Advances in Epidemiological Modeling and Control of Viruses

1st Edition - January 6, 2023
Editors: Hemen Dutta, Khalid Hattaf
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 9 5 5 7 - 3
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 9 5 5 8 - 0

Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strate… Read more

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Advances in Epidemiological Modeling and Control of Viruses covers recent and advanced research works in the field of epidemiological modeling, with special emphasis on new strategies to control the occurrence and reoccurrence of viruses. The models included in this book can be used to study the dynamics of different viruses, searching for control measures, and epidemic models under various effects and environments. This book covers different models and methods of modeling, including data-driven approaches. The authors and editors are experienced researchers, and each chapter has been designed to provide readers with leading-edge information on topics discussed.

Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
1: Global dynamics of a delayed reaction-diffusion viral infection in a cellular environment
Abstract
Acknowledgements
1.1. Introduction
1.2. Global convergence to the homogeneous solution
1.3. Numerical simulations
1.4. Spatiotemporal pattern formation
1.5. Conclusion and open problems
References
2: Hepatitis B virus transmission via epidemic model
Abstract
2.1. Introduction
2.2. Model formulation
2.3. Stability analysis
2.4. Simulation and concluding remarks
References
3: Global dynamics of an HCV model with full logistic terms and the host immune system
Abstract
Acknowledgements
3.1. Introduction
3.2. Previous works
3.3. Mathematical preliminaries
3.4. Modelling virus-immune system interaction with full logistic terms in both uninfected and infected cells
3.5. Analysis of the model
3.6. Numerical simulations
3.7. Conclusion and discussion
References
4: On a Novel SVEIRS Markov chain epidemic model with multiple discrete delays and infection rates: modeling and sensitivity analysis to determine vaccination effects
Abstract
4.1. Introduction
4.2. Description of the SVEIRS epidemic and the delays in the disease dynamics
4.3. Discretization of time and decomposition of the SVEIRS population over time
4.4. The SVEIRS stochastic process
4.5. Some special SVEIRS epidemic models
4.6. Numerical study: some prototype SVEIRS epidemic models and sensitivity analysis to determine the effects of infection and vaccination
4.7. Conclusion
References
5: Hopf bifurcation in an SIR epidemic model with psychological effect and distributed time delay
Abstract
Acknowledgements
5.1. Introduction
5.2. Model
5.3. Direction of bifurcation and stability of periodic solution
5.4. Example: a truncated exponential distribution
5.5. Numerical simulation
5.6. Discussion
Appendix 5.A. Matlab code for Fig. 5.8(b)
References
6: Modeling of the effects of media in the course of vaccination of rotavirus
Abstract
6.1. Introduction
6.2. Epidemic modeling
6.3. Existence of equilibria of system ϒ1
6.4. Stability of the equilibria
6.5. Optimal control problem
6.6. Efficacy analysis
6.7. Numerical simulations
6.8. Discussion
References
7: Mathematical models of early stage Covid-19 transmission in Sri Lanka
Abstract
7.1. Introduction
7.2. Mathematical model to estimate initial parameters
7.3. Mathematical models with heterogeneity of cases
7.4. Mathematical model with imported cases
7.5. Conclusion
References
8: Global stability of a diffusive HTLV-I infection model with mitosis and CTL immune response
Abstract
List of abbreviations
8.1. Introduction
8.2. Model formulation
8.3. Well-posedness of solutions
8.4. Steady state analysis
8.5. Global stability analysis
8.6. Numerical simulations
8.7. Conclusion and discussion
References
9: Mathematical tools and their applications in dengue epidemic data analytics
Abstract
9.1. Introduction
9.2. Fourier transformation
9.3. Wavelet analysis
9.4. Wavelet analysis in epidemiology and dengue
9.5. Conclusion
References
10: Covid-19 pandemic model: a graph theoretical perspective
Abstract
10.1. Introduction
10.2. Preliminaries
10.3. A survey of mathematical models on diseases
10.4. SEIRD model on Covid-19
10.5. Some results
10.6. Conclusion and recommendation
References
11: Towards nonmanifest chaos and order in biological structures by means of the multifractal paradigm
Abstract
11.1. Introduction
11.2. Mathematical model
11.3. Conclusions
References
12: Global stability of epidemic models under discontinuous treatment strategy
Abstract
12.1. Impact of discontinuous treatments on disease dynamics in an SIR epidemic model
12.2. Global stability of an SIS epidemic model with discontinuous treatment strategy
12.3. Global stability of an SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment strategy
References
Index

Hemen Dutta

Dr. Hemen Dutta PhD is a Professor at Gauhati University, India. He also served three other higher learning academic institutions in different capacities prior to joining the Gauhati University. His current research interests are in the areas of nonlinear analysis and mathematical modeling. He is a regular and guest editor of several international indexed journals. He has published 25 books, including Mathematical Modelling and Analysis of Infectious Diseases, New Trends in Applied Analysis and Computational Mathematics, Current Trends in Mathematical Analysis and Its Interdisciplinary Applications from Springer, Concise Introduction to Basic Real Analysis, Topics in Contemporary Mathematical Analysis and Applications, and Mathematical Methods in Engineering and Applied Sciences from CRC Press, and Fractional Order Analysis: Theory, Methods and Applications from Wiley, among others. Dr. Dutta is also an honorary research affiliate and speaker for several international and national events.

Affiliations and expertise

Professor, Department of Mathematics, Gauhati University, India

Khalid Hattaf

Khalid Hattaf is currently an Associate Professor at Centre Régional des Métiers de l'Education et de la Formation (CRMEF), Casablanca, Morocco. He received his Master in Numerical Analysis, Computers and Signal Processing from Mohammed I University, Oujda, Morocco. He obtained his Ph.D. in Mathematics and Computer Science from Hassan II University of Casablanca, Morocco. His research interests include mathematical modeling in virology, epidemiology, ecology and economics. He is also interested in mathematics education. He ranked among the Top 15 Moroccan researchers in Mathematics for the periods 2009-2013 and 2012-2016. Also, he has published one book, 10 book chapters and more than 100 papers in respected international journals. Recently, he has been featured among the top 2 percent of the world's most cited scientists in various disciplines, according to the American Stanford University ranking.

Affiliations and expertise

Associate Professor, Centre Régional des Métiers de l'Education et de la Formation (CRMEF), Casablanca, Morocco

Life Sciences

Physical Sciences & Engineering

Social Sciences & Humanities

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