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Alkhazzan A, Wang J, Nie Y, Khan H, Alzabut J. A novel SVIR epidemic model with jumps for understanding the dynamics of the spread of dual diseases. CHAOS (WOODBURY, N.Y.) 2024; 34:093119. [PMID: 39288776 DOI: 10.1063/5.0175352] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 08/19/2024] [Indexed: 09/19/2024]
Abstract
The emergence of multi-disease epidemics presents an escalating threat to global health. In response to this serious challenge, we present an innovative stochastic susceptible-vaccinated-infected-recovered epidemic model that addresses the dynamics of two diseases alongside intricate vaccination strategies. Our novel model undergoes a comprehensive exploration through both theoretical and numerical analyses. The stopping time concept, along with appropriate Lyapunov functions, allows us to explore the possibility of a globally positive solution. Through the derivation of reproduction numbers associated with the stochastic model, we establish criteria for the potential extinction of the diseases. The conditions under which one or both diseases may persist are explained. In the numerical aspect, we derive a computational scheme based on the Milstein method. The scheme will not only substantiate the theoretical results but also facilitate the examination of the impact of parameters on disease dynamics. Through examples and simulations, we have a crucial impact of varying parameters on the system's behavior.
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Affiliation(s)
- Abdulwasea Alkhazzan
- School of Mathematics and Statistics, Northwestern Polytechnical University, Shannxi 710072 Xi'an, People's Republic of China
- Department of Mathematics, Faculty of Science, Sana'a University, Sana'a, Yemen
| | - Jungang Wang
- School of Mathematics and Statistics, Northwestern Polytechnical University, Shannxi 710072 Xi'an, People's Republic of China
- MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi'an 710129, PR China
| | - Yufeng Nie
- School of Mathematics and Statistics, Northwestern Polytechnical University, Shannxi 710072 Xi'an, People's Republic of China
| | - Hasib Khan
- Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
- Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, 18000 Khyber Pakhtunkhwa, Pakistan
| | - Jehad Alzabut
- Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
- Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Türkiye
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2
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Sadki M, Allali K. Stochastic two-strain epidemic model with saturated incidence rates driven by Lévy noise. Math Biosci 2024; 375:109262. [PMID: 39038697 DOI: 10.1016/j.mbs.2024.109262] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Revised: 07/16/2024] [Accepted: 07/17/2024] [Indexed: 07/24/2024]
Abstract
In this paper, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations.
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Affiliation(s)
- Marya Sadki
- Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University of Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco.
| | - Karam Allali
- Laboratory of Mathematics, Computer Science and Applications, Faculty of Sciences and Technologies, University of Hassan II of Casablanca, PO Box 146, Mohammedia, Morocco
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3
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Kang S, Liu T, Liu H, Hu Y, Hou X. Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations. PLoS One 2024; 19:e0303300. [PMID: 38781238 PMCID: PMC11115323 DOI: 10.1371/journal.pone.0303300] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 04/23/2024] [Indexed: 05/25/2024] Open
Abstract
Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.
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Affiliation(s)
- Sida Kang
- School of Business Administration, University of Science and Technology Liaoning, Anshan, Liaoning, China
| | - Tianhao Liu
- Asia-Australia Business College, Liaoning University, Shenyang, Liaoning, China
| | - Hongyu Liu
- School of Business Administration, University of Science and Technology Liaoning, Anshan, Liaoning, China
| | - Yuhan Hu
- School of Science, University of Science and Technology Liaoning, Anshan, Liaoning, China
| | - Xilin Hou
- School of Business Administration, University of Science and Technology Liaoning, Anshan, Liaoning, China
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4
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Jian L, Bai X, Ma S. Stochastic dynamical analysis for the complex infectious disease model driven by multisource noises. PLoS One 2024; 19:e0296183. [PMID: 38175851 PMCID: PMC10766192 DOI: 10.1371/journal.pone.0296183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 12/07/2023] [Indexed: 01/06/2024] Open
Abstract
This paper mainly studies the dynamical behavior of the infectious disease model affected by white noise and Lévy noise. First, a stochastic model of infectious disease with secondary vaccination affected by noises is established. Besides, the existence and uniqueness of the global positive solution for the stochastic model are proved based on stochastic differential equations and Lyapunov function, then the asymptotic behavior of the disease-free equilibrium point is studied. Moreover, the sufficient conditions for the extinction of the disease are obtained and the analysis showed that different noise intensity could affect the extinction of infectious disease on different degree. Finally, the theoretical results are verified by numerical simulation and some suggestions have been put forward on how to prevent the spread of diseases are presented.
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Affiliation(s)
- Liqiong Jian
- The Blood Center of Ningxia Hui Autonomous Region, Yinchuan, China
| | - Xinyu Bai
- School of Mathematics and Information Science, North Minzu University, Yinchuan, China
| | - Shaojuan Ma
- School of Mathematics and Information Science, North Minzu University, Yinchuan, China
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5
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Bai X, Ma S. Stochastic dynamical behavior of COVID-19 model based on secondary vaccination. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:2980-2997. [PMID: 36899568 DOI: 10.3934/mbe.2023141] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
This paper mainly studies the dynamical behavior of a stochastic COVID-19 model. First, the stochastic COVID-19 model is built based on random perturbations, secondary vaccination and bilinear incidence. Second, in the proposed model, we prove the existence and uniqueness of the global positive solution using random Lyapunov function theory, and the sufficient conditions for disease extinction are obtained. It is analyzed that secondary vaccination can effectively control the spread of COVID-19 and the intensity of the random disturbance can promote the extinction of the infected population. Finally, the theoretical results are verified by numerical simulations.
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Affiliation(s)
- Xinyu Bai
- School of Mathematics and Information Science, North Minzu University, YinChuan 750021, China
| | - Shaojuan Ma
- School of Mathematics and Information Science, North Minzu University, YinChuan 750021, China
- Ningxia Key Laboratory of Intelligent Information and Big Data Processing Yinchuan, YinChuan 750021, China
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6
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Ghosh U, Thirthar AA, Mondal B, Majumdar P. Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY. TRANSACTION A, SCIENCE 2022; 46:1541-1554. [PMID: 36320931 PMCID: PMC9607782 DOI: 10.1007/s40995-022-01371-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/14/2022] [Accepted: 09/30/2022] [Indexed: 11/06/2022]
Abstract
In this paper, we have studied a fractional-order eco-epidemiological model incorporating fear, treatment, and hunting cooperation effects to explore the memory effect in the ecological system through Caputo-type fractional-order derivative. We have studied the behavior of different equilibrium points with the memory effect. The proposed system undergoes through Hopf bifurcation with respect to the memory parameter as the bifurcation parameter. We perform numerical simulations for different values of the memory parameter and some of model parameters. In the numerical results, it appears that the system is exhibiting a stable behavior from a period or chaotic nature with the increase in the memory effect. The system also exhibits two transcritical bifurcations with respect to the growth rate of the prey. At low values of prey's growth, all species go to extinction, at moderate values of prey's growth, only preys (susceptible and infected) can survive, and at higher values of prey's growth, all species survive simultaneously. The paper ended with some recommendations.
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Affiliation(s)
- Uttam Ghosh
- Department of Applied Mathematics, University of Calcutta, Kolkata, 700009 India
| | | | - Bapin Mondal
- Department of Applied Mathematics, University of Calcutta, Kolkata, 700009 India
| | - Prahlad Majumdar
- Department of Applied Mathematics, University of Calcutta, Kolkata, 700009 India
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Zhang G, Li Z, Din A. A stochastic SIQR epidemic model with Lévy jumps and three-time delays. APPLIED MATHEMATICS AND COMPUTATION 2022; 431:127329. [PMID: 35784101 PMCID: PMC9237465 DOI: 10.1016/j.amc.2022.127329] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Revised: 06/08/2022] [Accepted: 06/12/2022] [Indexed: 06/15/2023]
Abstract
Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China.
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Affiliation(s)
- Ge Zhang
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
- School of Statistics and Information, Xinjiang University of Finance & Economics, Urumqi, China
| | - Zhiming Li
- College of Mathematics and System Science, Xinjiang University, Urumqi, China
| | - Anwarud Din
- Department of Mathematics, Sun Yat-sen university, Guangzhou, China
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8
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Modeling and analysis on the transmission of covid-19 Pandemic in Ethiopia. ALEXANDRIA ENGINEERING JOURNAL 2022; 61. [PMCID: PMC8571074 DOI: 10.1016/j.aej.2021.10.054] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R0=1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally.
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9
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Baskonus HM, Gao W. Investigation of optical solitons to the nonlinear complex Kundu-Eckhaus and Zakharov-Kuznetsov-Benjamin-Bona-Mahony equations in conformable. OPTICAL AND QUANTUM ELECTRONICS 2022; 54:388. [PMID: 35692261 PMCID: PMC9167627 DOI: 10.1007/s11082-022-03774-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 04/22/2022] [Indexed: 06/15/2023]
Abstract
This research manuscript focuses on the extraction of dark-bright solitons and periodic wave distributions of two models, namely, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and complex Kundu-Eckhaus equation with conformable derivative. To reach these important properties, the generalized exponential rational function method is considered. To observe wave distributions in periodic and singular sense, dynamical behaviour modulus of solutions are also archived. Strain conditions for validity of results obtained in this paper are also reported.
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Affiliation(s)
- Haci Mehmet Baskonus
- Faculty of Education, Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey
| | - Wei Gao
- School of Information Science and Technology, Yunnan Normal University, Yunnan, China
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10
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A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects. ALEXANDRIA ENGINEERING JOURNAL 2022; 61:4779-4791. [PMCID: PMC8531468 DOI: 10.1016/j.aej.2021.10.030] [Citation(s) in RCA: 26] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2021] [Revised: 09/05/2021] [Accepted: 10/13/2021] [Indexed: 05/24/2023]
Abstract
A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R0≈6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease.
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11
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Sabbar Y, Kiouach D, Rajasekar SP, El-Idrissi SEA. The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case. CHAOS, SOLITONS, AND FRACTALS 2022; 159:112110. [PMID: 35502416 PMCID: PMC9035369 DOI: 10.1016/j.chaos.2022.112110] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Revised: 04/08/2022] [Accepted: 04/10/2022] [Indexed: 06/14/2023]
Abstract
This study concentrates on the analysis of a stochastic SIC epidemic system with an enhanced and general perturbation. Given the intricacy of some impulses caused by external disturbances, we integrate the quadratic Lévy noise into our model. We assort the long-run behavior of a perturbed SIC epidemic model presented in the form of a system of stochastic differential equations driven by second-order jumps. By ameliorating the hypotheses and using some new analytical techniques, we find the exact threshold value between extinction and ergodicity (persistence) of our system. The idea and analysis used in this paper generalize the work of N. T. Dieu et al. (2020), and offer an innovative approach to dealing with other random population models. Comparing our results with those of previous studies reveals that quadratic jump-diffusion has no impact on the threshold value, but it remarkably influences the dynamics of the infection and may worsen the pandemic situation. In order to illustrate this comparison and confirm our analysis, we perform numerical simulations with some real data of COVID-19 in Morocco. Furthermore, we arrive at the following results: (i) the time average of the different classes depends on the intensity of the noise (ii) the quadratic noise has a negative effect on disease duration (iii) the stationary density function of the population abruptly changes its shape at some values of the noise intensity. Mathematics Subject Classification 2020: 34A26; 34A12; 92D30; 37C10; 60H30; 60H10.
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Affiliation(s)
- Yassine Sabbar
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
| | - Driss Kiouach
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
| | - S P Rajasekar
- Department of Mathematics, Government Arts College for Women, Nilakottai 624202, Tamilnadu, India
| | - Salim El Azami El-Idrissi
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
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12
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Ahmad Z, El-Kafrawy SA, Alandijany TA, Giannino F, Mirza AA, El-Daly MM, Faizo AA, Bajrai LH, Kamal MA, Azhar EI. A global report on the dynamics of COVID-19 with quarantine and hospitalization: A fractional order model with non-local kernel. Comput Biol Chem 2022; 98:107645. [PMID: 35276575 PMCID: PMC8857780 DOI: 10.1016/j.compbiolchem.2022.107645] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Revised: 02/15/2022] [Accepted: 02/16/2022] [Indexed: 01/13/2023]
Abstract
In this paper, a compartmental mathematical model has been utilized to gain a better insight about the future dynamics of COVID-19. The total human population is divided into eight various compartments including susceptible, exposed, pre-asymptomatic, asymptomatic, symptomatic, quarantined, hospitalized and recovered or removed individuals. The problem was modeled in terms of highly nonlinear coupled system of classical order ordinary differential equations (ODEs) which was further generalized with the Atangana-Balaeanu (ABC) fractional derivative in Caputo sense with nonlocal kernel. Furthermore, some theoretical analyses have been done such as boundedness, positivity, existence and uniqueness of the considered. Disease-free and endemic equilibrium points were also assessed. The basic reproduction was calculated through next generation technique. Due to high risk of infection, in the present study, we have considered the reported cases from three continents namely Americas, Europe, and south-east Asia. The reported cases were considered between 1st May 2021 and 31st July 2021 and on the basis of this data, the spread of infection is predicted for the next 200 days. The graphical solution of the considered nonlinear fractional model was obtained via numerical scheme by implementing the MATLAB software. Based on the fitted values of parameters, the basic reproduction number ℜ0 for the case of America, Asia and Europe were calculated as ℜ0≈2.92819, ℜ0≈2.87970 and ℜ0≈2.23507 respectively. It is also observed that the spread of infection in America is comparatively high followed by Asia and Europe. Moreover, the effect of fractional parameter is shown on the dynamics of spread of infection among different classes. Additionally, the effect of quarantined and treatment of infected individuals is also shown graphically. From the present analysis it is observed that awareness of being quarantine and proper treatment can reduce the infection rate dramatically and a minimal variation in quarantine and treatment rates of infected individuals can lead us to decrease the rate of infection.
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Affiliation(s)
- Zubair Ahmad
- Dipartimento di Matematica e Fisica, Universit'a degli Studi della Campania "Luigi Vanvitelli", Caserta 81100, Italy.
| | - Sherif A El-Kafrawy
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Thamir A Alandijany
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Francesco Giannino
- Department of Agricultural Sciences, University of Naples Federico II, Portici, Italy.
| | - Ahmed A Mirza
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Mai M El-Daly
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Arwa A Faizo
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Leena H Bajrai
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Biochemistry Department, Faculty of Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
| | - Mohammad Amjad Kamal
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Institutes for Systems Genetics, Frontiers Science Center for Disease-related Molecular Network, West China Hospital, Sichuan University, Chengdu 610041, Sichuan, China; Department of Pharmacy, Faculty of Allied Health Sciences, Daffodil International University, Bangladesh; Enzymoics, 7 Peterlee place, Novel Global Community Educational Foundation, Hebersham, NSW 2770, Australia.
| | - Esam I Azhar
- Special Infectious Agents Unit, King Fahd Medical Research Center, King Abdulaziz University, Jeddah, Saudi Arabia; Department of Medical Laboratory Sciences, Faculty of Applied Medical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia.
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Predicting the spread of COVID-19 with a machine learning technique and multiplicative calculus. Soft comput 2022; 26:8017-8024. [PMID: 35431642 PMCID: PMC8994092 DOI: 10.1007/s00500-022-06996-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 03/02/2022] [Indexed: 11/15/2022]
Abstract
This paper aims to generate a universal well-fitted mathematical model to aid global representation of the spread of the coronavirus (COVID-19) disease. The model aims to identify the importance of the measures to be taken in order to stop the spread of the virus. It describes the diffusion of the virus in normal life with and without precaution. It is a data-driven parametric dependent function, for which the parameters are extracted from the data and the exponential function derived using multiplicative calculus. The results of the proposed model are compared to real recorded data from different countries and the performance of this model is investigated using error analysis theory. We stress that all statistics, collected data, etc., included in this study were extracted from official website of the World Health Organization (WHO). Therefore, the obtained results demonstrate its applicability and efficiency.
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Aldawish I, Ibrahim RW. A new mathematical model of multi-faced COVID-19 formulated by fractional derivative chains. ADVANCES IN CONTINUOUS AND DISCRETE MODELS 2022; 2022:6. [PMID: 35450202 PMCID: PMC8777456 DOI: 10.1186/s13662-022-03677-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Accepted: 12/14/2021] [Indexed: 11/16/2022]
Abstract
It has been reported that there are seven different types of coronaviruses realized by individuals, containing those responsible for the SARS, MERS, and COVID-19 epidemics. Nowadays, numerous designs of COVID-19 are investigated using different operators of fractional calculus. Most of these mathematical models describe only one type of COVID-19 (infected and asymptomatic). In this study, we aim to present an altered growth of two or more types of COVID-19. Our technique is based on the ABC-fractional derivative operator. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion between infected and asymptomatic people. The consequence is accordingly connected with a macroscopic rule for the individuals. In this analysis, we utilize the concept of a fractional chain. This type of chain is a fractional differential-difference equation combining continuous and discrete variables. The existence of solutions is recognized by formulating a matrix theory. The solution of the approximated system is shown to have a minimax point at the origin.
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Affiliation(s)
- Ibtisam Aldawish
- Department of Mathematics and Statistics, College of Science, IMSIU (Imam Mohammad Ibn Saud Islamic University), Riyadh, Saudi Arabia
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15
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Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View. MATHEMATICS 2021. [DOI: 10.3390/math9233122] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
In this article, we propose a novel mathematical model for the spread of COVID-19 involving environmental white noise. The new stochastic model was studied for the existence and persistence of the disease, as well as the extinction of the disease. We noticed that the existence and extinction of the disease are dependent on R0 (the reproduction number). Then, a numerical scheme was developed for the computational analysis of the model; with the existing values of the parameters in the literature, we obtained the related simulations, which gave us more realistic numerical data for the future prediction. The mentioned stochastic model was analyzed for different values of σ1,σ2 and β1,β2, and both the stochastic and the deterministic models were compared for the future prediction of the spread of COVID-19.
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Usmani BA, Ali M, Hasan MA, Siddiqui AR, Siddiqi S, Lim AG, Qazi SA. The Impact of Disease Control Measures on the Spread of COVID-19 in the Province of Sindh, Pakistan. PLoS One 2021; 16:e0260129. [PMID: 34793543 PMCID: PMC8601461 DOI: 10.1371/journal.pone.0260129] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Accepted: 11/03/2021] [Indexed: 11/25/2022] Open
Abstract
The province of Sindh reported the first COVID-19 case in Pakistan on 26th February 2020. The Government of Sindh has employed numerous control measures to limit its spread. However, for low-and middle-income countries such as Pakistan, the management protocols for controlling a pandemic are not always as definitive as they would be in other developed nations. Given the dire socio-economic conditions of Sindh, continuation of province-wise lockdowns may inadvertently cause a potential economic breakdown. By using a data driven SEIR modelling framework, this paper describes the evolution of the epidemic projections because of government control measures. The data from reported COVID-19 prevalence and google mobility is used to parameterize the model at different time points. These time points correspond to the government's call for advice on the prerequisite actions required to curtail the spread of COVID-19 in Sindh. Our model predicted the epidemic peak to occur by 18th June 2020 with approximately 3500 reported cases at that peak, this projection correlated with the actual recorded peak during the first wave of the disease in Sindh. The impact of the governmental control actions and religious ceremonies on the epidemic profile during this first wave of COVID-19 are clearly reflected in the model outcomes through variations in the epidemic peaks. We also report these variations by displaying the trajectory of the epidemics had the control measures been guided differently; the epidemic peak may have occurred as early as the end of May 2020 with approximately 5000 reported cases per day had there been no control measures and as late as August 2020 with only around 2000 cases at the peak had the lockdown continued, nearly flattening the epidemic curve.
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Affiliation(s)
- Bilal Ahmed Usmani
- Department of Biomedical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
- Centre of Infectious Disease Modeling, NED University of Engineering and Technology, Karachi, Pakistan
| | - Mustafain Ali
- Department of Biomedical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
- Centre of Infectious Disease Modeling, NED University of Engineering and Technology, Karachi, Pakistan
| | - Muhammad Abul Hasan
- Department of Biomedical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
- Neuro-Computation Lab, National Centre of Artificial Intelligence, NED University of Engineering and Technology, Karachi, Pakistan
| | | | - Sameen Siddiqi
- Department of Community Health Sciences, Aga Khan University, Karachi, Pakistan
| | - Aaron Guanliang Lim
- Population Health Sciences, Bristol Medical School, University of Bristol, Bristol, United Kingdom
| | - Saad Ahmed Qazi
- Department of Electrical Engineering, NED University of Engineering and Technology, Karachi, Pakistan
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17
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Cengizci S, Cengizci AD, Uğur Ö. A mathematical model for human-to-human transmission of COVID-19: a case study for Turkey's data. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:9787-9805. [PMID: 34814369 DOI: 10.3934/mbe.2021480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this study, a mathematical model for simulating the human-to-human transmission of the novel coronavirus disease (COVID-19) is presented for Turkey's data. For this purpose, the total population is classified into eight epidemiological compartments, including the super-spreaders. The local stability and sensitivity analysis in terms of the model parameters are discussed, and the basic reproduction number, R0, is derived. The system of nonlinear ordinary differential equations is solved by using the Galerkin finite element method in the FEniCS environment. Furthermore, to guide the interested reader in reproducing the results and/or performing their own simulations, a sample solver is provided. Numerical simulations show that the proposed model is quite convenient for Turkey's data when used with appropriate parameters.
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Affiliation(s)
- Süleyman Cengizci
- Computer Programming, Antalya Bilim University, Antalya 07190, Turkey
- Institute of Applied Mathematics, Middle East Technical University, Ankara 06800, Turkey
| | | | - Ömür Uğur
- Institute of Applied Mathematics, Middle East Technical University, Ankara 06800, Turkey
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18
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Atangana A, İğret Araz S. Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia. RESULTS IN PHYSICS 2021; 29:104694. [PMID: 36968003 PMCID: PMC10025579 DOI: 10.1016/j.rinp.2021.104694] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2021] [Revised: 08/09/2021] [Accepted: 08/11/2021] [Indexed: 05/21/2023]
Abstract
Several collected data representing the spread of some infectious diseases have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish flu and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns, a clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely. The idea was first applied in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature.
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Affiliation(s)
- Abdon Atangana
- Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
| | - Seda İğret Araz
- Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
- Department of Mathematic Education, Faculty of Education, Siirt University, Siirt 56100, Turkey
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19
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Sioofy Khoojine A, Shadabfar M, Hosseini VR, Kordestani H. Network Autoregressive Model for the Prediction of COVID-19 Considering the Disease Interaction in Neighboring Countries. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1267. [PMID: 34681991 PMCID: PMC8535150 DOI: 10.3390/e23101267] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/08/2021] [Revised: 09/20/2021] [Accepted: 09/25/2021] [Indexed: 12/11/2022]
Abstract
Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of total currently infected cases with coronavirus disease 2019 (COVID-19) in Iran until the end of December 2021 in view of the disease interactions within the neighboring countries in the region. For this purpose, the COVID-19 data were initially collected for seven regional nations, including Iran, Turkey, Iraq, Azerbaijan, Armenia, Afghanistan, and Pakistan. Thenceforth, a network was established over these countries, and the correlation of the disease data was calculated. Upon introducing the main structure of the NAR model, a mathematical platform was subsequently provided to further incorporate the correlation matrix into the prediction process. In addition, the maximum likelihood estimation (MLE) was utilized to determine the model parameters and optimize the forecasting accuracy. Thereafter, the number of infected cases up to December 2021 in Iran was predicted by importing the correlation matrix into the NAR model formed to observe the impact of the disease interactions in the neighboring countries. In addition, the autoregressive integrated moving average (ARIMA) was used as a benchmark to compare and validate the NAR model outcomes. The results reveal that COVID-19 data in Iran have passed the fifth peak and continue on a downward trend to bring the number of total currently infected cases below 480,000 by the end of 2021. Additionally, 20%, 50%, 80% and 95% quantiles are provided along with the point estimation to model the uncertainty in the forecast.
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Affiliation(s)
- Arash Sioofy Khoojine
- Faculty of Economics and Business Administration, Yibin University, Yibin 644000, China;
| | - Mahdi Shadabfar
- Center for Infrastructure Sustainability and Resilience Research, Department of Civil Engineering, Sharif University of Technology, Tehran 145888-9694, Iran
| | | | - Hadi Kordestani
- Department of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China;
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20
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Abreu Z, Cantin G, Silva CJ. Analysis of a COVID-19 compartmental model: a mathematical and computational approach. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:7979-7998. [PMID: 34814285 DOI: 10.3934/mbe.2021396] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.
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Affiliation(s)
- Zita Abreu
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
| | - Guillaume Cantin
- Laboratoire de Mathématiques Appliquées, FR-CNRS-3335, 25, Rue Philippe Lebon, Le Havre Normandie 76063, France
| | - Cristiana J Silva
- Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
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21
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Nawaz Y, Arif MS, Ashraf MU. Development of Explicit Schemes for Diffusive SEAIR COVID-19 Epidemic Spreading Model: An Application to Computational Biology. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY. TRANSACTION A, SCIENCE 2021; 45:2109-2119. [PMID: 34539151 PMCID: PMC8435406 DOI: 10.1007/s40995-021-01214-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Accepted: 08/25/2021] [Indexed: 10/28/2022]
Abstract
In this contribution, a first-order time scheme is proposed for finding solutions to partial differential equations (PDEs). A mathematical model of the COVID-19 epidemic is modified where the recovery rate of exposed individuals is also considered. The linear stability of the equilibrium states for the modified COVID-19 model is given by finding its Jacobian and applying Routh-Hurwitz criteria on characteristic polynomial. The proposed scheme provides the first-order accuracy in time and second-order accuracy in space. The stability of the proposed scheme is given using the von Neumann stability criterion for standard parabolic PDEs. The consistency for the proposed scheme is also given by expanding the involved terms in it using the Taylor series. The scheme can be used to obtain the condition of getting a positive solution. The stability region of the scheme can be enlarged by choosing suitable values of the contained parameter. Finally, a comparison of the proposed scheme is made with the existing non-standard finite difference method. The results indicate that the non-standard classical technique is incapable of preserving the unique characteristics of the model's epidemiologically significant solutions, whereas the proposed approaches are capable of doing so. A computational code for the proposed discrete model scheme may be made available to readers upon request for convenience.
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Affiliation(s)
- Yasir Nawaz
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000 Pakistan
| | - Muhammad Shoaib Arif
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000 Pakistan
| | - Muhammad Usman Ashraf
- Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Islamabad, Pakistan
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22
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Ayoobi N, Sharifrazi D, Alizadehsani R, Shoeibi A, Gorriz JM, Moosaei H, Khosravi A, Nahavandi S, Gholamzadeh Chofreh A, Goni FA, Klemeš JJ, Mosavi A. Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods. RESULTS IN PHYSICS 2021; 27:104495. [PMID: 34221854 PMCID: PMC8233414 DOI: 10.1016/j.rinp.2021.104495] [Citation(s) in RCA: 46] [Impact Index Per Article: 15.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/19/2021] [Accepted: 06/22/2021] [Indexed: 05/17/2023]
Abstract
The first known case of Coronavirus disease 2019 (COVID-19) was identified in December 2019. It has spread worldwide, leading to an ongoing pandemic, imposed restrictions and costs to many countries. Predicting the number of new cases and deaths during this period can be a useful step in predicting the costs and facilities required in the future. The purpose of this study is to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days. The motivation for predicting every n days (instead of just every day) is the investigation of the possibility of computational cost reduction and still achieving reasonable performance. Such a scenario may be encountered in real-time forecasting of time series. Six different deep learning methods are examined on the data adopted from the WHO website. Three methods are LSTM, Convolutional LSTM, and GRU. The bidirectional extension is then considered for each method to forecast the rate of new cases and new deaths in Australia and Iran countries. This study is novel as it carries out a comprehensive evaluation of the aforementioned three deep learning methods and their bidirectional extensions to perform prediction on COVID-19 new cases and new death rate time series. To the best of our knowledge, this is the first time that Bi-GRU and Bi-Conv-LSTM models are used for prediction on COVID-19 new cases and new deaths time series. The evaluation of the methods is presented in the form of graphs and Friedman statistical test. The results show that the bidirectional models have lower errors than other models. A several error evaluation metrics are presented to compare all models, and finally, the superiority of bidirectional methods is determined. This research could be useful for organisations working against COVID-19 and determining their long-term plans.
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Key Words
- ANFIS, Adaptive Network-based Fuzzy Inference System
- ANN, Artificial Neural Network
- AU, Australia
- Bi-Conv-LSTM, Bidirectional Convolutional Long Short Term Memory
- Bi-GRU, Bidirectional Gated Recurrent Unit
- Bi-LSTM, Bidirectional Long Short-Term Memory
- Bidirectional
- COVID-19 Prediction
- COVID-19, Coronavirus Disease 2019
- Conv-LSTM, Convolutional Long Short Term Memory
- Convolutional Long Short Term Memory (Conv-LSTM)
- DL, Deep Learning
- DLSTM, Delayed Long Short-Term Memory
- Deep learning
- EMRO, Eastern Mediterranean Regional Office
- ES, Exponential Smoothing
- EV, Explained Variance
- GRU, Gated Recurrent Unit
- Gated Recurrent Unit (GRU)
- IR, Iran
- LR, Linear Regression
- LSTM, Long Short-Term Memory
- Lasso, Least Absolute Shrinkage and Selection Operator
- Long Short Term Memory (LSTM)
- MAE, Mean Absolute Error
- MAPE, Mean Absolute Percentage Error
- MERS, Middle East Respiratory Syndrome
- ML, Machine Learning
- MLP-ICA, Multi-layered Perceptron-Imperialist Competitive Calculation
- MSE, Mean Square Error
- MSLE, Mean Squared Log Error
- Machine learning
- New Cases of COVID-19
- New Deaths of COVID-19
- PRISMA, Preferred Reporting Items for Precise Surveys and Meta-Analyses
- RMSE, Root Mean Square Error
- RMSLE, Root Mean Squared Log Error
- RNN, Repetitive Neural Network
- ReLU, Rectified Linear Unit
- SARS, Serious Intense Respiratory Disorder
- SARS-COV, SARS coronavirus
- SARS-COV-2, Serious Intense Respiratory Disorder Coronavirus 2
- SVM, Support Vector Machine
- VAE, Variational Auto Encoder
- WHO, World Health Organization
- WPRO, Western Pacific Regional Office
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Affiliation(s)
- Nooshin Ayoobi
- Department of Mathematics, Savitribai Phule Pune University, Pune 411007, India
| | - Danial Sharifrazi
- Department of Computer Engineering, School of Technical and Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran
| | - Roohallah Alizadehsani
- Institute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Waurn Ponds, VIC 3217, Australia
| | - Afshin Shoeibi
- Computer Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran
- Faculty of Electrical and Computer Engineering, Biomedical Data Acquisition Lab, K. N. Toosi University of Technology, Tehran, Iran
| | - Juan M Gorriz
- Department of Signal Theory, Networking and Communications, Universidad de Granada, Spain
| | - Hossein Moosaei
- Department of Mathematics, Faculty of Science, University of Bojnord, Iran
| | - Abbas Khosravi
- Institute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Waurn Ponds, VIC 3217, Australia
| | - Saeid Nahavandi
- Institute for Intelligent Systems Research and Innovation (IISRI), Deakin University, Waurn Ponds, VIC 3217, Australia
| | - Abdoulmohammad Gholamzadeh Chofreh
- Sustainable Process Integration Laboratory - SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of Technology - VUT Brno, Technická 2896/2, 616 69 Brno, Czech Republic
| | - Feybi Ariani Goni
- Department of Management, Faculty of Business and Management, Brno University of Technology - VUT Brno, Kolejní 2906/4, 612 00 Brno, Czech Republic
| | - Jiří Jaromír Klemeš
- Sustainable Process Integration Laboratory - SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of Technology - VUT Brno, Technická 2896/2, 616 69 Brno, Czech Republic
| | - Amir Mosavi
- John von Neumann Faculty of Informatics, Obuda University, 1034 Budapest, Hungary
- School of Economics and Business, Norwegian University of Life Sciences, 1430 Ås, Norway
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23
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Shadabfar M, Mahsuli M, Sioofy Khoojine A, Hosseini VR. Time-variant reliability-based prediction of COVID-19 spread using extended SEIVR model and Monte Carlo sampling. RESULTS IN PHYSICS 2021; 26:104364. [PMID: 34094819 PMCID: PMC8169594 DOI: 10.1016/j.rinp.2021.104364] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2021] [Revised: 05/17/2021] [Accepted: 05/19/2021] [Indexed: 05/12/2023]
Abstract
A probabilistic method is proposed in this study to predict the spreading profile of the coronavirus disease 2019 (COVID-19) in the United State (US) via time-variant reliability analysis. To this end, an extended susceptible-exposed-infected-vaccinated-recovered (SEIVR) epidemic model is first established deterministically, considering the quarantine and vaccination effects, and then applied to the available COVID-19 data from US. Afterwards, the prediction results are described as a time-series of the number of people infected, recovered, and dead. Upon introducing the extended SEIVR model into a limit-state function and defining the model parameters including transmission, recovery, and mortality rates as random variables, the problem is transformed into a reliability model and analyzed by the Monte Carlo sampling. The findings are subsequently given in the form of exceedance probabilities (EPs) of the three main outputs, namely, the maximum number of infected cases, the total number of recovered cases, and the total number of fatal cases. Afterwards, by incorporating time into the formulation of the reliability problem, the EPs are calculated over time and presented as 3D probability graphs, illustrating the relationship between the number of cases affected (i.e., infected, recovered, or dead), exceedance probability, and time. The results for the US demonstrate that, by the end of 2021, the number of the infected (active) cases decreases to 0.8 million and number of cases recovered and fatalities increases to 41.3 million and 0.6 million, respectively.
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Affiliation(s)
- Mahdi Shadabfar
- Center for Infrastructure Sustainability and Resilience Research, Department of Civil Engineering, Sharif University of Technology, Tehran 145888-9694, Iran
| | - Mojtaba Mahsuli
- Center for Infrastructure Sustainability and Resilience Research, Department of Civil Engineering, Sharif University of Technology, Tehran 145888-9694, Iran
| | - Arash Sioofy Khoojine
- Faculty of Economics and Business Administration, Yibin University, Yibin 644000, China
- School of Mathematics and Statistics, Shanghai Jiao Tong University, Shanghai, China
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24
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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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