021-06721-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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61
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Attia RAM, Tian J, Lu D, Aguilar JFG, Khater MMA. Unstable novel and accurate soliton wave solutions of the nonlinear biological population model. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES 2022. [DOI: 10.1080/25765299.2021.2024652] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Raghda A. M. Attia
- School of Management and Economics, Jiangsu University of Science and Technology, Zhenjiang, China
| | - Jian Tian
- School of Management and Economics, Jiangsu University of Science and Technology, Zhenjiang, China
| | - Dianchen Lu
- Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, China
| | | | - Mostafa M. A. Khater
- Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, China
- Department of Basic Science, Obour High Institute for Engineering and Technology, Cairo, Egypt
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62
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AlArjani A, Nasseef MT, Kamal SM, Rao BVS, Mahmud M, Uddin MS. Application of Mathematical Modeling in Prediction of COVID-19 Transmission Dynamics. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2022; 47:10163-10186. [PMID: 35018276 PMCID: PMC8739391 DOI: 10.1007/s13369-021-06419-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2021] [Accepted: 11/17/2021] [Indexed: 12/23/2022]
Abstract
The entire world has been affected by the outbreak of COVID-19 since early 2020. Human carriers are largely the spreaders of this new disease, and it spreads much faster compared to previously identified coronaviruses and other flu viruses. Although vaccines have been invented and released, it will still be a challenge to overcome this disease. To save lives, it is important to better understand how the virus is transmitted from one host to another and how future areas of infection can be predicted. Recently, the second wave of infection has hit multiple countries, and governments have implemented necessary measures to tackle the spread of the virus. We investigated the three phases of COVID-19 research through a selected list of mathematical modeling articles. To take the necessary measures, it is important to understand the transmission dynamics of the disease, and mathematical modeling has been considered a proven technique in predicting such dynamics. To this end, this paper summarizes all the available mathematical models that have been used in predicting the transmission of COVID-19. A total of nine mathematical models have been thoroughly reviewed and characterized in this work, so as to understand the intrinsic properties of each model in predicting disease transmission dynamics. The application of these nine models in predicting COVID-19 transmission dynamics is presented with a case study, along with detailed comparisons of these models. Toward the end of the paper, key behavioral properties of each model, relevant challenges and future directions are discussed.
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Affiliation(s)
- Ali AlArjani
- Department of Mechanical & Industrial Engineering, College of Engineering, Prince Sattam Bin Abdulaziz University, AlKharj, 16273 Saudi Arabia
| | - Md Taufiq Nasseef
- Douglas Hospital Research Center, Department of Psychiatry, School of Medicine, McGill University, Montreal, QC Canada
| | - Sanaa M. Kamal
- Department of Internal Medicine, College of medicine, Prince Sattam Bin Abdulaziz University, AlKharj, 11942 Saudi Arabia
| | - B. V. Subba Rao
- Dept of Information Technology, PVP Siddhartha Institute of Technology, Chalasani Nagar, Kanuru, Vijayawada, Andhra Pradesh 520007 India
| | - Mufti Mahmud
- Department of Computer Science, Nottingham Trent University, Clifton, Nottingham, NG11 8NS UK
- Medical Technologies Innovation Facility, Nottingham Trent University, Clifton, Nottingham, NG11 8NS UK
- Computing and Informatics Research Centre, Nottingham Trent University, Clifton, Nottingham, NG11 8NS UK
| | - Md Sharif Uddin
- Department of Mechanical & Industrial Engineering, Prince Sattam Bin Abdulaziz University, AlKharj, 16273 Saudi Arabia
- Department of Mathematics, Jahangirnagar University, Savar, Dhaka, 1342 Bangladesh
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63
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Hu B, Wang Z, Xu M, Wang D. Quasilinearization method for an impulsive integro-differential system with delay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:612-623. [PMID: 34903004 DOI: 10.3934/mbe.2022027] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this paper, we obtain solution sequences converging uniformly and quadratically to extremal solutions of an impulsive integro-differential system with delay. The main tools are the method of quasilinearization and the monotone iterative. The results obtained are more general and applicable than previous studies, especially the quadratic convergence of the solution for a class of integro-differential equations, which have been involved little by now.
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Affiliation(s)
- Bing Hu
- Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Zhizhi Wang
- Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Minbo Xu
- Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Dingjiang Wang
- Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China
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64
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Abstract
This study presents a structure preserving nonstandard finite difference scheme to analyze a susceptible-infected-treatment-recovered (SITR) dynamical model of coronavirus 2019 (covid-19) with bimodal virus transmission in susceptible population. The underlying model incorporates the possible treatment measures as the emerging scenario of covid-19 vaccines. Keeping in view the fact that the real time data for covid-19 is updated at discrete time steps, we propose a new structure preserving numerical scheme for the proposed model. The proposed numerical scheme produces realistic solutions of the complex bi-modal SITR nonlinear model, converges unconditionally to steady states and reflects dynamical consistency with continuous sense of the model. The analysis of the model reveals that the model remains stable at the steady state points. The basic reproduction number Rcovid falls less than 1 when treatment rate is increased and disease will die out. On the other hand, it predicts that human population may face devastating effects of pandemic if the treatment measures are not strictly implemented.
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65
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Yang B, Yu Z, Cai Y. A spread model of COVID-19 with some strict anti-epidemic measures. NONLINEAR DYNAMICS 2022; 109:265-284. [PMID: 35283556 PMCID: PMC8900482 DOI: 10.1007/s11071-022-07244-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2021] [Accepted: 01/17/2022] [Indexed: 05/09/2023]
Abstract
In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.
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Affiliation(s)
- Bo Yang
- Department of Automation, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
| | - Zhenhua Yu
- Institute of Systems Security and Control, College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an, 710054 People’s Republic of China
| | - Yuanli Cai
- Department of Automation, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
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66
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Caputo fractional-order SEIRP model for COVID-19 Pandemic. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:829-845. [PMCID: PMC8096164 DOI: 10.1016/j.aej.2021.04.097] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Revised: 04/25/2021] [Accepted: 04/27/2021] [Indexed: 06/15/2023]
Abstract
We propose a Caputo-based fractional compartmental model for the dynamics of the novel COVID-19 pandemic. The newly proposed nonlinear fractional order model is an extension of a recently formulated integer-order COVID-19 mathematical model. Using basic concepts such as continuity and Banach fixed-point theorem, existence and uniqueness of the solution to the proposed model were shown. Furthermore, we analyze the stability of the model in the context of Ulam-Hyers and generalized Ulam-Hyers stability criteria. The concept of next-generation matrix was used to compute the basic reproduction number R0, a number that determines the spread or otherwise of the disease into the general population. We also investigated the local asymptotic stability for the derived disease-free equilibrium point. Numerical simulation of the constructed epidemic model was carried out using the fractional Adam-Bashforth-Moulton method to validate the obtained theoretical results.
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67
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Numerical Solutions of the Mathematical Models on the Digestive System and COVID-19 Pandemic by Hermite Wavelet Technique. Symmetry (Basel) 2021. [DOI: 10.3390/sym13122428] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system by considering different parameters such as sleep factor, tension, food rate, death rate, and medicine. Here, we discussed how these parameters influence the digestive system and showed them through figures and tables. Another fractional model is used on the COVID-19 pandemic. This model is defined by a system of fractional-ODEs including five variables, called S (susceptible), E (exposed), I (infected), Q (quarantined), and R (recovered). The proposed wavelet technique investigates these two models. Here, we express the modeled equation in terms of the Hermite wavelets along with the collocation scheme. Then, using the properties of wavelets, we convert the modeled equation into a system of algebraic equations. We use the Newton–Raphson method to solve these nonlinear algebraic equations. The obtained results are compared with numerical solutions and the Runge–Kutta method (R–K method), which is expressed through tables and graphs. The HWM computational time (consumes less time) is better than that of the R–K method.
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Hasoon JN, Fadel AH, Hameed RS, Mostafa SA, Khalaf BA, Mohammed MA, Nedoma J. COVID-19 anomaly detection and classification method based on supervised machine learning of chest X-ray images. RESULTS IN PHYSICS 2021; 31:105045. [PMID: 34840938 PMCID: PMC8607738 DOI: 10.1016/j.rinp.2021.105045] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Revised: 11/19/2021] [Accepted: 11/19/2021] [Indexed: 05/03/2023]
Abstract
The term COVID-19 is an abbreviation of Coronavirus 2019, which is considered a global pandemic that threatens the lives of millions of people. Early detection of the disease offers ample opportunity of recovery and prevention of spreading. This paper proposes a method for classification and early detection of COVID-19 through image processing using X-ray images. A set of procedures are applied, including preprocessing (image noise removal, image thresholding, and morphological operation), Region of Interest (ROI) detection and segmentation, feature extraction, (Local binary pattern (LBP), Histogram of Gradient (HOG), and Haralick texture features) and classification (K-Nearest Neighbor (KNN) and Support Vector Machine (SVM)). The combinations of the feature extraction operators and classifiers results in six models, namely LBP-KNN, HOG-KNN, Haralick-KNN, LBP-SVM, HOG-SVM, and Haralick-SVM. The six models are tested based on test samples of 5,000 images with the percentage of training of 5-folds cross-validation. The evaluation results show high diagnosis accuracy from 89.2% up to 98.66%. The LBP-KNN model outperforms the other models in which it achieves an average accuracy of 98.66%, a sensitivity of 97.76%, specificity of 100%, and precision of 100%. The proposed method for early detection and classification of COVID-19 through image processing using X-ray images is proven to be usable in which it provides an end-to-end structure without the need for manual feature extraction and manual selection methods.
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Affiliation(s)
- Jamal N Hasoon
- Department of Computer Science, Mustansiriyah University, 10001 Baghdad, Iraq
| | - Ali Hussein Fadel
- Department of Computer Science, University of Diyala, 32001 Diyala, Iraq
| | - Rasha Subhi Hameed
- Department of Computer Science, University of Diyala, 32001 Diyala, Iraq
| | - Salama A Mostafa
- Faculty of Computer Science and Information Technology, Universiti Tun Hussein Onn Malaysia, 86400 Johor, Malaysia
| | - Bashar Ahmed Khalaf
- Department of Medical Instruments Engineering Techniques, Bilad Alrafidain University College, 32001 Diyala, Iraq
| | - Mazin Abed Mohammed
- College of Computer Science and Information Technology, University of Anbar, Anbar 31001, Iraq
| | - Jan Nedoma
- Department of Telecommunications, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, 70800 Ostrava, Czech Republic
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69
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Interval type-2 fuzzy brain emotional control design for the synchronization of 4D nonlinear hyperchaotic systems. Soft comput 2021. [DOI: 10.1007/s00500-021-06197-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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70
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Ahmad S, Ullah A, Akgül A, Abdeljawad T. Numerical analysis of fractional human liver model in fuzzy environment. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2021. [DOI: 10.1080/16583655.2021.2006894] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Affiliation(s)
- Shabir Ahmad
- Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan
| | - Aman Ullah
- Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan
| | - Ali Akgül
- Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, Turkey
| | - Thabet Abdeljawad
- Department of Mathematics and Science, Prince Sultan University, Riyadh, Saudi Arabia
- Department of Medical Research, China Medical University, Taichung, Taiwan
- Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
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71
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Xu X, Li Z, Wang R, Zhao L. Analysis of the Evolution of User Emotion and Opinion Leaders' Information Dissemination Behavior in the Knowledge Q&A Community during COVID-19. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2021; 18:12252. [PMID: 34832009 PMCID: PMC8618384 DOI: 10.3390/ijerph182212252] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Revised: 11/13/2021] [Accepted: 11/18/2021] [Indexed: 12/23/2022]
Abstract
Since its emergence in 2019, COVID-19 has quickly triggered widespread public discussion on social media. From 26 February 2020 to 26 September 2020, this study collected data on COVID-19-related posts in the knowledge Q&A community, identified 220 opinion leaders of this community, and used social network analysis and sentiment analysis to analyze the information exchange behavior and emotional evolution of the opinion leaders during COVID-19. The results show that the COVID-19 topic community could be divided into seven main categories. The information dissemination of opinion leader information dissemination network had low efficiency, multiple paths, and a high degree of control. In addition, the emotional evolution of users showed obvious phased characteristics. User emotion changed from initially strong negative to strong positive over the course of the pandemic and eventually tended to be objective and neutral as time passed and the event stabilized.
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Affiliation(s)
- Xu Xu
- School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China; (X.X.); (L.Z.)
| | - Zhigang Li
- School of Management Science, Chengdu University of Technology, Chengdu 610059, China;
| | - Rui Wang
- School of Management Science, Chengdu University of Technology, Chengdu 610059, China;
| | - Li Zhao
- School of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China; (X.X.); (L.Z.)
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72
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Maurício de Carvalho JPS, Moreira-Pinto B. A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine. CHAOS, SOLITONS, AND FRACTALS 2021; 151:111275. [PMID: 34334968 PMCID: PMC8302849 DOI: 10.1016/j.chaos.2021.111275] [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: 06/04/2021] [Revised: 07/09/2021] [Accepted: 07/13/2021] [Indexed: 06/13/2023]
Abstract
Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fractional derivative and of reinfection rate. The results are discussed from a biological point of view.
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Affiliation(s)
| | - Beatriz Moreira-Pinto
- UCIBIO, REQUIMTE, Faculty of Pharmacy, University of Porto Rua de Jorge Viterdo Ferreira, 228, Porto 4050-313, Portugal
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73
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Martínez-Guerra R, Flores-Flores JP. An algorithm for the robust estimation of the COVID-19 pandemic's population by considering undetected individuals. APPLIED MATHEMATICS AND COMPUTATION 2021; 405:126273. [PMID: 33850338 PMCID: PMC8030733 DOI: 10.1016/j.amc.2021.126273] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Revised: 03/19/2021] [Accepted: 04/05/2021] [Indexed: 05/16/2023]
Abstract
Due to the current COVID-19 pandemic, much effort has been put on studying the spread of infectious diseases to propose more adequate health politics. The most effective surveillance system consists of doing massive tests. Nonetheless, many countries cannot afford this class of health campaigns due to limited resources. Thus, a transmission model is a viable alternative to study the dynamics of the pandemic. The most used are the Susceptible, Infected and Removed type models (SIR). In this study, we tackle the population estimation problem of the A-SIR model, which takes into account asymptomatic or undetected individuals. By means of an algebraic differential approach, we design a model-free (no copy system) reduced-order estimation algorithm (observer) to determine the different non-measured population groups. We study two types of estimation algorithms: Proportional and Proportional-Integral. Both shown fast convergence speed, as well as a minimal estimation error. Additionally, we introduce random fluctuations in our analysis to represent changes in the external conditions and which result in poor measurements. The numerical results reveal that both model-free estimators are robust despite the presence of these fluctuations. As a point of reference, we apply the classical Luenberger type observer to our estimation problem and compare the results. Finally, we consider real data of infected individuals in Mexico City, reported from February 2020 to March 2021, and estimate the non-measured populations. Our work's main goal is to proportionate a simple and therefore, an accessible methodology to estimate the behavior of the COVID-19 pandemic from the available data, such that the competent authorities can propose more adequate health politics.
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Affiliation(s)
- Rafael Martínez-Guerra
- Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, Mexico City 07360, Mexico
| | - Juan Pablo Flores-Flores
- Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, Mexico City 07360, Mexico
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74
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Padmanabhan R, Abed HS, Meskin N, Khattab T, Shraim M, Al-Hitmi MA. A review of mathematical model-based scenario analysis and interventions for COVID-19. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2021; 209:106301. [PMID: 34392001 PMCID: PMC8314871 DOI: 10.1016/j.cmpb.2021.106301] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2021] [Accepted: 07/17/2021] [Indexed: 05/11/2023]
Abstract
Mathematical model-based analysis has proven its potential as a critical tool in the battle against COVID-19 by enabling better understanding of the disease transmission dynamics, deeper analysis of the cost-effectiveness of various scenarios, and more accurate forecast of the trends with and without interventions. However, due to the outpouring of information and disparity between reported mathematical models, there exists a need for a more concise and unified discussion pertaining to the mathematical modeling of COVID-19 to overcome related skepticism. Towards this goal, this paper presents a review of mathematical model-based scenario analysis and interventions for COVID-19 with the main objectives of (1) including a brief overview of the existing reviews on mathematical models, (2) providing an integrated framework to unify models, (3) investigating various mitigation strategies and model parameters that reflect the effect of interventions, (4) discussing different mathematical models used to conduct scenario-based analysis, and (5) surveying active control methods used to combat COVID-19.
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Affiliation(s)
| | - Hadeel S Abed
- Department of Electrical Engineering, Qatar University, Qatar.
| | - Nader Meskin
- Department of Electrical Engineering, Qatar University, Qatar.
| | - Tamer Khattab
- Department of Electrical Engineering, Qatar University, Qatar.
| | - Mujahed Shraim
- Department of Public Health, College of Health Sciences, QU Health, Qatar University, Qatar.
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75
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Sitthiwirattham T, Zeb A, Chasreechai S, Eskandari Z, Tilioua M, Djilali S. Analysis of a discrete mathematical COVID-19 model. RESULTS IN PHYSICS 2021; 28:104668. [PMID: 34401224 PMCID: PMC8357495 DOI: 10.1016/j.rinp.2021.104668] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Revised: 08/05/2021] [Accepted: 08/05/2021] [Indexed: 05/04/2023]
Abstract
To describe the main propagation of the COVID-19 and has to find the control for the rapid spread of this viral disease in real life, in current manuscript a discrete form of the SEIR model is discussed. The main aim of this is to describe the viral disease in simplest way and the basic properties that are related with the nature of curves for susceptible and infected individuals are discussed here. The elementary numerical examples are given by using the real data of India and Algeria.
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Affiliation(s)
- Thanin Sitthiwirattham
- Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, Thailand
| | - Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, 22060, Khyber Pakhtunkhwa, Pakistan
| | - Saowaluck Chasreechai
- Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Zohreh Eskandari
- Department of Mathematical Sciences, Shahrekord University, Shahrekord, Iran
| | - Mouhcine Tilioua
- Department of Mathematics, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box. 509 Boutalamine, 52000 Errachidia, Morocco
| | - Salih Djilali
- Laboratoire d'Analyse Non Linéaire et Mathématiques Appliquées, Université de Tlemcen, Tlemcen, Algeria
- Department of Mathematics, Faculty of Exact Sciences and Computer Science, Hassiba Benbouali University, Chlef, Algeria
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76
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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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77
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Al-Sadi W, Alkhazan A, Abdullah TQS, Al-Soswa M. Stability and existence the solution for a coupled system of hybrid fractional differential equation with uniqueness. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES 2021. [DOI: 10.1080/25765299.2021.1968617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022] Open
Affiliation(s)
- Wadhah Al-Sadi
- School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, China
- Department of Mathematics, College of Science, Sana'a University, Sana'a, Sana'a, Yemen
| | - AbdulWasea Alkhazan
- Department of Mathematics, College of Science, Northwestern Polytechnical University, Xi'an, Shannxi, China
- Department of Mathematics, College of Science, Sana'a University, Sana'a, Sana'a, Yemen
| | - Tariq Q. S. Abdullah
- School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, China
| | - Mohammed Al-Soswa
- School of Information Engineering, Chang′an University, Xi′an, Shannxi, China
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78
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Khan MS, samreen M, Ozair M, Hussain T, Gómez-Aguilar JF. Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19. EUROPEAN PHYSICAL JOURNAL PLUS 2021; 136:853. [PMID: 34426778 PMCID: PMC8372232 DOI: 10.1140/epjp/s13360-021-01862-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2021] [Accepted: 08/11/2021] [Indexed: 05/06/2023]
Abstract
In this article, a mathematical model for hypertensive or diabetic patients open to COVID-19 is considered along with a set of first-order nonlinear differential equations. Moreover, the method of piecewise arguments is used to discretize the continuous system. The mathematical system is said to reveal six equilibria, namely, extinction equilibrium, boundary equilibrium, quarantined-free equilibrium, exposure-free equilibrium, endemic equilibrium, and the equilibrium free from susceptible population. Local stability conditions are developed for our discrete-time mathematical system about each of its equilibrium point. The existence of period-doubling bifurcation and chaos is studied in the absence of isolated population. It is shown that our system will become unstable and experiences the chaos when the quarantined compartment is empty, which is true in biological meanings. The existence of Neimark-Sacker bifurcation is studied for the endemic equilibrium point. Moreover, it is shown numerically that our discrete-time mathematical system experiences the period-doubling bifurcation about its endemic equilibrium. To control the period-doubling bifurcation, Neimark-Sacker bifurcation, a generalized hybrid control methodology is used. Moreover, this model is analyzed along with generalized hybrid control in order to eliminate chaos and oscillation epidemiologically presenting the significance of quarantine in the COVID-19 environment.
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Affiliation(s)
| | - Maria samreen
- Department of Mathematics, Quaid-I-Azam University, Islamabad, 44230 Pakistan
| | - Muhammad Ozair
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
| | - Takasar Hussain
- Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, Pakistan
| | - J. F. Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos México
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79
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Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model. ALEXANDRIA ENGINEERING JOURNAL 2021; 60:4121-4130. [PMCID: PMC7938760 DOI: 10.1016/j.aej.2021.02.036] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Revised: 02/20/2021] [Accepted: 02/22/2021] [Indexed: 05/26/2023]
Abstract
Novel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results.
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80
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Javeed S, Anjum S, Alimgeer KS, Atif M, Khan MS, Farooq WA, Hanif A, Ahmad H, Yao SW. A novel mathematical model for COVID-19 with remedial strategies. RESULTS IN PHYSICS 2021; 27:104248. [PMID: 33996398 PMCID: PMC8106240 DOI: 10.1016/j.rinp.2021.104248] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2021] [Revised: 04/20/2021] [Accepted: 04/22/2021] [Indexed: 06/12/2023]
Abstract
Coronavirus (COVID-19) outbreak from Wuhan, Hubei province in China and spread out all over the World. In this work, a new mathematical model is proposed. The model consists the system of ODEs. The developed model describes the transmission pathways by employing non constant transmission rates with respect to the conditions of environment and epidemiology. There are many mathematical models purposed by many scientists. In this model, "α E " and "α I ", transmission coefficients of the exposed cases to susceptible and infectious cases to susceptible respectively, are included. " δ " as a governmental action and restriction against the spread of coronavirus is also introduced. The RK method of order four (RK4) is employed to solve the model equations. The results are presented for four countries i.e., Pakistan, Italy, Japan, and Spain etc. The parametric study is also performed to validate the proposed model.
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Affiliation(s)
- Shumaila Javeed
- Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
| | - Subtain Anjum
- Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
| | - Khurram Saleem Alimgeer
- Electrical and Computer Engineering Department, COMSATS University Islamabad, Islamabad Campus, Pakistan
| | - M Atif
- Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
| | - Mansoor Shaukat Khan
- Department of Mathematics, COMSATS University Islamabad, Park Road, Chak Shahzad Islamabad, Pakistan
| | - W Aslam Farooq
- Department of Physics and Astronomy, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
| | - Atif Hanif
- Botany and Microbiology Department, King Saud University, Riyadh 11451, Saudi Arabia
| | - Hijaz Ahmad
- Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
- Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
| | - Shao-Wen Yao
- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
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81
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Aouiti C, Rezeg MB. Impulsive multidirectional associative memory neural networks: New results. INT J BIOMATH 2021. [DOI: 10.1142/s1793524521500601] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
An Impulsive Multidirectional Associative Memory Neural Network (IMAMNN) with time-varying and leakage delays is proposed. Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work. Moreover, two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.
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Affiliation(s)
- Chaouki Aouiti
- Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, Research Units of Mathematics and Applications UR13ES47, 7021 Zarzouna, Bizerta, Tunisia
| | - Mahjouba Ben Rezeg
- Department of Mathematics, Faculty of Sciences of Bizerta, University of Carthage, Research Units of Mathematics and Applications UR13ES47, 7021 Zarzouna, Bizerta, Tunisia
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82
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Alzaid SS, Alkahtani BST. On study of fractional order epidemic model of COVID-19 under non-singular Mittag-Leffler kernel. RESULTS IN PHYSICS 2021; 26:104402. [PMID: 34189025 PMCID: PMC8216059 DOI: 10.1016/j.rinp.2021.104402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Revised: 05/23/2021] [Accepted: 05/27/2021] [Indexed: 06/13/2023]
Abstract
This paper investigates the analysis of the fraction mathematical model of the novel coronavirus (COVID-19), which is indeed a source of threat all over the globe. This paper deals with the transmission mechanism by some affected parameters in the problem. The said study is carried out by the consideration of a fractional-order epidemic model describing the dynamics of COVID-19 under a non-singular kernel type of derivative. The concerned model examine via non-singular fractional-order derivative known as Atangana-Baleanu derivative in Caputo sense (ABC). The problem analyzes for qualitative analysis and determines at least one solution by applying the approach of fixed point theory. The uniqueness of the solution is derived by the Banach contraction theorem. For iterative solution, the technique of iterative fractional-order Adams-Bashforth scheme is applied. Numerical simulation for the proposed scheme is performed at various fractional-order lying between 0, 1 and for integer-order 1. We also compare the compartmental quantities of the said model at two different effective contact rates of β . All the compartments show convergence and stability with growing time. The simulation of the iterative techniques is also compared with the Laplace Adomian decomposition method (LADM). Good comparative results for the whole density have been achieved by different fractional orders and obtain the stability faster at the low fractional orders while slowly at higher-order.
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Affiliation(s)
- Sara Salem Alzaid
- Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia
| | - Badr Saad T Alkahtani
- Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia
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83
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Khan H, Ibrahim M, Abdel-Aty AH, Khashan MM, Khan FA, Khan A. A fractional order Covid-19 epidemic model with Mittag-Leffler kernel. CHAOS, SOLITONS, AND FRACTALS 2021; 148:111030. [PMID: 34002105 PMCID: PMC8114791 DOI: 10.1016/j.chaos.2021.111030] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Revised: 04/24/2021] [Accepted: 04/27/2021] [Indexed: 05/05/2023]
Abstract
In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; ` ` S c ″ which denotes susceptible class, ` ` E c ″ represents exposed population, ` ` I c ″ is the class for infected people who have been developed with COVID-19 and can cause spread in the population. The recovered class is denoted by ` ` R c ″ and ` ` V c ″ is the concentration of COVID-19 virus in the area. The computational study shows us that the spread will be continued for long time and the recovery reduces the infection rate. The numerical scheme is based on the Lagrange's interpolation polynomial and the numerical results for the suggested model are similar to the integer order which gives us the applicability of the numerical scheme and effectiveness of the fractional order derivative.
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Affiliation(s)
- Hasib Khan
- Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
| | - Muhammad Ibrahim
- Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
| | - Abdel-Haleem Abdel-Aty
- Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia
- Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
| | - M Motawi Khashan
- Department of Basic Sciences, Common First Year, King Saud University, Riyadh 11451, Saudi Arabia
| | - Farhat Ali Khan
- Department of Pharmacy, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan
| | - Aziz Khan
- Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
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84
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Chen Z, Dassios A, Kuan V, Lim JW, Qu Y, Surya B, Zhao H. A two-phase dynamic contagion model for COVID-19. RESULTS IN PHYSICS 2021; 26:104264. [PMID: 34002126 PMCID: PMC8116323 DOI: 10.1016/j.rinp.2021.104264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2021] [Revised: 04/12/2021] [Accepted: 04/13/2021] [Indexed: 05/27/2023]
Abstract
In this paper, we propose a continuous-time stochastic intensity model, namely, two-phase dynamic contagion process (2P-DCP), for modelling the epidemic contagion of COVID-19 and investigating the lockdown effect based on the dynamic contagion model introduced by Dassios and Zhao [24]. It allows randomness to the infectivity of individuals rather than a constant reproduction number as assumed by standard models. Key epidemiological quantities, such as the distribution of final epidemic size and expected epidemic duration, are derived and estimated based on real data for various regions and countries. The associated time lag of the effect of intervention in each country or region is estimated. Our results are consistent with the incubation time of COVID-19 found by recent medical study. We demonstrate that our model could potentially be a valuable tool in the modeling of COVID-19. More importantly, the proposed model of 2P-DCP could also be used as an important tool in epidemiological modelling as this type of contagion models with very simple structures is adequate to describe the evolution of regional epidemic and worldwide pandemic.
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Affiliation(s)
| | | | | | | | | | - Budhi Surya
- Victoria University of Wellington, New Zealand
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85
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Shringi S, Sharma H, Rathie PN, Bansal JC, Nagar A. Modified SIRD Model for COVID-19 Spread Prediction for Northern and Southern States of India. CHAOS, SOLITONS, AND FRACTALS 2021; 148:111039. [PMID: 34007123 PMCID: PMC8120454 DOI: 10.1016/j.chaos.2021.111039] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 03/31/2021] [Accepted: 05/02/2021] [Indexed: 05/03/2023]
Abstract
The Severe Acute Respiratory Syndrome Coronavirus 2 (SAR-CoV-2) is the strain of coronavirus that causes coronavirus disease (COVID-19), the respiratory illness that resulted in COVID-19 pandemic in early December 2019. Due to lack of knowledge of the epidemiological cycle and absence of any type of vaccine or medications, the Government issued various non-pharmacological measures to end the COVID-19 pandemic. Several researchers applied the Susceptible-Infected-Recovered-Deceased (SIRD) compartmental epidemiology process model to identifying the effect of different governments intervention methods enforced to mollify the spread of COVID-19 epidemic. In this paper, we aim to provide a modified SIRD model for COVID-19 spread prediction. We have analyzed the data of the Northern and Southern states of India from January 30, 2020, to October 24, 2020 using the proposed SIRD model and existing SIRD model. We have made the predictions with reasonable assumptions based on real data, considering that the precise course of an epidemic is highly dependent on how and when quarantine, isolation, and precautionary measures were imposed. The proposed method gives better approximation values of new cases, R0 (Reproductive Number), daily deaths, daily infectious, transmission rate, and recovered individuals.Through the analysis of the reported results, the proposed SIRD model can be an effective method for investigating the effect of government interventions on COVID-19 associated transmission and mortality rate at the time of epidemic.
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86
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Alla Hamou A, Azroul E, Lamrani Alaoui A. Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies. INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS 2021; 7:142. [PMID: 34226872 PMCID: PMC8241535 DOI: 10.1007/s40819-021-01086-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Accepted: 05/06/2021] [Indexed: 01/24/2023]
Abstract
In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.
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Affiliation(s)
- Abdelouahed Alla Hamou
- Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar Al Mahraz, Sidi Mohamed Ben Abdellah University, B.P. 1796, 30000 Fez, Morocco
| | - Elhoussine Azroul
- Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar Al Mahraz, Sidi Mohamed Ben Abdellah University, B.P. 1796, 30000 Fez, Morocco
| | - Abdelilah Lamrani Alaoui
- Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar Al Mahraz, Sidi Mohamed Ben Abdellah University, B.P. 1796, 30000 Fez, Morocco
- Department of Mathematics, Regional Center of Education and Professional Training, B.P. 49, 30000 Fez, Morocco
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87
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Vivas-Cortez M, Ali MA, Budak H, Kalsoom H, Agarwal P. Some New Hermite-Hadamard and Related Inequalities for Convex Functions via ( p, q)-Integral. ENTROPY 2021; 23:e23070828. [PMID: 34209714 PMCID: PMC8305804 DOI: 10.3390/e23070828] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Revised: 05/23/2021] [Accepted: 05/26/2021] [Indexed: 12/23/2022]
Abstract
In this investigation, for convex functions, some new (p,q)-Hermite-Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1- can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.
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Affiliation(s)
- Miguel Vivas-Cortez
- Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, University of Buenos Aires, Av. 12 de octubre 1076 y Roca, Apartado Postal 17-01-2184, Sede Quito, Ecuador;
| | - Muhammad Aamir Ali
- Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
- Correspondence: (M.A.A.); (H.K.)
| | - Hüseyin Budak
- Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey;
| | - Humaira Kalsoom
- Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
- Correspondence: (M.A.A.); (H.K.)
| | - Praveen Agarwal
- Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India;
- Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
- International Center for Basic and Applied Sciences, Jaipur 302029, India
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88
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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: 14] [Impact Index Per Article: 4.7] [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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89
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Abraha T, Basir FA, Obsu LL, Torres DFM. Farming awareness based optimum interventions for crop pest control. MATHEMATICAL BIOSCIENCES AND ENGINEERING 2021; 18:5364-5391. [PMID: 34517492 DOI: 10.3934/mbe.2021272] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pest-free and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pest-free and coexistence equilibria is shown using the Routh-Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.
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Affiliation(s)
- Teklebirhan Abraha
- Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia
| | - Fahad Al Basir
- Department of Mathematics, Asansol Girls' College, West Bengal 713304, India
| | - Legesse Lemecha Obsu
- Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia
| | - Delfim F M Torres
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
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90
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Rihan FA, Alsakaji HJ. Analysis of a stochastic HBV infection model with delayed immune response. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:5194-5220. [PMID: 34517484 DOI: 10.3934/mbe.2021264] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.
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Affiliation(s)
- Fathalla A Rihan
- Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE
| | - Hebatallah J Alsakaji
- Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain 15551, UAE
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91
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Bright and Singular Optical Solitons in Nonlinear Negative-Index Materials with Quadratic–Cubic Nonlinearity. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2021. [DOI: 10.1007/s13369-020-05194-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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92
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Beigi A, Yousefpour A, Yasami A, Gómez-Aguilar JF, Bekiros S, Jahanshahi H. Application of reinforcement learning for effective vaccination strategies of coronavirus disease 2019 (COVID-19). EUROPEAN PHYSICAL JOURNAL PLUS 2021; 136:609. [PMID: 34094796 PMCID: PMC8166378 DOI: 10.1140/epjp/s13360-021-01620-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2021] [Accepted: 05/26/2021] [Indexed: 05/08/2023]
Abstract
Since December 2019, the new coronavirus has raged in China and subsequently all over the world. From the first days, researchers have tried to discover vaccines to combat the epidemic. Several vaccines are now available as a result of the contributions of those researchers. As a matter of fact, the available vaccines should be used in effective and efficient manners to put the pandemic to an end. Hence, a major problem now is how to efficiently distribute these available vaccines among various components of the population. Using mathematical modeling and reinforcement learning control approaches, the present article aims to address this issue. To this end, a deterministic Susceptible-Exposed-Infectious-Recovered-type model with additional vaccine components is proposed. The proposed mathematical model can be used to simulate the consequences of vaccination policies. Then, the suppression of the outbreak is taken to account. The main objective is to reduce the effects of Covid-19 and its domino effects which stem from its spreading and progression. Therefore, to reach optimal policies, reinforcement learning optimal control is implemented, and four different optimal strategies are extracted. Demonstrating the efficacy of the proposed methods, finally, numerical simulations are presented.
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Affiliation(s)
- Alireza Beigi
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - Amin Yousefpour
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - Amirreza Yasami
- School of Mechanical Engineering, College of Engineering, University of Tehran, 14399‒57131 Tehran, Iran
| | - J. F. Gómez-Aguilar
- CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490 Cuernavaca, Morelos Mexico
| | - Stelios Bekiros
- Department of Banking and Finance, FEMA, , University of Malta, Msida, MSD 2080 Malta
- Department of Economics, European University Institute, Via delle Fontanelle, 18, 50014 Florence, Italy
| | - Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg, R3T 5V6 Canada
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93
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Fatima B, Alqudah MA, Zaman G, Jarad F, Abdeljawad T. Modeling the transmission dynamics of middle eastern respiratory syndrome coronavirus with the impact of media coverage. RESULTS IN PHYSICS 2021; 24:104053. [PMID: 33777666 PMCID: PMC7987584 DOI: 10.1016/j.rinp.2021.104053] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2021] [Revised: 02/28/2021] [Accepted: 03/03/2021] [Indexed: 05/29/2023]
Abstract
Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R 0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.
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Affiliation(s)
- BiBi Fatima
- Department of Mathematics, University of Malakand, Chakdara Dir Lower Khyber Pakhtunkhawa, Pakistan
| | - Manar A Alqudah
- Department of Mathematical Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671,Saudi Arabia
| | - Gul Zaman
- Department of Mathematics, University of Malakand, Chakdara Dir Lower Khyber Pakhtunkhawa, Pakistan
| | - Fahd Jarad
- Department of Mathematics, Çankaya University, Etimesgut, Ankara, Turkey
- Department of Medical Research, China Medical University, Taichung 40402, Taiwan
| | - Thabet Abdeljawad
- Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
- Department of Medical Research, China Medical University, Taichung 40402, Taiwan
- Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
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94
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Ndondo AM, Kasereka SK, Bisuta SF, Kyamakya K, Doungmo EFG, Ngoie RBM. Analysis, modeling and optimal control of COVID-19 outbreak with three forms of infection in Democratic Republic of the Congo. RESULTS IN PHYSICS 2021; 24:104096. [PMID: 33816092 PMCID: PMC7999905 DOI: 10.1016/j.rinp.2021.104096] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 03/02/2021] [Accepted: 03/16/2021] [Indexed: 05/15/2023]
Abstract
This paper deals with modeling and simulation of the novel coronavirus in which the infectious individuals are divided into three subgroups representing three forms of infection. The rigorous analysis of the mathematical model is provided. We provide also a rigorous derivation of the basic reproduction numberR 0 . ForR 0 < 1 , we prove that the Disease Free Equilibium (DFE) is Globally Asymptotically Stable (GAS), thus COVID-19 extincts; whereas forR 0 > 1 , we found the co-existing phenomena under some assumptions and parametric values. Elasticity indices forR 0 with respect to different parameters are calculated with baseline parameter values estimated. We also prove that a transcritical bifurcation occurs atR 0 = 1 . Taking into account the control strategies like screening, treatment and isolation (social distancing measures), we present the optimal control problem of minimizing the cost due to the application of these measures. By reducing the values of some parameters, such as death rates (representing a management effort for all categories of people) and recovered rates (representing the action of reduction in transmission, improved screening, treatment for individuals diagnosed positive to COVID-19 and the implementation of barrier measures limiting contamination for undiagnosed individuals), it appears that after 140 - 170 days, the peak of the pandemic is reached and shows that by continuing with this strategy, COVID-19 could be eliminated in the population.
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Affiliation(s)
- A M Ndondo
- University of Lubumbashi, Mathematics and Computer Science Department, Lubumbashi, Democratic Republic of the Congo
- Artificial intelligence, BIg data and modeLing simulation Research Center (ABIL), Kinshasa, Democratic Republic of the Congo
- Université Nouveaux Horizons, Faculty of Computer Science, Lubumbashi, Democratic Republic of the Congo
| | - S K Kasereka
- University of Kinshasa, Mathematics and Computer Science Department, Kinshasa, Democratic Republic of the Congo
- Artificial intelligence, BIg data and modeLing simulation Research Center (ABIL), Kinshasa, Democratic Republic of the Congo
| | - S F Bisuta
- University of Kinshasa, Pneumology Department, University Clinics of Kinshasa, Democratic Republic of the Congo
- Artificial intelligence, BIg data and modeLing simulation Research Center (ABIL), Kinshasa, Democratic Republic of the Congo
| | - K Kyamakya
- Alpen-Adria-Universitaet Klagenfurt, Institute of Smart Systems Technologies, Department of Mathematical Sciences, Klagenfurt, Austria
| | - E F G Doungmo
- University of South Africa, College of Science, Engineering & Technology, Department of Mathematical Sciences, Florida 003, South Africa
| | - R-B M Ngoie
- Institut Supérieur Pédagogique, Department of Mathematics, Mbanza-Ngungu, Congo
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95
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Boudaoui A, El Hadj Moussa Y, Hammouch Z, Ullah S. A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel. CHAOS, SOLITONS, AND FRACTALS 2021; 146:110859. [PMID: 33776249 PMCID: PMC7980231 DOI: 10.1016/j.chaos.2021.110859] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2020] [Revised: 03/07/2021] [Accepted: 03/08/2021] [Indexed: 05/21/2023]
Abstract
In this paper, we investigate an epidemic model of the novel coronavirus disease or COVID-19 using the Caputo-Fabrizio derivative. We discuss the existence and uniqueness of solution for the model under consideration, by using the the Picard-Lindelöf theorem. Further, using an efficient numerical approach we present an iterative scheme for the solutions of proposed fractional model. Finally, many numerical simulations are presented for various values of the fractional order to demonstrate the impact of some effective and commonly used interventions to mitigate this novel infection. From the simulation results we conclude that the fractional order epidemic model provides more insights about the disease dynamics.
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Affiliation(s)
- Ahmed Boudaoui
- Laboratory of Mathematics Modeling and Applications, University of Adrar, National Road No. 06, 01000, Adrar, Algeria
| | - Yacine El Hadj Moussa
- Department of Probability and Statistics, University Djillali liabes, L.P 89, Sidi Bel Abbes 22000, Algeria
| | - Zakia Hammouch
- Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam
- Department of Medical Research, China Medical University Hospital, Taichung, Taiwan
- Département des Sciences, École Normale Supérieure, Moulay Ismail University of Meknes, Morocco
| | - Saif Ullah
- Department of Mathematics, University of Peshawar Khyber Pakhtunkhwa, Pakistan
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96
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Liu L, Chen M, Li T, Wang H. Composite Anti-Disturbance Reference Model L2-$L_{\infty }$ Control for Helicopter Slung Load System. J INTELL ROBOT SYST 2021. [DOI: 10.1007/s10846-020-01276-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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97
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Babaei A, Jafari H, Banihashemi S, Ahmadi M. Mathematical analysis of a stochastic model for spread of Coronavirus. CHAOS, SOLITONS, AND FRACTALS 2021; 145:110788. [PMID: 33642704 PMCID: PMC7894125 DOI: 10.1016/j.chaos.2021.110788] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2020] [Revised: 02/09/2021] [Accepted: 02/12/2021] [Indexed: 05/09/2023]
Abstract
This paper is associated to investigate a stochastic SEIAQHR model for transmission of Coronavirus disease 2019 that is a recent great crisis in numerous societies. This stochastic pandemic model is established due to several safety protocols, for instance social-distancing, mask and quarantine. Three white noises are added to three of the main parameters of the system to represent the impact of randomness in the environment on the considered model. Also, the unique solvability of the presented stochastic model is proved. Moreover, a collocation approach based on the Legendre polynomials is presented to obtain the numerical solution of this system. Finally, some simulations are provided to survey the obtained results of this pandemic model and to identify the theoretical findings.
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Affiliation(s)
- A Babaei
- Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
| | - H Jafari
- Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
- Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan
- Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli, 71, Baku, AZ1007, Azerbaijan
| | - S Banihashemi
- Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
| | - M Ahmadi
- Department of Applied Mathematics, University of Mazandaran, Babolsar, Iran
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98
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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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99
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Cao Q, Wang G. New findings on global exponential stability of inertial neural networks with both time-varying and distributed delays. J EXP THEOR ARTIF IN 2021. [DOI: 10.1080/0952813x.2021.1883744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Qian Cao
- College of Mathematics and Physics, Hunan University of Arts and Science, Changde, P. R. China
| | - Guoqiu Wang
- Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), College of Mathematics and Statistics, Hunan Normal University, Changsha, P. R. China
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100
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Tyagi S, Martha SC, Abbas S, Debbouche A. Mathematical modeling and analysis for controlling the spread of infectious diseases. CHAOS, SOLITONS, AND FRACTALS 2021; 144:110707. [PMID: 33558795 PMCID: PMC7857024 DOI: 10.1016/j.chaos.2021.110707] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Revised: 01/16/2021] [Accepted: 01/18/2021] [Indexed: 05/31/2023]
Abstract
In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.
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Affiliation(s)
- Swati Tyagi
- Department of Mathematics, Chandigarh University, Chandigarh-140413, India
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab-140001, India
| | - Subash C Martha
- Department of Mathematics, Indian Institute of Technology Ropar, Punjab-140001, India
| | - Syed Abbas
- School of Basic Sciences, Indian Institute of Technology Mandi, H.P.-175005, India
| | - Amar Debbouche
- Department of Mathematics, Guelma University, Guelma 24000, Algeria
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