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Jiménez EAV, Martínez JM, Zuniga LDH, Victoria JGR. Discrete models for analyzing the behavior of COVID-19 pandemic in the State of Mexico, Mexico. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:286-317. [PMID: 36650767 DOI: 10.3934/mbe.2023014] [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: 06/17/2023]
Abstract
In this paper we analyze the behavior of the COVID-19 pandemic during a certain period of the year 2020 in the state of Mexico, Mexico. For this, we will use the discrete models obtained by the first, third and fourth authors of this work. The first is a one-dimensional model, and the second is two-dimensional, both non-linear. It is assumed that the population of the state of Mexico is constant and that the parameters used are the infection capacity, which we will initially assume to be constant, and the recovery and mortality parameters in that state. We will show that even when the statistical data obtained are disperse, and the process could be stabilized, this has been slow due to chaotic mitigation, creating situations of economic, social, health and political deterioration in that region of the country. We note that the observed results of the behavior of the epidemic during that period for the first variants of the virus have continued to be observed for the later variants, which has not allowed the eradication of the pandemic.
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Joshi H, Jha BK, Yavuz M. Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:213-240. [PMID: 36650763 DOI: 10.3934/mbe.2023010] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.
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Affiliation(s)
- Hardik Joshi
- School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
| | - Brajesh Kumar Jha
- Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar 382007, India
| | - Mehmet Yavuz
- Department of Mathematics and Computer Sciences, Necmettin Erbakan University, Konya 42090, Türkiye
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Shadi R, Fakharian A, Khaloozadeh H. Modeling and Analysis of COVID-19 Spread: The Impacts of Nonpharmaceutical Protocols. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2022; 2022:7706447. [PMID: 36092782 PMCID: PMC9462995 DOI: 10.1155/2022/7706447] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/21/2022] [Revised: 07/14/2022] [Accepted: 08/07/2022] [Indexed: 11/20/2022]
Abstract
In this study, the extended SEIR dynamical model is formulated to investigate the spread of coronavirus disease (COVID-19) via a special focus on contact with asymptomatic and self-isolated infected individuals. Furthermore, a mathematical analysis of the model, including positivity, boundedness, and local and global stability of the disease-free and endemic equilibrium points in terms of the basic reproduction number, is presented. The sensitivity analysis indicates that reducing the disease contact rate and the transmissibility factor related to asymptomatic individuals, along with increasing the quarantine/self-isolation rate and the contact-tracing process, from the view of flattening the curve for novel coronavirus, are crucial to the reduction in disease-related deaths.
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Affiliation(s)
- Reza Shadi
- Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
| | - Ahmad Fakharian
- Department of Electrical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
| | - Hamid Khaloozadeh
- Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran
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Abbes A, Ouannas A, Shawagfeh N, Jahanshahi H. The fractional-order discrete COVID-19 pandemic model: stability and chaos. NONLINEAR DYNAMICS 2022; 111:965-983. [PMID: 35992382 PMCID: PMC9376916 DOI: 10.1007/s11071-022-07766-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
This paper presents and investigates a new fractional discrete COVID-19 model which involves three variables: the new daily cases, additional severe cases and deaths. Here, we analyze the stability of the equilibrium point at different values of the fractional order. Using maximum Lyapunov exponents, phase attractors, bifurcation diagrams, the 0-1 test and approximation entropy (ApEn), it is shown that the dynamic behaviors of the model change from stable to chaotic behavior by varying the fractional orders. Besides showing that the fractional discrete model fits the real data of the pandemic, the simulation findings also show that the numbers of new daily cases, additional severe cases and deaths exhibit chaotic behavior without any effective attempts to curb the epidemic.
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Affiliation(s)
- Abderrahmane Abbes
- Department of Mathematics, The University of Jordan, Amman, 11942 Jordan
| | - Adel Ouannas
- Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, 04000 Oum El Bouaghi, Algeria
| | - Nabil Shawagfeh
- Department of Mathematics, The University of Jordan, Amman, 11942 Jordan
| | - Hadi Jahanshahi
- Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6 Canada
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Abbes A, Ouannas A, Shawagfeh N, Grassi G. The effect of the Caputo fractional difference operator on a new discrete COVID-19 model. RESULTS IN PHYSICS 2022; 39:105797. [PMID: 35818497 PMCID: PMC9259007 DOI: 10.1016/j.rinp.2022.105797] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Revised: 06/27/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
This study aims to generalize the discrete integer-order SEIR model to obtain the novel discrete fractional-order SEIR model of COVID-19 and study its dynamic characteristics. Here, we determine the equilibrium points of the model and discuss the stability analysis of these points in detail. Then, the non-linear dynamic behaviors of the suggested discrete fractional model for commensurate and incommensurate fractional orders are investigated through several numerical techniques, including maximum Lyapunov exponents, phase attractors, bifurcation diagrams and C 0 algorithm. Finally, we fitted the model with actual data to verify the accuracy of our mathematical study of the stability of the fractional discrete COVID-19 model.
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Affiliation(s)
- Abderrahmane Abbes
- Department of Mathematics, The University of Jordan, Amman, 11942, Jordan
| | - Adel Ouannas
- Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi, 04000, Algeria
| | - Nabil Shawagfeh
- Department of Mathematics, The University of Jordan, Amman, 11942, Jordan
| | - Giuseppe Grassi
- Dipartimento Ingegneria Innovazione, Universita del Salento, Lecce, 73100, Italy
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Anggriani N, Beay LK. Modeling of COVID-19 spread with self-isolation at home and hospitalized classes. RESULTS IN PHYSICS 2022; 36:105378. [PMID: 35280116 PMCID: PMC8896885 DOI: 10.1016/j.rinp.2022.105378] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Revised: 02/17/2022] [Accepted: 02/22/2022] [Indexed: 05/21/2023]
Abstract
This work examines the impacts of self-isolation and hospitalization on the population dynamics of the Corona-Virus Disease. We developed a new nonlinear deterministic model eight classes compartment, with self-isolation and hospitalized being the most effective tools. There are (Susceptible S C ( t ) , Exposed E ( t ) , Asymptomatic infected I A ( t ) , Symptomatic infected A S ( t ) , Self-isolation T M ( t ) , Hospitalized T H ( t ) , Healed H ( t ) , and Susceptible individuals previously infected H C ( t ) ). The expression of basic reproduction number R 0 comes from the next-generation matrix method. With suitably constructed Lyapunov functions, the global asymptotic stability of the non-endemic equilibria Σ 0 for R 0 < 1 and that of endemic equilibria Σ ∗ for R 0 > 1 are established. The computed value of R 0 = 3 . 120277403 proves the endemic level of the epidemic. The outbreak will lessen if a policy is enforced like self-isolation and hospitalization. This is related to those policies that can reduce the number of direct contacts between infected and susceptible individuals or waning immunity individuals. Various simulations are presented to appreciate self-isolation at home and hospitalized strategies if applied sensibly. By performing a global sensitivity analysis, we can obtain parameter values that affect the model through a combination of Latin Hypercube Sampling and Partial Rating Correlation Coefficients methods to determine the parameters that affect the number of reproductions and the increase in the number of COVID cases. The results obtained show that the rate of self-isolation at home and the rate of hospitalism have a negative relationship. On the other hand, infections will decrease when the two parameters increase. From the sensitivity of the results, we formulate a control model using optimal control theory by considering two control variables. The result shows that the control strategies minimize the spread of the COVID infection in the population.
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Affiliation(s)
- Nursanti Anggriani
- Department of Mathematics, Universitas Padjadjaran, Jln. Raya Bandung-Sumedang Km. 21 Jatinangor, Kab. Sumedang 45363 Jawa Barat, Indonesia
| | - Lazarus Kalvein Beay
- Post Doctoral Program, Department of Mathematics, Universitas Padjadjaran, Jln. Raya Bandung-Sumedang Km. 21 Jatinangor, Kab. Sumedang 45363 Jawa Barat, Indonesia
- Department of Education and Culture, Provincial Government of Moluccas, Ambon, Indonesia
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Li XP, Bayatti HA, Din A, Zeb A. A vigorous study of fractional order COVID-19 model via ABC derivatives. RESULTS IN PHYSICS 2021; 29:104737. [PMID: 34485028 PMCID: PMC8401151 DOI: 10.1016/j.rinp.2021.104737] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2021] [Revised: 08/19/2021] [Accepted: 08/20/2021] [Indexed: 05/08/2023]
Abstract
The newly arose irresistible sickness known as the Covid illness (COVID-19), is a highly infectious viral disease. This disease caused millions of tainted cases internationally and still represent a disturbing circumstance for the human lives. As of late, numerous mathematical compartmental models have been considered to even more likely comprehend the Covid illness. The greater part of these models depends on integer-order derivatives which cannot catch the fading memory and crossover behavior found in many biological phenomena. Along these lines, the Covid illness in this paper is studied by investigating the elements of COVID-19 contamination utilizing the non-integer Atangana-Baleanu-Caputo derivative. Using the fixed-point approach, the existence and uniqueness of the integral of the fractional model for COVID is further deliberated. Along with Ulam-Hyers stability analysis, for the given model, all basic properties are studied. Furthermore, numerical simulations are performed using Newton polynomial and Adams Bashforth approaches for determining the impact of parameters change on the dynamical behavior of the systems.
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Affiliation(s)
- Xiao-Ping Li
- College of Mathematics and Information Science, Xiangnan University, Chenzhou 423000, P. R. China
| | - Hilal Al Bayatti
- College of Computer Sciences, Applied Science University, P.O. Box 5055, Kingdom of Bahrain
| | - Anwarud Din
- Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China
| | - Anwar Zeb
- Department of Mathematics, COMSATS University Islamabad, Abbottabad, 22060, Khyber Pakhtunkhwa, Pakistan
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