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Qurban M, Khaliq A, Nisar KS, Shah NA. Dynamics and control of a plant-herbivore model incorporating Allee's effect. Heliyon 2024; 10:e30754. [PMID: 38826754 PMCID: PMC11141269 DOI: 10.1016/j.heliyon.2024.e30754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Revised: 04/18/2024] [Accepted: 05/03/2024] [Indexed: 06/04/2024] Open
Abstract
This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect. We specifically investigate a model that incorporates a strong predator functional response to better understand the system's qualitative behavior at positive equilibrium points. In the present study, we explore the topological classifications at fixed points, stability analysis, Neimark-Sacker, Transcritical bifurcation and State feedback control in the two-dimensional discrete-time plant-herbivore model. It is proved that for all involved parameters ς 1 , ϱ 1 , γ 1 and ϒ 1 , discrete-time plant-herbivore model has boundary and interior fixed points: c 1 = ( 0 , 0 ) , c 2 = ( ς 1 - 1 ϱ 1 , 0 ) and c 3 = ( ϒ 1 ( 1 - γ 1 ) 2 γ 1 - 1 , γ 1 ( 2 ς 1 + ϱ 1 ϒ 1 - 2 ) - ϱ 1 ϒ 1 + 1 - ς 1 2 γ 1 - 1 ) respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: c 1 = ( 0 , 0 ) , c 2 = ( ς 1 - 1 ϱ 1 , 0 ) and c 3 = ( ϒ 1 ( 1 - γ 1 ) 2 γ 1 - 1 , γ 1 ( 2 ς 1 + ϱ 1 ϒ 1 - 2 ) - ϱ 1 ϒ 1 + 1 - ς 1 2 γ 1 - 1 ) . Our investigation uncovers that the boundary equilibrium c 2 = ( ς 1 - 1 ϱ 1 , 0 ) experiences a transcritical bifurcation, whereas the unique positive steady-state c 3 = ( ϒ 1 ( 1 - γ 1 ) 2 γ 1 - 1 , γ 1 ( 2 ς 1 + ϱ 1 ϒ 1 - 2 ) - ϱ 1 ϒ 1 + 1 - ς 1 2 γ 1 - 1 ) of the discrete-time plant-herbivore model undergoes a Neimark-Sacker bifurcation. To address the periodic fluctuations in grapevine population density and other unpredictable behaviors observed in the model, we propose implementing state feedback chaos control. To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent. These visual representations enhance the clarity of our research outcomes and further validate the effectiveness of the chaos control approach.
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Affiliation(s)
- Muhammad Qurban
- Department of Mathematics, Riphah International University, Lahore, Pakistan
| | - Abdul Khaliq
- Department of Mathematics, Riphah International University, Lahore, Pakistan
| | - Kottakkaran Scooppy Nisar
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
| | - Nehad Ali Shah
- Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea
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2
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Witbooi PJ, Abiodun GJ, Maharaj R. Modeling the effect of imported malaria on the elimination programme in KwaZulu-Natal province of South Africa. Pan Afr Med J 2024; 47:80. [PMID: 38708136 PMCID: PMC11068472 DOI: 10.11604/pamj.2024.47.80.35882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2022] [Accepted: 02/19/2024] [Indexed: 05/07/2024] Open
Abstract
Introduction with imported malaria cases in a given population, the question arises as to what extent the local cases are a consequence of the imports or not. We perform a modeling analysis for a specific area, in a region aspiring for malaria-free status. Methods data on malaria cases over ten years is subjected to a compartmental model which is assumed to be operating close to the equilibrium state. Two of the parameters of the model are fitted to the decadal data. The other parameters in the model are sourced from the literature. The model is utilized to simulate the malaria prevalence with or without imported cases. Results in any given year the annual average of 460 imported cases, resulted in an end-of-year season malaria prevalence of 257 local active infectious cases, whereas without the imports the malaria prevalence at the end of the season would have been fewer than 10 active infectious cases. We calculate the numerical value of the basic reproduction number for the model, which reveals the extent to which the disease is being eliminated from the population or not. Conclusion without the imported cases, over the ten seasons of malaria, 2008-2018, the KwaZulu-Natal province would have been malaria-free over at least the last 7 years of the decade indicated. This simple methodology works well even in situations where data is limited.
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Affiliation(s)
- Peter Joseph Witbooi
- Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
| | - Gbenga Jacob Abiodun
- Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
- Department of Mathematics, Southern Methodist University, Dallas, TX 75275, USA
| | - Rajendra Maharaj
- Office of Malaria Research, South African Medical Research Council, Durban, South Africa
- School of Life Sciences, College of Agriculture, Engineering and Sciences, University of KwaZulu-Natal, South Africa
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3
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Teklu SW, Meshesha AA, Ullah S. Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis. Sci Rep 2024; 14:1508. [PMID: 38233520 PMCID: PMC10794199 DOI: 10.1038/s41598-024-51670-y] [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: 08/25/2023] [Accepted: 01/08/2024] [Indexed: 01/19/2024] Open
Abstract
In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard-Lindelöf criteria we have proved the model solutions' existence and uniqueness, using the next generation matrix approach we calculated the model basic reproduction number, we computed the model equilibrium points and investigated their stabilities, using the three time-dependent control variables (prevention measure, non-inflammatory infection treatment measure, and inflammatory infection treatment measure) and from the formulated fractional order model we re-formulated the fractional order optimal control problem. The necessary optimality conditions for the Tinea capitis fractional order optimal control problem and the existence of optimal control strategies are derived and presented by using Pontryagin's Maximum Principle. Also, the study carried out the sensitivity and numerical analysis to investigate the most sensitive parameters and to verify the qualitative analysis results. Finally, we performed the cost-effective analysis to investigate the most cost-effective measures from the possible proposed control measures, and from the findings we can suggest that implementing prevention measures only is the most cost-effective control measure that stakeholders should consider.
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Affiliation(s)
- Shewafera Wondimagegnhu Teklu
- Department of Mathematics, College of Natural and Computational Sciences, Debre Berhan University, 445, Debre Berhan, Ethiopia.
| | - Abebe Addise Meshesha
- Department of Surgery, College of Health Science, Debre Berhan University, 445, Debre Berhan, Ethiopia
| | - Saif Ullah
- Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan
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4
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Gokila C, Sambath M, Balachandran K, Ma YK. Stationary distribution and global stability of stochastic predator-prey model with disease in prey population. JOURNAL OF BIOLOGICAL DYNAMICS 2023; 17:2164803. [PMID: 36648149 DOI: 10.1080/17513758.2022.2164803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2021] [Accepted: 12/29/2022] [Indexed: 06/17/2023]
Abstract
In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented.
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Affiliation(s)
- C Gokila
- Department of Mathematics, Periyar University, Salem, India
- Department of Mathematics, Sri Eshwar College of Engineering, Coimbatore, India
| | - M Sambath
- Department of Mathematics, Periyar University, Salem, India
| | - K Balachandran
- Department of Mathematics, Bharathiar University, Coimbatore, India
| | - Yong-Ki Ma
- Department of Applied Mathematics, Kongju National University, Chungcheongnam-do,Republic of Korea
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5
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Cao J, Udhayakumar K, Rakkiyappan R, Li X, Lu J. A Comprehensive Review of Continuous-/Discontinuous-Time Fractional-Order Multidimensional Neural Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:5476-5496. [PMID: 34962883 DOI: 10.1109/tnnls.2021.3129829] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
The dynamical study of continuous-/discontinuous-time fractional-order neural networks (FONNs) has been thoroughly explored, and several publications have been made available. This study is designed to give an exhaustive review of the dynamical studies of multidimensional FONNs in continuous/discontinuous time, including Hopfield NNs (HNNs), Cohen-Grossberg NNs, and bidirectional associative memory NNs, and similar models are considered in real ( [Formula: see text]), complex ( [Formula: see text]), quaternion ( [Formula: see text]), and octonion ( [Formula: see text]) fields. Since, in practice, delays are unavoidable, theoretical findings from multidimensional FONNs with various types of delays are thoroughly evaluated. Some required and adequate stability and synchronization requirements are also mentioned for fractional-order NNs without delays.
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Sun Q, Tan D, Zhang S. Epidemic threshold of a COVID-19 model with gaussian white noise and semi-Markov switching. JOURNAL OF THE FRANKLIN INSTITUTE 2023; 360:6846-6861. [PMID: 37251516 PMCID: PMC10152832 DOI: 10.1016/j.jfranklin.2023.04.035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/16/2022] [Revised: 03/13/2023] [Accepted: 04/29/2023] [Indexed: 05/31/2023]
Abstract
In this study, we investigate the COVID-19 propagation dynamics using a stochastic SIQR model with Gaussian white noise and semi-Markovian switching, focusing on the impacts of Gaussian white noise and semi-Markovian switching on the propagation dynamics of COVID-19. It is suggested that the fate of COVID-19 is entirely determined by the basic reproduction number R0, under mild extra conditions. By making sensitivity analysis on R0, we found that the effect of quarantine rate on R0 was more significant compared to transmission rate. Our results demonstrate that: (i) The presence of Gaussian white noise, while reducing the basic reproduction number R0 of COVID-19, also poses more challenges for the prediction and control of COVID-19 propagation. (ii) The conditional holding time distribution has a significant effect on the kinetics of COVID-19. (iii) The semi-Markov switching and Gaussian white noise can support irregular recurrence of COVID-19 outbreaks.
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Affiliation(s)
- Qianqian Sun
- Xiamen Institute of Technology, China
- School of Science, Jimei University, China
| | - Dejun Tan
- Xiamen Institute of Technology, China
| | - Shuwen Zhang
- Xiamen Institute of Technology, China
- School of Science, Jimei University, China
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7
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Shah K, Amin R, Abdeljawad T. Utilization of Haar wavelet collocation technique for fractal-fractional order problem. Heliyon 2023; 9:e17123. [PMID: 37360113 PMCID: PMC10285150 DOI: 10.1016/j.heliyon.2023.e17123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 06/07/2023] [Accepted: 06/07/2023] [Indexed: 06/28/2023] Open
Abstract
This work is devoted for establishing adequate results for the qualitative theory as well as approximate solution of "fractal-fractional order differential equations" (F-FDEs). For the required numerical results, we use Haar wavelet collocation (H-W-C) method which has very rarely utilized for F-FDEs. We establish the general algorithm for F-FDEs to compute numerical solution for the considered class. Also, we establish a result devoted to the qualitative theory via Banach fixed point result. A results devoted to Ulam-Hyers (U-H) stability are also included. Two pertinent examples are given along with the comparison and different norms of errors displayed in figures as well as tables.
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Affiliation(s)
- Kamal Shah
- Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
- Department of Mathematics, University of Malakand, Chakdara, Dir(L) 18000, KPK, Pakistan
| | - Rohul Amin
- Department of Mathematics, University of Peshawar, KPK, Pakistan
| | - Thabet Abdeljawad
- Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
- Department of Medical Research, China Medical University, Taichung 40402, Taiwan
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Akter S, Islam MS, Hossain T. Dynamical properties of single species stage structured model with Michaelis-Menten type harvesting on adult population and linear harvesting on juvenile population. Heliyon 2023; 9:e15709. [PMID: 37159678 PMCID: PMC10163657 DOI: 10.1016/j.heliyon.2023.e15709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2022] [Revised: 04/14/2023] [Accepted: 04/19/2023] [Indexed: 05/11/2023] Open
Abstract
A very common and effective way for investigating future demographics is the study of stage structured models. The focus of this article is to propose a modified model to study the impact of population harvesting on their juvenile and adult stages, and analyze the dynamical properties from both qualitative and numerical perspective. It studies single species stage structured model with linear harvesting on juvenile group and Michaelis-Menten type harvesting on adult group. We exploit general ideas in mathematical modeling process to study the dynamical properties and their biological, ecological, and economic implications. It discusses that bi-stability phenomena may exist, global asymptotic stability at boundary equilibrium points and internal equilibrium points are investigated from construction of suitable Lyapunov and Dulac functions. It has been observed that a suitable linear harvesting on juvenile population can feasibly be carry out along with Michaelis-Menten type harvesting on adult population without endangering extinction of any group of population.
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Al-Shawba AA, Abdullah FA, Azmi A, Akbar MA, Nisar KS. Compatible extension of the (G'/G)-expansion approach for equations with conformable derivative. Heliyon 2023; 9:e15717. [PMID: 37206045 PMCID: PMC10189178 DOI: 10.1016/j.heliyon.2023.e15717] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/02/2022] [Revised: 04/15/2023] [Accepted: 04/19/2023] [Indexed: 05/21/2023] Open
Abstract
In this study, the compatible extensions of the (G'/G)-expansion approach and the generalized (G'/G)-expansion scheme are proposed to generate scores of radical closed-form solutions of nonlinear fractional evolution equations. The originality and improvements of the extensions are confirmed by their application to the fractional space-time paired Burgers equations. The application of the proposed extensions highlights their effectiveness by providing dissimilar solutions for assorted physical forms in nonlinear science. In order to explain some of the wave solutions geometrically, we represent them as two- and three-dimensional graphs. The results demonstrate that the techniques presented in this study are effective and straightforward ways to address a variety of equations in mathematical physics with conformable derivative.
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Affiliation(s)
| | - Farah A. Abdullah
- School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia
| | - Amirah Azmi
- School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia
| | - M. Ali Akbar
- Department of Applied Mathematics, University of Rajshahi, Bangladesh
| | - Kottakkaran Sooppy Nisar
- Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
- School of Technology, Woxsen University, Hyderabad, 502345, Telangana State, India
- Corresponding author. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia.
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10
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Ahmed SA, Saadeh R, Qazza A, Elzaki TM. Modified conformable double Laplace-Sumudu approach with applications. Heliyon 2023; 9:e15891. [PMID: 37168890 PMCID: PMC10165409 DOI: 10.1016/j.heliyon.2023.e15891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Revised: 04/16/2023] [Accepted: 04/25/2023] [Indexed: 05/13/2023] Open
Abstract
In this study, we combine two novel methods, the conformable double Laplace-Sumudu transform (CDLST) and the modified decomposition technique. We use the new approach called conformable double Laplace-Sumudu modified decomposition (CDLSMD) method, to solve some nonlinear fractional partial differential equations. We present the essential properties of the CDLST and produce new results. Furthermore, five interesting examples are discussed and analyzed to show the efficiency and applicability of the presented method. The results obtained show the strength of the proposed method in solving different types of problems.
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Affiliation(s)
- Shams A. Ahmed
- Department of Mathematic, Jouf University, Tubarjal, Saudi Arabia
- Department of Mathematic, University of Gezira, Sudan
| | - Rania Saadeh
- Department of Mathematic, Zarqa University, Zarqa, 13110, Jordan
- Corresponding author.
| | - Ahmad Qazza
- Department of Mathematic, Zarqa University, Zarqa, 13110, Jordan
| | - Tarig M. Elzaki
- Department of Mathematic, Alkamil, Jeddah, University of Jeddah, Kingdom of Saudi Arabia
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11
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Abdou MA, Ouahid L, Al Shahrani JS, Owyed S. Novel analytical techniques for HIV-1 infection of CD4 + T cells on fractional order in mathematical biology. INDIAN JOURNAL OF PHYSICS AND PROCEEDINGS OF THE INDIAN ASSOCIATION FOR THE CULTIVATION OF SCIENCE (2004) 2023; 97:2319-2325. [PMID: 37317689 PMCID: PMC10119542 DOI: 10.1007/s12648-022-02559-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: 04/25/2022] [Accepted: 12/07/2022] [Indexed: 06/16/2023]
Abstract
In this research, we present an analytical analysis of HIV-1 infection of CD4 + T cells with a conformable derivative model (CDM) in biology. An improved Υ ' / Υ -expansion method is used to investigate this model analytically to construct a new exact traveling wave solution, namely, exponential function, trigonometric function, and the hyperbolic function, which can be further studied for more (FNEE) fractional nonlinear evolution equations in biology. Also, we provide some graphs in 2D plots that demonstrate how accurate the results will be produced using analytical approaches.
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Affiliation(s)
- M. A. Abdou
- Physics Department, College of Science, University of Bisha, P.O. Box 344, Bisha, 61922 Kingdom of Saudi Arabia
| | - L. Ouahid
- Physics Department, College of Science, University of Bisha, P.O. Box 344, Bisha, 61922 Kingdom of Saudi Arabia
| | - J. S. Al Shahrani
- Mathematics Department, College of Science, University of Bisha, P.O. Box 344, Bisha, 61922 Kingdom of Saudi Arabia
| | - S. Owyed
- Mathematics Department, College of Science, University of Bisha, P.O. Box 344, Bisha, 61922 Kingdom of Saudi Arabia
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Alshehri A, Shah Z, Jan R. Mathematical study of the dynamics of lymphatic filariasis infection via fractional-calculus. EUROPEAN PHYSICAL JOURNAL PLUS 2023; 138:280. [PMID: 37008752 PMCID: PMC10040084 DOI: 10.1140/epjp/s13360-023-03881-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 03/09/2023] [Indexed: 06/19/2023]
Abstract
The infection of lymphatic filariasis (LF) is the primary cause of poverty and disability in individuals living with the disease. Many organizations globally are working toward mitigating the disease's impact and enhancing the quality of life of the affected patients. It is paramount to inspect the transmission pattern of this infection to provide effective interventions for its prevention and control. Here, we formulate an epidemic model for the progression process of LF with acute and chronic infection in the fractional framework. The basic concept of the novel Atangana-Baleanu operator is presented for the analysis of suggested system. We determine the basic reproduction number of the system via the approach of next-generation matrix and investigate the equilibria of the system for stability analysis. We have shown the impact of input factors on the outcomes of reproduction parameter with the help of partial rank correlation coefficient approach and visualize the most critical factors. To conceptualize the time series analysis of the suggested dynamics, we propose utilizing a numerical approach. The solution pathways of the system are illustrated to demonstrate how different settings affect the system. We demonstrate the dynamics of the infection numerically to educate the policy makers and health authorities about the mechanisms necessary for management and control.
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Affiliation(s)
- Ahmed Alshehri
- Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
| | - Zahir Shah
- Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat, 28420 KPK Pakistan
| | - Rashid Jan
- Department of Mathematics, University of Swabi, Swabi, 23561 Pakistan
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Kubra KT, Ali R. Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: a case study of Pakistan. MODELING EARTH SYSTEMS AND ENVIRONMENT 2023:1-18. [PMID: 37361699 PMCID: PMC10019432 DOI: 10.1007/s40808-023-01747-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2022] [Accepted: 02/11/2023] [Indexed: 03/18/2023]
Abstract
In this paper, a five-compartment model is used to explore the dynamics of the COVID-19 pandemic, taking the vaccination campaign into account. The present model consists of five components that lead to a system of five ordinary differential equations. In this paper, we examined the disease from the perspective of a fractal fractional derivative in the Caputo sense with a power law type kernal. The model is also fitted with real data for Pakistan between June 1, 2020, and March 8, 2021. The fundamental mathematical characteristics of the model have been investigated thoroughly. We have calculated the equilibrium points and the reproduction number for the model and obtained the feasible region for the system. The existence and stability criteria of the model have been validated using the Banach fixed point theory and the Picard successive approximation technique. Furthermore, we have conducted stability analysis for both the disease-free and endemic equilibrium states. On the basis of sensitivity analysis and the dynamics of the threshold parameter, we have estimated the effectiveness of vaccination and identified potential control strategies for the disease using the proposed model outbreaks. The stability of the concerned solution in Ulam-Hyers and Ulam-Hyers-Rassias sense is also investigated. For the proposed problem, some results regarding basic reproduction numbers and stability analysis for various parameters are represented graphically. Matlab software is used for numerical illustrations. Graphical representations are given for different fractional orders and for various parametric values.
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Affiliation(s)
- Khadija Tul Kubra
- Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000 Pakistan
| | - Rooh Ali
- Department of Mathematics, Government College University Faisalabad, Faisalabad, 38000 Pakistan
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14
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Dickson S, Padmasekaran S, Kumar P. Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination. INTERNATIONAL JOURNAL OF DYNAMICS AND CONTROL 2023; 11:1-17. [PMID: 37360278 PMCID: PMC9988609 DOI: 10.1007/s40435-023-01146-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2023] [Revised: 02/04/2023] [Accepted: 02/13/2023] [Indexed: 03/08/2023]
Abstract
In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.
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Affiliation(s)
- S. Dickson
- Mathematics, Periyar University, Periyar Palakalainagar, Salem, Tamilnadu 636011 India
| | - S. Padmasekaran
- Mathematics, Periyar University, Periyar Palakalainagar, Salem, Tamilnadu 636011 India
| | - Pushpendra Kumar
- Institute for the Future of Knowledge, University of Johannesburg, P.O. Box 524, Auckland Park, 2006 South Africa
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15
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Liu P, Ikram R, Khan A, Din A. The measles epidemic model assessment under real statistics: an application of stochastic optimal control theory. Comput Methods Biomech Biomed Engin 2023; 26:138-159. [PMID: 35297714 DOI: 10.1080/10255842.2022.2050222] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
A stochastic epidemic model with random noise transmission is taken into account, describing the dynamics of the measles viral infection. The basic reproductive number is calculated corresponding to the stochastic model. It is determined that, given initial positive data, the model has bounded, unique, and positive solution. Additionally, utilizing stochastic Lyapunov functional theory, we study the extinction of the disease. Stationary distribution and extinction of the infection are examined by providing sufficient conditions. We employed optimal control principles and examined stochastic control systems to regulate the transmission of the virus using environmental factors. Graphical representations have been offered for simplicity of comprehending in order to further verify the acquired analytical findings.
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Affiliation(s)
- Peijiang Liu
- School of Statistics and Mathematics, Guangdong University of Finance and Economics, Big data and Educational Statistics Application Laboratory, Guangzhou, PR China.,School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou, PR China
| | - Rukhsar Ikram
- Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhwa, Pakistan
| | - Amir Khan
- Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), Bangkok, Thailand
| | - Anwarud Din
- Department of Mathematics, Sun Yat-sen University, Guangzhou, PR China
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16
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Xia Y, Li Q, Jiao W, Lan Y. Dynamic mechanism of eliminating COVID-19 vaccine hesitancy through web search. Front Public Health 2023; 11:1018378. [PMID: 36794073 PMCID: PMC9922755 DOI: 10.3389/fpubh.2023.1018378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Accepted: 01/12/2023] [Indexed: 02/03/2023] Open
Abstract
This research focuses on the research problem of eliminating COVID-19 vaccine hesitancy through web search. A dynamic model of eliminating COVID-19 vaccine hesitancy through web search is constructed based on the Logistic model, the elimination degree is quantified, the elimination function is defined to analyze the dynamic elimination effect, and the model parameter estimation method is proposed. The numerical solution, process parameters, initial value parameters and stationary point parameters of the model are simulated, respectively, and the mechanism of elimination is deeply analyzed to determine the key time period. Based on the real data of web search and COVID-19 vaccination, data modeling is carried out from two aspects: full sample and segmented sample, and the rationality of the model is verified. On this basis, the model is used to carry out dynamic prediction and verified to have certain medium-term prediction ability. Through this research, the methods of eliminating vaccine hesitancy are enriched, and a new practical idea is provided for eliminating vaccine hesitancy. It also provides a method to predict the quantity of COVID-19 vaccination, provides theoretical guidance for dynamically adjusting the public health policy of the COVID-19, and can provide reference for the vaccination of other vaccines.
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Affiliation(s)
| | | | | | - Yuexin Lan
- Research Center of Network Public Opinion Governance, China People's Police University, Langfang, China
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17
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Khan MA, Alias N, Khan I, Salama FM, Eldin SM. A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation. Sci Rep 2023; 13:1549. [PMID: 36707653 PMCID: PMC9883294 DOI: 10.1038/s41598-023-28741-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2022] [Accepted: 01/24/2023] [Indexed: 01/29/2023] Open
Abstract
In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.
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Affiliation(s)
- Muhammad Asim Khan
- grid.410877.d0000 0001 2296 1505Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor Malaysia
| | - Norma Alias
- grid.410877.d0000 0001 2296 1505Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor Malaysia
| | - Ilyas Khan
- grid.449051.d0000 0004 0441 5633Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952 Saudi Arabia
| | - Fouad Mohammad Salama
- grid.412135.00000 0001 1091 0356Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
| | - Sayed M. Eldin
- grid.440865.b0000 0004 0377 3762Center of Research, Faculty of Engineering, Future University in Egypt, 11835 New Cairo, Egypt
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18
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Arif MS, Abodayeh K, Ejaz A. On the stability of the diffusive and non-diffusive predator-prey system with consuming resources and disease in prey species. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:5066-5093. [PMID: 36896536 DOI: 10.3934/mbe.2023235] [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: 06/18/2023]
Abstract
This research deals with formulating a multi-species eco-epidemiological mathematical model when the interacting species compete for the same food sources and the prey species have some infection. It is assumed that infection does not spread vertically. Infectious diseases severely affect the population dynamics of prey and predator. One of the most important factors in population dynamics is the movement of species in the habitat in search of resources or protection. The ecological influences of diffusion on the population density of both species are studied. The study also deals with the analysis of the effects of diffusion on the fixed points of the proposed model. The fixed points of the model are sorted out. The Lyapunov function is constructed for the proposed model. The fixed points of the proposed model are analyzed through the use of the Lyapunov stability criterion. It is proved that coexisting fixed points remain stable under the effects of self-diffusion, whereas, in the case of cross-diffusion, Turing instability exists conditionally. Moreover, a two-stage explicit numerical scheme is constructed, and the stability of the said scheme is found by using von Neumann stability analysis. Simulations are performed by using the constructed scheme to discuss the model's phase portraits and time-series solution. Many scenarios are discussed to display the present study's significance. The impacts of the transmission parameter 𝛾 and food resource f on the population density of species are presented in plots. It is verified that the availability of common food resources greatly influences the dynamics of such models. It is shown that all three classes, i.e., the predator, susceptible prey and infected prey, can coexist in the habitat, and this coexistence has a stable nature. Hence, in the realistic scenarios of predator-prey ecology, the results of the study show the importance of food availability for the interacting species.
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Affiliation(s)
- Muhammad Shoaib Arif
- Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
| | - Kamaleldin Abodayeh
- Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
| | - Asad Ejaz
- Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
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19
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Mukdasai K, Sabir Z, Raja MAZ, Singkibud P, Sadat R, Ali MR. A computational supervised neural network procedure for the fractional SIQ mathematical model. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2023; 232:535-546. [PMID: 36619194 PMCID: PMC9811870 DOI: 10.1140/epjs/s11734-022-00738-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Accepted: 11/28/2022] [Indexed: 05/28/2023]
Abstract
The purpose of the current work is to provide the numerical solutions of the fractional mathematical system of the susceptible, infected and quarantine (SIQ) system based on the lockdown effects of the coronavirus disease. These investigations provide more accurateness by using the fractional SIQ system. The investigations based on the nonlinear, integer and mathematical form of the SIQ model together with the effects of lockdown are also presented in this work. The impact of the lockdown is classified into the susceptible/infection/quarantine categories, which is based on the system of differential models. The fractional study is provided to find the accurate as well as realistic solutions of the SIQ model using the artificial intelligence (AI) performances along with the scale conjugate gradient (SCG) design, i.e., AI-SCG. The fractional-order derivatives have been used to solve three different cases of the nonlinear SIQ differential model. The statics to perform the numerical results of the fractional SIQ dynamical system are 7% for validation, 82% for training and 11% for testing. To observe the exactness of the AI-SCG procedure, the comparison of the numerical attained performances of the results is presented with the reference Adam solutions. For the validation, authentication, aptitude, consistency and validity of the AI-SCG solver, the computing numerical results have been provided based on the error histograms, state transition measures, correlation/regression values and mean square error. Supplementary Information The online version contains supplementary material available at 10.1140/epjs/s11734-022-00738-9.
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Affiliation(s)
- Kanit Mukdasai
- Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002 Thailand
| | - Zulqurnain Sabir
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
- Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002 Taiwan, ROC
| | - Peerapongpat Singkibud
- Department of Applied Mathematics and Statistics, Faculty of Science and Liberal Arts, Rajamangala University of Technology Isan, Nakhon Ratchasima, 30000 Thailand
| | - R. Sadat
- Department of Mathematics, Faculty of Engineering, Zagazig University, Zagazig, Egypt
| | - Mohamed R. Ali
- Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835 Egypt
- Basic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt
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20
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Lu Z, Chen Y, Yu Y, Ren G, Xu C, Ma W, Meng X. The effect mitigation measures for COVID-19 by a fractional-order SEIHRDP model with individuals migration. ISA TRANSACTIONS 2023; 132:582-597. [PMID: 36567189 PMCID: PMC9748852 DOI: 10.1016/j.isatra.2022.12.006] [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] [Received: 08/05/2020] [Revised: 11/22/2022] [Accepted: 12/10/2022] [Indexed: 06/13/2023]
Abstract
In this paper, the generalized SEIHRDP (susceptible-exposed-infective-hospitalized-recovered-death-insusceptible) fractional-order epidemic model is established with individual migration. Firstly, the global properties of the proposed system are studied. Particularly, the sensitivity of parameters to the basic reproduction number are analyzed both theoretically and numerically. Secondly, according to the real data in India and Brazil, it can all be concluded that the bilinear incidence rate has a better description of COVID-19 transmission. Meanwhile, multi-peak situation is considered in China, and it is shown that the proposed system can better predict the next peak. Finally, taking individual migration between Los Angeles and New York as an example, the spread of COVID-19 between cities can be effectively controlled by limiting individual movement, enhancing nucleic acid testing and reducing individual contact.
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Affiliation(s)
- Zhenzhen Lu
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, PR China
| | - YangQuan Chen
- Mechatronics, Embedded Systems and Automation Lab, University of California, Merced, CA 95343, USA
| | - Yongguang Yu
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, PR China.
| | - Guojian Ren
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, PR China
| | - Conghui Xu
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, PR China
| | - Weiyuan Ma
- School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730000, PR China
| | - Xiangyun Meng
- Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, PR China
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21
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Sabir Z, Raja MAZ, Alhazmi SE, Gupta M, Arbi A, Baba IA. Applications of artificial neural network to solve the nonlinear COVID-19 mathematical model based on the dynamics of SIQ. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2022. [DOI: 10.1080/16583655.2022.2119734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
Affiliation(s)
- Zulqurnain Sabir
- Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan
| | - Muhammad Asif Zahoor Raja
- Future Technology Research Center, National Yunlin University of Science and Technology, Douliou, Taiwan
| | - Sharifah E. Alhazmi
- Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
| | - Manoj Gupta
- Department of Electronics and Communication Engineering, JECRC University, Jaipur, Rajasthan, India
| | - Adnène Arbi
- Laboratory of Engineering Mathematics (LR01ES13), Tunisia Polytechnic School, University of Carthage, Tunis, Tunisia
- Department of Advanced Sciences and Technologies, National School of Advanced Sciences and Technologies of Borj Cedria, University of Carthage, Tunis, Tunisia
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22
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Islam MS, Hossain T, Islam MS, Saha BB. Dynamical behaviour of single photobioreactor with variable yield coefficient. Heliyon 2022; 8:e12187. [PMID: 36590535 PMCID: PMC9794888 DOI: 10.1016/j.heliyon.2022.e12187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Revised: 10/25/2022] [Accepted: 11/30/2022] [Indexed: 12/13/2022] Open
Abstract
Scholars studied chemostat model with variable yield coefficient and a growth rate in Monod expression for the existence of natural oscillations in a bioreactor. This article explores dynamical properties of a similar simple model, analytically and numerically, in which the growth rate is a modified Haldane expression. Study includes determination of analytic conditions for existence of steady-state washout and no washout solutions, optimization of the performance of the bioreactor when no washout solution occurs, stability of the optimized steady state solution, and the ranges of the parameter values for which natural oscillations (Hopf Bifurcation) take place. Investigation shows that it is possible to gain natural oscillations for much smaller values of the substrate concentration compared to Monod-based earlier works.
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Affiliation(s)
- Md. Shariful Islam
- Department of Mathematics, University of Dhaka, Bangladesh,Corresponding author.
| | - Touhid Hossain
- Department of Mathematics, University of Dhaka, Bangladesh
| | - Mir Shariful Islam
- Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan,International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan,Department of Oceanography, University of Dhaka, Bangladesh
| | - Bidyut Baran Saha
- Mechanical Engineering Department, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan,International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
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23
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El-Saka HAA, Obaya I, Lee S, Jang B. Fractional model for Middle East respiratory syndrome coronavirus on a complex heterogeneous network. Sci Rep 2022; 12:20706. [PMID: 36456670 PMCID: PMC9713123 DOI: 10.1038/s41598-022-24814-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2022] [Accepted: 11/21/2022] [Indexed: 12/05/2022] Open
Abstract
In this paper, we present a new fractional epidemiological model on a heterogeneous network to investigate Middle East respiratory syndrome (MERS-CoV), which is caused by a virus in the coronavirus family. We also consider the development of equations for the camel population, given that it is the primary animal source of the virus, as well as direct human interaction with this population. The model is configured in an SIS form for both the human population and the camel population. We study the equilibrium positions of the system and the conditions for the existence of each of them, as well as the local stability of each equilibrium position. Then, we provide some numerical examples that compare real data and numerical results.
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Affiliation(s)
- H. A. A. El-Saka
- grid.462079.e0000 0004 4699 2981Mathematics Department, Faculty of Science, Damietta University, New Damietta, 34517 Egypt
| | - Ibrahim Obaya
- Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt ,grid.10251.370000000103426662Department of Mathematics, Faculty of Science, Mansoura University, P.O. Box 64, Mansoura, 35516 Egypt
| | - Seyeon Lee
- grid.419553.f0000 0004 0500 6567Division of Industrial Mathematics, National Institute for Mathematical Sciences, Daejeon, 34047 Republic of Korea ,grid.42687.3f0000 0004 0381 814XDepartment of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919 Republic of Korea
| | - Bongsoo Jang
- grid.42687.3f0000 0004 0381 814XDepartment of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan, 44919 Republic of Korea
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24
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Addai E, Zhang L, Asamoah JKK, Preko AK, Arthur YD. Fractal-fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics. PARTIAL DIFFERENTIAL EQUATIONS IN APPLIED MATHEMATICS : A SPIN-OFF OF APPLIED MATHEMATICS LETTERS 2022; 6:100455. [PMID: 36277845 PMCID: PMC9576209 DOI: 10.1016/j.padiff.2022.100455] [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: 07/11/2022] [Revised: 10/07/2022] [Accepted: 10/11/2022] [Indexed: 11/08/2022]
Abstract
This paper proposes a new fractal-fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo-Fabrizio fractional order derivative. Caputo-Fabrizio fractal-fractional order is particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal-fractional order is varied.
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Affiliation(s)
- Emmanuel Addai
- College of Biomedical Engineering, Taiyuan University of Technology, Shanxi Taiyuan 030024, China,Department of Mathematics, Taiyuan University of Technology, Shanxi Taiyuan 030024, China,Corresponding authors
| | - Lingling Zhang
- Department of Mathematics, Taiyuan University of Technology, Shanxi Taiyuan 030024, China,Corresponding authors
| | - Joshua Kiddy K. Asamoah
- Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
| | - Ama Kyerewaa Preko
- College of Teacher Education, Zhejiang Normal University, Zhejiang Jinhua, 321004, China
| | - Yarhands Dissou Arthur
- Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana
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25
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Silva DM, Secchi AR. Recursive state and parameter estimation of COVID-19 circulating variants dynamics. Sci Rep 2022; 12:15879. [PMID: 36151226 PMCID: PMC9508243 DOI: 10.1038/s41598-022-18208-6] [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] [Received: 12/21/2021] [Accepted: 08/08/2022] [Indexed: 11/29/2022] Open
Abstract
COVID-19 pandemic response with non-pharmaceutical interventions is an intrinsic control problem. Governments weigh social distancing policies to avoid overload in the health system without significant economic impact. The mutability of the SARS-CoV-2 virus, vaccination coverage, and mobility restriction measures change epidemic dynamics over time. A model-based control strategy requires reliable predictions to be efficient on a long-term basis. In this paper, a SEIR-based model is proposed considering dynamic feedback estimation. State and parameter estimations are performed on state estimators using augmented states. Three methods were implemented: constrained extended Kalman filter (CEKF), CEKF and smoother (CEKF & S), and moving horizon estimator (MHE). The parameters estimation was based on vaccine efficacy studies regarding transmissibility, severity of the disease, and lethality. Social distancing was assumed as a measured disturbance calculated using Google mobility data. Data from six federative units from Brazil were used to evaluate the proposed strategy. State and parameter estimations were performed from 1 October 2020 to 1 July 2021, during which Zeta and Gamma variants emerged. Simulation results showed that lethality increased between 11 and 30% for Zeta mutations and between 44 and 107% for Gamma mutations. In addition, transmissibility increased between 10 and 37% for the Zeta variant and between 43 and 119% for the Gamma variant. Furthermore, parameter estimation indicated temporal underreporting changes in hospitalized and deceased individuals. Overall, the estimation strategy showed to be suitable for dynamic feedback as simulation results presented an efficient detection and dynamic characterization of circulating variants.
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Affiliation(s)
- Daniel Martins Silva
- Chemical Engineering Program/COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21941-942, Brazil.
| | - Argimiro Resende Secchi
- Chemical Engineering Program/COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, 21941-942, Brazil
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26
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El‐Sayed AMA, Arafa A, Hagag A. Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2022; 39:NUM22915. [PMID: 36245569 PMCID: PMC9537912 DOI: 10.1002/num.22915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 06/25/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. There is no known vaccination or medicine until our time because the unknown aspects of the virus are more significant than our theoretical and experimental knowledge. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the disease's possibility and severity. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the disease's progress. In this study, we propose using a fractional-order SEIARPQ model with the Caputo sense to model the coronavirus (COVID-19) pandemic, which has never been done before in the literature. The stability analysis, existence, uniqueness theorems, and numerical solutions of such a model are displayed. All results were numerically simulated using MATLAB programming. The current study supports the applicability and influence of fractional operators on real-world problems.
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Affiliation(s)
- Ahmed M. A. El‐Sayed
- Department of Mathematics, Faculty of ScienceAlexandria UniversityAlexandriaEgypt
| | - Anas Arafa
- Department of Mathematics, College of Science and ArtsQassim UniversityAl MithnabSaudi Arabia
- Department of Mathematics and Computer Science, Faculty of SciencePort Said UniversityPort SaidEgypt
| | - Ahmed Hagag
- Department of Basic Science, Faculty of EngineeringSinai UniversityIsmailiaEgypt
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27
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Qurashi MA, Rashid S, Jarad F. A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:12950-12980. [PMID: 36654030 DOI: 10.3934/mbe.2022605] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order δ with constant fractal-dimension ϖ, δ with changing ϖ, and δ with changing both δ and ϖ. White noise concentration has a significant impact on how bacterial infections are treated.
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Affiliation(s)
- Maysaa Al Qurashi
- Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia
- Department of Mathematics, Saudi Electronic University, Riyadh, Saudi Arabia
| | - Saima Rashid
- Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
| | - Fahd Jarad
- Department of Physics, Government College University, Faisalabad 38000, Pakistan
- Department of Mathmatics, Cankaya University, Ankara, Turkey
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
- Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
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28
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The New Versions of Hermite–Hadamard Inequalities for Pre-invex Fuzzy-Interval-Valued Mappings via Fuzzy Riemann Integrals. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-022-00127-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractIn this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings (F-I∙V-Ms), which we term fuzzy-interval Hermite–Hadamard inequalities and fuzzy-interval Hermite–Hadamard–Fejér inequalities. This fuzzy order relation is defined as the level of the fuzzy-interval space by the Kulisch–Miranker order relation. There are also some new exceptional instances mentioned. The theory proposed in this research is shown with practical examples that demonstrate its usefulness. This paper's approaches and methodologies might serve as a springboard for future study in this field.
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29
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Hong M, Ren F, Yang Y. Synchronization of Stochastic Multi-Weights Complex Networks with Lévy Noise and Markovian Switching. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10993-5] [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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30
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Sintunavarat W, Turab A. Mathematical analysis of an extended SEIR model of COVID-19 using the ABC-fractional operator. MATHEMATICS AND COMPUTERS IN SIMULATION 2022; 198:65-84. [PMID: 35194306 PMCID: PMC8851883 DOI: 10.1016/j.matcom.2022.02.009] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2021] [Revised: 01/31/2022] [Accepted: 02/07/2022] [Indexed: 05/31/2023]
Abstract
This paper aims to suggest a time-fractionalS P E P I P A I P S P H P R P model of the COVID-19 pandemic disease in the sense of the Atangana-Baleanu-Caputo operator. The proposed model consists of six compartments: susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized and recovered population. We prove the existence and uniqueness of solutions to the proposed model via fixed point theory. Furthermore, a stability analysis in the context of Ulam-Hyers and the generalized Ulam-Hyers criterion is also discussed. For the approximate solution of the suggested model, we use a well-known and efficient numerical technique, namely the Toufik-Atangana numerical scheme, which validates the importance of arbitrary order derivative ϑ and our obtained theoretical results. Finally, a concise analysis of the simulation is proposed to explain the spread of the infection in society.
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Affiliation(s)
- Wutiphol Sintunavarat
- Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand
| | - Ali Turab
- Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathum Thani 12120, Thailand
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31
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Partohaghighi M, Kumar V, Akgül A. Comparative Study of the Fractional-Order Crime System as a Social Epidemic of the USA Scenario. INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS 2022; 8:190. [PMID: 35875468 PMCID: PMC9288354 DOI: 10.1007/s40819-022-01399-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Accepted: 06/21/2022] [Indexed: 10/26/2022]
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32
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Multistability analysis of delayed recurrent neural networks with a class of piecewise nonlinear activation functions. Neural Netw 2022; 152:80-89. [DOI: 10.1016/j.neunet.2022.04.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 04/11/2022] [Accepted: 04/14/2022] [Indexed: 11/15/2022]
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33
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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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34
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Salama FM, Ali U, Ali A. Numerical Solution of Two-Dimensional Time Fractional Mobile/Immobile Equation Using Explicit Group Methods. INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS 2022; 8:188. [PMID: 35860425 PMCID: PMC9284974 DOI: 10.1007/s40819-022-01408-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Accepted: 07/04/2022] [Indexed: 11/27/2022]
Abstract
In this paper, we shall present the development of two explicit group schemes, namely, fractional explicit group (FEG) and modified fractional explicit group (MFEG) methods for solving the time fractional mobile/immobile equation in two space dimensions.
The presented methods are formulated based on two Crank-Nicolson (C-N) finite difference schemes established at two different grid spacings. The stability and convergence of order \documentclass[12pt]{minimal}
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\begin{document}$$O(\tau ^{2-\alpha }+h^2)$$\end{document}O(τ2-α+h2) are rigorously proven using Fourier analysis. Several numerical experiments are conducted to verify the efficiency of the proposed methods. Meanwhile, numerical results show that the FEG and MFEG algorithms are able to reduce the computational times and iterations effectively while preserving good accuracy in comparison to the C-N finite difference method.
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Affiliation(s)
- Fouad Mohammad Salama
- School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Gelugor, Penang Malaysia
| | - Umair Ali
- Department of Applied Mathematics and Statistics, Institute of Space Technology, 44000 Islamabad, Islamabad Pakistan
| | - Ajmal Ali
- Department of Mathematics, Virtual University of Pakistan, 54000 Lahore, Lahore Pakistan
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35
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Arshad S, Khalid S, Javed S, Amin N, Nawaz F. Modeling the impact of the vaccine on the COVID-19 epidemic transmission via fractional derivative. EUROPEAN PHYSICAL JOURNAL PLUS 2022; 137:802. [PMID: 35845824 PMCID: PMC9272881 DOI: 10.1140/epjp/s13360-022-02988-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/11/2022] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
To achieve the goal of ceasing the spread of COVID-19 entirely it is essential to understand the dynamical behavior of the proliferation of the virus at an intense level. Studying this disease simply based on experimental analysis is very time consuming and expensive. Mathematical modeling might play a worthy role in this regard. By incorporating the mathematical frameworks with the available disease data it will be beneficial and economical to understand the key factors involved in the spread of COVID-19. As there are many vaccines available globally at present, henceforth, by including the effect of vaccination into the model will also support to understand the visible influence of the vaccine on the spread of COVID-19 virus. There are several ways to mathematically formulate the effect of disease on the population like deterministic modeling, stochastic modeling or fractional order modeling etc. Fractional order derivative modeling is one of the fundamental methods to understand real-world problems and evaluate accurate situations. In this article, a fractional order epidemic model S p E p I p E r p R p D p Q p V p on the spread of COVID-19 is presented. S p E p I p E r p R p D p Q p V p consists of eight compartments of population namely susceptible, exposed, infective, recovered, the quarantine population, recovered-exposed, and dead population. The fractional order derivative is considered in the Caputo sense. For the prophecy and tenacity of the epidemic, we compute the reproduction number R 0 . Using fixed point theory, the existence and uniqueness of the solutions of fractional order derivative have been studied. Furthermore, we are using the generalized Adams-Bashforth-Moulton method, to obtain the approximate solution of the fractional-order COVID-19 model. Finally, numerical results and illustrative graphic simulation are given. Our results suggest that to reduce the number of cases of COVID-19 we should reduce the contact rate of the people if the population is not fully vaccinated. However, to tackle the issue of reducing the social distancing and lock down, which have very negative impact on the economy as well as on the mental health of the people, it is much better to increase the vaccine rate and get the whole nation to be fully vaccinated.
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Affiliation(s)
- Sadia Arshad
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000 Pakistan
| | - Sadia Khalid
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000 Pakistan
| | - Sana Javed
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000 Pakistan
| | - Naima Amin
- Department of Physics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000 Pakistan
| | - Fariha Nawaz
- Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, 54000 Pakistan
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36
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Teklu SW, Terefe BB. Mathematical modeling analysis on the dynamics of university students animosity towards mathematics with optimal control theory. Sci Rep 2022; 12:11578. [PMID: 35803995 PMCID: PMC9270411 DOI: 10.1038/s41598-022-15376-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 06/23/2022] [Indexed: 11/10/2022] Open
Abstract
Animosity towards mathematics is a very common worldwide problem and it is usually caused by wrong information, low participation, low challenge tolerance, falling further behind, being unemployed, and avoiding the advanced math classes needed for success in many careers. In this study, we have considered and formulated the new SEATS compartmental mathematical model with optimal control theory to analyze the dynamics of university students' animosity towards mathematics. We applied the next-generation matrix, Ruth-Hurwitz criteria, Lyapunov function, and Volterra-Lyapunov stable matrices to show local and global stability of equilibrium points of the model respectively. The study demonstrated that the animosity-free equilibrium point is both locally and globally asymptotically stable whenever the model basic reproduction number is less than unity, whereas the animosity-dominance equilibrium point is both locally and globally asymptotically stable when the model basic reproduction number is greater than unity. Finally, we applied numerical ode45 solvers using the Runge-Kutta method and we have carried out numerical simulations and shown that applying both prevention and treatment controls is the best strategy to minimize and possibly eradicate the animosity-infection in the community under consideration.
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Affiliation(s)
- Shewafera Wondimagegnhu Teklu
- Department of Mathematics, Collage of Natural and Computational Sciences, Debre Berhan University, Debre Berhan, Ethiopia.
| | - Birhanu Baye Terefe
- Department of Mathematics, Collage of Natural and Computational Sciences, Debre Berhan University, Debre Berhan, Ethiopia
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37
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Kong L, Duan M, Shi J, Hong J, Chang Z, Zhang Z. Compartmental structures used in modeling COVID-19: a scoping review. Infect Dis Poverty 2022; 11:72. [PMID: 35729655 PMCID: PMC9209832 DOI: 10.1186/s40249-022-01001-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2022] [Accepted: 06/10/2022] [Indexed: 12/23/2022] Open
Abstract
Background The coronavirus disease 2019 (COVID-19) epidemic, considered as the worst global public health event in nearly a century, has severely affected more than 200 countries and regions around the world. To effectively prevent and control the epidemic, researchers have widely employed dynamic models to predict and simulate the epidemic’s development, understand the spread rule, evaluate the effects of intervention measures, inform vaccination strategies, and assist in the formulation of prevention and control measures. In this review, we aimed to sort out the compartmental structures used in COVID-19 dynamic models and provide reference for the dynamic modeling for COVID-19 and other infectious diseases in the future. Main text A scoping review on the compartmental structures used in modeling COVID-19 was conducted. In this scoping review, 241 research articles published before May 14, 2021 were analyzed to better understand the model types and compartmental structures used in modeling COVID-19. Three types of dynamics models were analyzed: compartment models expanded based on susceptible-exposed-infected-recovered (SEIR) model, meta-population models, and agent-based models. The expanded compartments based on SEIR model are mainly according to the COVID-19 transmission characteristics, public health interventions, and age structure. The meta-population models and the agent-based models, as a trade-off for more complex model structures, basic susceptible-exposed-infected-recovered or simply expanded compartmental structures were generally adopted. Conclusion There has been a great deal of models to understand the spread of COVID-19, and to help prevention and control strategies. Researchers build compartments according to actual situation, research objectives and complexity of models used. As the COVID-19 epidemic remains uncertain and poses a major challenge to humans, researchers still need dynamic models as the main tool to predict dynamics, evaluate intervention effects, and provide scientific evidence for the development of prevention and control strategies. The compartmental structures reviewed in this study provide guidance for future modeling for COVID-19, and also offer recommendations for the dynamic modeling of other infectious diseases. Graphical Abstract
Supplementary Information The online version contains supplementary material available at 10.1186/s40249-022-01001-y.
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Affiliation(s)
- Lingcai Kong
- Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China
| | - Mengwei Duan
- Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China
| | - Jin Shi
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China
| | - Jie Hong
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China
| | - Zhaorui Chang
- Division of Infectious Disease, Key Laboratory of Surveillance and Early-Warning on Infectious Disease, Chinese Center for Disease Control and Prevention, Beijing, China
| | - Zhijie Zhang
- Department of Epidemiology and Health Statistics, Fudan University, Shanghai, 200032, China.
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38
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Kamrujjaman M, Keya KN, Bulut U, Islam MR, Mohebujjaman M. Spatio-temporal solutions of a diffusive directed dynamics model with harvesting. JOURNAL OF APPLIED MATHEMATICS & COMPUTING 2022; 69:603-630. [PMID: 35755609 PMCID: PMC9208362 DOI: 10.1007/s12190-022-01742-x] [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: 08/25/2021] [Revised: 04/14/2022] [Accepted: 04/19/2022] [Indexed: 06/15/2023]
Abstract
UNLABELLED The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with harvesting effect in a heterogeneous environment, where all functions are spatially distributed in time series. The dispersal dynamics describe the growth of the species, which is distributed according to the resource function with no-flux boundary conditions. The analysis investigates the existence, positivity, persistence, and stability of solutions for both time-periodic and spatial functions. The carrying capacity and the distribution function are either arbitrary or proportional. It is observed that if harvesting exceeds the growth rate, then eventually, the population drops down to extinction. Several numerical examples are considered to support the theoretical results. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s12190-022-01742-x.
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Affiliation(s)
- Md. Kamrujjaman
- Department of Mathematics, University of Dhaka, Dhaka, 1000 Bangladesh
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta T2N 1N4 Canada
| | - Kamrun Nahar Keya
- Department of Mathematics and Statistics, Texas Tech University, Lubbock, 79410 Texas USA
| | - Ummugul Bulut
- Department of Mathematical, Physical, and Engineering Sciences, Texas A &M University-San Antonio, San Antonio, 78224 Texas USA
| | - Md Rafiul Islam
- Department of Mathematics, Iowa State University, Ames, 50011 Iowa USA
| | - Muhammad Mohebujjaman
- Department of Mathematics and Physics, Texas A &M International University, Laredo, Texas 78041 USA
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39
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Cao Q. Positive almost periodicity on a n-species food chain system incorporating time-varying delays and polluted environments. J EXP THEOR ARTIF IN 2022. [DOI: 10.1080/0952813x.2022.2080279] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Qian Cao
- College of Mathematics and Physics, Hunan University of Arts and Science, Changde, Hunan, P. R. China
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40
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Yazgan R, Hajjaji S, Chérif F. Weighted Pseudo Almost-Automorphic Solutions of Quaternion-Valued RNNs With Mixed Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10890-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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41
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Ali HM, Ali AS, Mahmoud M, Abdel-Aty AH. Analytical approximate solutions of fractional nonlinear DrinfeldSokolovWilson model using modified Mittag-Leffler function. JOURNAL OF OCEAN ENGINEERING AND SCIENCE 2022. [DOI: 10.1016/j.joes.2022.06.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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42
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Wang B, Yang L, Han Y. Intervention strategies for epidemic spreading on bipartite metapopulation networks. Phys Rev E 2022; 105:064305. [PMID: 35854601 DOI: 10.1103/physreve.105.064305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2021] [Accepted: 05/11/2022] [Indexed: 06/15/2023]
Abstract
Intervention strategies are of great significance for controlling large-scale outbreaks of epidemics. Since the spread of epidemic depends largely on the movement of individuals and the heterogeneity of the network structure, understanding potential factors that affect the epidemic is fundamental for the design of reasonable intervention strategies to suppress the epidemic. So far, most of previous studies mainly consider intervention strategies on the network composed of a single type of locations, while ignoring the movement behavior of individuals to and from locations that are composed of different types, i.e., residences and public places, which often presents heterogeneous structure. In addition, the transmission rate in public places with different population flows is heterogeneous. Inspired by the above observation, we build a bipartite metapopulation network model and propose intervention strategies based on the importance of public places. With the Markovian Chain approach, we derive the epidemic threshold under intervention strategies. Experimental results show that, compared with the uniform intervention to residences or public places, nonuniform intervention to public places is more effective for suppressing the epidemic with an increased epidemic threshold. Specifically, interventions to public places with large degree can further suppress the epidemic. Our study opens a new path for understanding the spatial epidemic spread and provides guidance for the design of intervention strategies for epidemics in the future.
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Affiliation(s)
- Bing Wang
- School of Computer Engineering and Science, Shanghai University, Shanghai 200444, People's Republic of China
| | - Lizhen Yang
- School of Computer Engineering and Science, Shanghai University, Shanghai 200444, People's Republic of China
| | - Yuexing Han
- School of Computer Engineering and Science, Shanghai University, Shanghai 200444, People's Republic of China
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43
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Aouiti C, Jallouli H, Zhu Q, Huang T, Shi K. New Results on Finite/Fixed-Time Stabilization of Stochastic Second-Order Neutral-Type Neural Networks with Mixed Delays. Neural Process Lett 2022. [DOI: 10.1007/s11063-022-10868-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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44
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Ibrahim RW, Baleanu D. Convoluted fractional differentials of various forms utilizing the generalized Raina's function description with applications. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2022. [DOI: 10.1080/16583655.2022.2070836] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Rabha W. Ibrahim
- The Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, USA
| | - Dumitru Baleanu
- Department of Mathematics, Cankaya University, Ankara, Turkey
- Institute of Space Sciences, Magurele-Bucharest, Romania
- Department of Medical Research, China Medical University, Taichung, Taiwan
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45
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Khan MB, Zaini HG, Santos-García G, Mohammed PO, Soliman MS. Riemann–Liouville Fractional Integral Inequalities for Generalized Harmonically Convex Fuzzy-Interval-Valued Functions. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-022-00081-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractThe framework of fuzzy-interval-valued functions (FIVFs) is a generalization of interval-valued functions (IVF) and single-valued functions. To discuss convexity with these kinds of functions, in this article, we introduce and investigate the harmonically $$\mathsf{h}$$
h
-convexity for FIVFs through fuzzy-order relation (FOR). Using this class of harmonically $$\mathsf{h}$$
h
-convex FIVFs ($$\mathcal{H}-\mathsf{h}$$
H
-
h
-convex FIVFs), we prove some Hermite–Hadamard (H⋅H) and Hermite–Hadamard–Fejér (H⋅H Fejér) type inequalities via fuzzy interval Riemann–Liouville fractional integral (FI Riemann–Liouville fractional integral). The concepts and techniques of this paper are refinements and generalizations of many results which are proved in the literature.
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46
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Khan H, Ahmad F, Tunç O, Idrees M. On fractal-fractional Covid-19 mathematical model. CHAOS, SOLITONS, AND FRACTALS 2022; 157:111937. [PMID: 36249286 PMCID: PMC9552777 DOI: 10.1016/j.chaos.2022.111937] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Revised: 02/18/2022] [Accepted: 02/19/2022] [Indexed: 05/31/2023]
Abstract
In this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.
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Affiliation(s)
- Hasib Khan
- Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, Pakistan
| | - Farooq Ahmad
- Department of Mathematics, Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan
| | - Osman Tunç
- Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Campus, 65080, Van-Turkey
| | - Muhammad Idrees
- Department of Mathematics, Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan
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47
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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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48
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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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49
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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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50
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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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