| Description |
1 online resource (337 p.) |
| Series |
River Publishers series in communication and networking |
| Contents |
Preface xi List of Figures xv List of Tables xxiii List of Contributors xxv List of Abbreviations xxix 1 Mathematical Modelling of COVID-19 Dynamics with Reinfection Using Fractional Order 1 1.1 Introduction 2 1.2 SEIQR Model for COVID-19 Spread 3 1.3 Fractional-Order SEIQR Model 8 1.4 Existence of Equilibrium Points 8 1.5 Stability of the System 10 1.6 Optimal Control Analysis 11 1.7 Numerical Simulations 13 1.7.1 Impact of Reinfected Population Rate (m) 13 1.7.2 Bifurcation Analysis 14 1.8 Conclusion 20 2 Stability Analysis of Caputo⁰́₃Fabrizio Fractional-order Epidemic Model of a Novel Coronavirus (COVID-19) 25 2.1 Introduction 26 2.2 Preliminaries 27 2.3 Model Formulation 28 2.4 Existence Criteria of Caputo⁰́₃Fabrizio Model by Picard Approximation 30 2.5 Stability Analysis by the Equilibrium States 34 2.6 Numerical Computations by Data Values 36 2.6.1 COVID-19 Model with Vaccination 42 2.7 Conclusion 47 3 Impact of Vaccination on COVID-19 to Control its Spread: A Case Study of India 51 3.1 Introduction 52 3.2 Mathematical Modelling 54 3.2.1 Equilibrium Points 57 3.3 Stability 59 3.4 Numerical Simulation 60 3.5 Conclusion 62 4 A Computational Approach for Regulation of Biomedical Waste Expulsion in a Novel Coronavirus Pandemic 65 4.1 Introduction 66 4.2 Literature Review 68 4.2.1 BMW disposal 68 4.2.1.1 Mechanical processes 69 4.2.1.2 Thermal processes 69 4.2.1.3 Chemical processes 73 4.2.1.4 Irradiation processes 73 4.2.1.5 Biological processes 73 4.3 Latest Methodology 73 4.4 Emission New Rules 75 4.5 Effects on Nature 76 4.6 Conclusion 77 5 Solution for Fractional-order Pneumonia⁰́₃COVID-19 Co-infection 83 5.1 Introduction 84 5.2 Formulation of Fractional Order Mathematical Model 85 5.2.1 Preliminaries of fractional order in Caputo sense 85 5.2.2 Existence of positivity and boundedness of solutions 89 5.2.3 Equilibrium points and basic reproduction number 91 5.3 Stability Analysis 92 5.4 Numerical Simulation 96 5.5 Conclusion 104 6 Optimal Control to Curtail the Spread of COVID-19 through Social Gatherings: A Mathematical Model 109 6.1 Introduction 110 6.2 Mathematical Model 111 6.3 Optimal Control 115 6.4 Numerical Simulation 118 6.5 Conclusion 122 7 Effectiveness of a Booster Dose of COVID-19 Vaccine 125 7.1 Introduction 125 7.2 Mathematical Model 127 7.2.1 Equilibrium point 129 7.2.2 Basic reproduction number 133 7.3 Stability Analysis 135 7.3.1 Local stability 135 7.3.2 Global stability 138 7.4 Numerical Simulation 140 7.5 Conclusion 146 8 Impact of Post-COVID-19 Pandemic on Quality Education among School and College Student 151 8.1 Introduction 152 8.2 Research Gap 153 8.3 Research Objectives 153 8.4 Research Hypothesis 154 8.5 Methodology 154 8.6 Limitations of the Study 163 8.7 Future Prospective of Research 164 8.8 Conclusion 164 9 A Mathematical Model for the Dynamics of the Violence Epidemic Spreading due to Misinformation 167 9.1 Introduction 168 9.2 Previous Studies 169 9.3 An Overview on Misinformation 171 9.3.1 Intention is not creating violence 172 9.3.2 Intention is to create violence 172 9.4 Mathematical Model of Spreading Misinformation 172 9.4.1 Equilibrium analysis 176 9.4.2 Stability analysis 176 9.4.2.1 Stability at E0 (S⁸́₇,E⁸́₇, C⁸́₇, I⁸́₇, Z⁸́₇) 176 9.4.2.2 Stability at E⁸́₇ (S⁸́₇,E⁸́₇, C⁸́₇, I⁸́₇, Z⁸́₇) 177 9.4.3 Basic reproduction bumber 178 9.5 Numerical Simulations 181 9.5.1 State Trajectories of Intentional Spread 184 9.5.2 State Trajectories for Spread with Other Intentions 186 9.5.3 Bifurcation analysis 187 9.6 Results and Discussion 189 9.7 Conclusion 192 10 Diseased Predator⁰́₃Prey Model Incorporating Herd Behaviour in Prey: A Study Under an Alternative Food Source Scenario 197 10.1 Introduction 198 10.2 Mathematical Model Formulation 199 10.3 Qualitative Analysis of the Model 200 10.3.1 Existence of points of equilibria 201 10.3.2 Stability analysis 202 10.3.2.1 The prey-only equilibrium 202 10.3.2.2 Dynamical behavior near the trivial equilibrium point 203 10.3.2.3 Disease-free equilibrium point 204 10.3.2.4 Endemic equilibrium point 205 10.3.3 Transversality condition for Hopf bifurcation 206 10.3.4 Global stability analysis 207 10.4 Numerical Simulation 208 10.5 Conclusion 211 11 A COVID-19-related Atangana⁰́₃Baleanu Fractional Model for Unemployed Youths 215 11.1 Introduction 216 11.2 The Conceptual Model 217 11.3 Mathematical Analysis 221 11.3.1 Existence of solution 222 11.3.2 Uniqueness of solution 226 11.3.3 Positive solution 226 11.3.4 Equilibrium points 227 11.3.5 Stability analysis 227 11.4 Derivation of the Numerical Method 228 11.5 Numerical Results and Discussion 233 11.6 Conclusion 236 12 A Fractional-order SVIR Model with Two Infection Classes for COVID-19 in India 241 12.1 Introduction 242 12.2 Preliminaries 243 12.3 Formulation of Model 245 12.3.1 Existence and uniqueness of the solution 248 12.3.2 Equilibrium points 249 12.4 Calculation of Basic Reproduction Number 250 12.5 Stability 251 12.5.1 251 12.5.2 Local stability of the endemic equilibrium point E1 253 12.6 Memory Trace and Hereditary Trait 257 12.7 Numerical Simulation 259 12.8 Conclusion 262 13 Forecasting of a COVID-19 Model using LSTM 267 13.1 Introduction 268 13.2 Methodology 274 13.2.1 Long short-term memory (LSTM) 274 13.2.2 How does LSTM work 275 13.3 Data Preparation 278 13.4 The Proposed LSTM Model 279 13.5 Root Mean Square Error (RMSE) 279 13.6 Experimental Results 281 13.7 Conclusions and Future Work 281 14 Simulation of COVID-19 Cases in India using AR and ANN Models 287 14.1 Introduction 288 14.2 Literature 289 14.3 Data 291 14.4 Methodology 293 14.5 Results and Discussion 298 14.6 Conclusions 301 Index 359 About the Editors 361 |
| Summary |
This book addresses issues during the Covid phase and post-Covid phase through mathematical modeling |
| Notes |
Description based upon print version of record |
|
Dr. Mandeep Mittal started his career in the education industry in 2000 with the Amity Group. Currently, he is working as Head and Associate Professor in the Department of Mathematics, Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida. He earned his post doctorate from Hanyang University, South Korea, 2016, Ph.D. (2012) from the University of Delhi, India, and postgraduation in Applied Mathematics from IIT-Roorkee, India (2000). He has published more than 70 research papers in International Journals and International conferences. He authored one book with Narosa Publication on C language and edited five research books with IGI Global and Springer. He is a series editor of Inventory Optimization, Springer Singapore Pvt. Ltd. He was awarded Best Faculty Award by the Amity School of Engineering and Technology, New Delhi for the year 2016-2017. He guided four Ph.D. scholars, and six students working with him in the area inventory control and management. He also served as Dean of Students Activities at Amity School of Engineering and Technology, Delhi, for nine years, and worked as Head, Department of Mathematics in the same institute for one year. He is a member of editorial boards of Revista Investigacion Operacional, Journal of Control and Systems Engineering and Journal of Advances in Management Sciences and Information Systems. He has actively participated as a core member of organizing committees of international conferences in India and outside India. Professor Nita H. Shah received her Ph.D. in Statistics from Gujarat University in 1994. She is Head of Department of the Department of Mathematics in Gujarat University, India. She is Postdoctoral Visiting Research Fellow of the University of New Brunswick, Canada. Professor Nita's research interests include inventory modeling in supply chain, robotic modeling, mathematical modeling of infectious diseases, image processing, dynamical systems and its applications. She has completed 3 UGC sponsored projects and has published 13 monographs, 5 textbooks and 475+ peer-reviewed research papers. Five edited books have been prepared for IGI Global and Springer with co-editor Dr. Mandeep Mittal. Her papers are published in high impact Elsevier, Inderscience, Springer, and Taylor and Francis journals. Google Scholar, shows citations of over 3795 and the maximum number of citations for a single paper is over 207. The H-index is 27 up to August 16, 2022 and i-10 index is 97. She has guided 28 Ph.D. students and 15 M.Phil. students. She has travelled in USA, Singapore, Canada, South Africa, Malaysia and Indonesia to give talks |
| Subject |
COVID-19 (Disease) -- Transmission -- Mathematical models
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COMPUTERS / Data Modeling & Design
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MEDICAL / Infectious Diseases
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| Form |
Electronic book
|
| Author |
Mittal, Mandeep, 1978- editor.
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Shah, Nita H., editor.
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| ISBN |
9781003807124 |
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1003807127 |
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9781032623146 |
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1032623144 |
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9781003807155 |
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1003807151 |
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