Mathematical Analysis of Infectious Diseases

1st Edition - June 1, 2022
Editors: Praveen Agarwal, Juan J. Nieto, Delfim F.M. Torres
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 0 5 0 4 - 6
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 0 4 5 8 - 2

Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases. Epidemic mathematical modeling and analysis is import… Read more

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Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases. Epidemic mathematical modeling and analysis is important, not only to understand disease progression, but also to provide predictions about the evolution of disease. One of the main focuses of the book is the transmission dynamics of the infectious diseases like COVID-19 and the intervention strategies. It also discusses optimal control strategies like vaccination and plasma transfusion and their potential effectiveness on infections using compartmental and mathematical models in epidemiology like SI, SIR, SICA, and SEIR.

The book also covers topics like: biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of infectious diseases, mathematical modeling and analysis of diagnosis rate effects and prediction of viruses, data-driven graphical analysis of epidemic trends, dynamic simulation and scenario analysis of the spread of diseases, and the systematic review of the mathematical modeling of infectious disease like coronaviruses.

Cover image
Title page
Table of Contents
Copyright
Contributors
Preface
Chapter 1: Spatiotemporal dynamics of the first wave of the COVID-19 epidemic in Brazil
Abstract
1.1. Introduction
1.2. Materials and methods
1.3. Results
1.4. Discussion
1.5. Final remarks
References
Chapter 2: Transport and optimal control of vaccination dynamics for COVID-19
Abstract
Acknowledgements
2.1. Introduction
2.2. Vaccine transport model
2.3. Initial mathematical model for COVID-19
2.4. Mathematical model for COVID-19 with vaccination
2.5. Optimal control
2.6. Numerical results
2.7. Conclusion
References
Chapter 3: COVID-19's pandemic: a new way of thinking through linear combinations of proportions
Abstract
Acknowledgements
3.1. Introduction
3.2. Estimation of linear combinations of proportions
3.3. Material and methods
3.4. Results and discussion
3.5. Conclusion
References
Chapter 4: Stochastic SICA epidemic model with jump Lévy processes
Abstract
Acknowledgements
4.1. Introduction
4.2. Existence and uniqueness of a global positive solution
4.3. Extinction
4.4. Persistence in the mean
4.5. Numerical results
4.6. Conclusion
References
Chapter 5: Examining the correlation between the weather conditions and COVID-19 pandemic in Galicia
Abstract
5.1. Introduction
5.2. Fuzzy sets
5.3. Results
5.4. Conclusions
References
Chapter 6: A fractional-order malaria model with temporary immunity
Abstract
6.1. Introduction
6.2. Preliminaries on fractional calculus
6.3. Model description
6.4. Basic properties of the ABC malaria model
6.5. The analysis
6.6. Numerical solution of fractional malaria model
6.7. Discussion
6.8. Conclusion
References
Chapter 7: Parameter identification in epidemiological models
Abstract
Acknowledgements
7.1. Introduction
7.2. SEIJR models for closed systems
7.3. Uncertainty quantification by Bayesian techniques
7.4. Effect of nonpharmaceutical actions
7.5. SEIJR model including migration
7.6. Optimization approach to control
7.7. Conclusions
References
Chapter 8: Lyapunov functions and stability analysis of fractional-order systems
Abstract
Acknowledgements
8.1. Introduction
8.2. Preliminaries
8.3. Useful fractional derivative estimates
8.4. An application
8.5. Conclusion
References
Chapter 9: Some key concepts of mathematical epidemiology
Abstract
Acknowledgement
9.1. Introduction
9.2. A short historical introduction
9.3. Equilibria, the basic reproduction number and final size relation
9.4. Sojourn time, delay, and incidence forms
9.5. Numerical simulations
9.6. Herpes modeling
9.7. Conclusion
References
Chapter 10: Analytical solutions and parameter estimation of the SIR epidemic model
Abstract
10.1. Introduction
10.2. The SIR model
10.3. Second-order systems equivalent to SIR
10.4. Indeterminate analytical solution
10.5. Inverse parametric solution
10.6. Analysis of the incidence variable
10.7. Asymptotic analysis of the SIR model
10.8. Numerical approximation
10.9. Cast study I: application to influenza A
10.10. Cast study II: application to COVID-19
10.11. Discussion and conclusions
Appendix 10.A. The Lambert W function and related integrals
Appendix 10.B. Differential fields
References
Chapter 11: Global stability of a diffusive SEIR epidemic model with distributed delay
Abstract
Acknowledgement
11.1. Introduction
11.2. Mathematical model
11.3. Analysis of the model
11.4. Numerical simulations
11.5. Concluding remarks
References
Chapter 12: Application of fractional order differential equations in modeling viral disease transmission
Abstract
12.1. Introduction
12.2. Preliminaries
12.3. Mathematical model of the AH1N1/09 influenza transmission
12.4. Equilibrium points
12.5. Existence of solution
12.6. Optimal control approach
12.7. Numerical results
12.8. Conclusion
References
Chapter 13: Role of immune effector responses during HCV infection: a mathematical study
Abstract
13.1. Introduction
13.2. The mathematical model
13.3. Optimal control problem
13.4. Numerical simulations
13.5. Discussion and conclusion
References
Chapter 14: Modeling the impact of isolation during an outbreak of Ebola virus
Abstract
14.1. Introduction
14.2. Mathematical model
14.3. Mathematical analysis of the model
14.4. Numerical simulation
14.5. Optimal control of the spread of the virus
14.6. Conclusions
References
Chapter 15: Application of the stochastic arithmetic to validate the results of nonlinear fractional model of HIV infection for CD8+T-cells
Abstract
15.1. Introduction
15.2. Preliminaries
15.3. Nonlinear model of HIV infection for CD8+T cells
15.4. Existence of solution
15.5. Special solution via iteration approach
15.6. Application of the HATM to solve the model
15.7. Control of accuracy by the CESTAC method and the CADNA library
15.8. Numerical results
15.9. Conclusion
References
Chapter 16: Existence of solutions of modified fractional integral equation models for endemic infectious diseases
Abstract
Acknowledgements
16.1. Introduction and preliminaries
16.2. Fixed point theorems
16.3. Coupled fixed point theorems
16.4. Application
References
Chapter 17: Numerical solution of a fractional epidemic model via general Lagrange scaling functions with bibliometric analysis
Abstract
17.1. Introduction
17.2. Preliminaries
17.3. GLSF Riemann-Liouville pseudo-operational matrix
17.4. Computational method
17.5. Error analysis
17.6. Numerical results and discussion
17.7. Conclusion
References
Index

Praveen Agarwal

Dr. Praveen Agarwal is currently a Full Professor and VicePrincipal at Anand International College of Engineering, Jaipur, India. Dr. P. Agarwal was born in Jaipur (India) on August 18, 1979. After completing his schooling, he earned his Master’s degree from Rajasthan University in 2000. In 2006, he earned his Ph. D. (Mathematics) at the Malviya National Institute of Technology (MNIT) in Jaipur, India, one of the highest-ranking universities in India. Recently, Prof. Agarwal is listed as the World's Top 2% Scientist 2020 and 21, Released by Stanford University Dr. Agarwal has been actively involved in research as well as pedagogical activities for the last 20 years. His major research interests include Special Functions, Fractional Calculus, Numerical Analysis, Differential and Difference Equations, Inequalities, and Fixed Point Theorems. He is an excellent scholar, dedicated teacher, and prolific researcher. He has published 9 research monographs and edited volumes and more than 250 publications (with almost 100 mathematicians all over the world) in prestigious national and international mathematics journals. Dr. Agarwal worked previously either as a regular faculty or as a visiting professor and scientist in universities in several countries, including India, Germany, Turkey, South Korea, the UK, Russia, Malaysia, and Thailand. He has held several positions including Visiting Professor, Visiting Scientist, and Professor at various universities in different parts of the world. Especially, he was awarded the most respected International Centre for Mathematical Sciences (ICMS) Group Research Fellowship to work with Prof. Dr. Michael Ruzhansky-Imperial College London at ICMS Centre, Scotland, UK, and during 2017-18, he was awarded the most respected TUBITAK Visiting Scientist Fellowship to work with Prof. Dr. Onur at AhiEvran University, Turkey. He has been awarded by Most Outstanding Researcher-2018 (Award for contribution to Mathematics) by the Union Minister of Human Resource Development of India, Mr. Prakash Javadekar 2018. According to Google Scholar, Dr. Agarwal is cited more than 4, 580 times, and on Scopus, his work is cited more than 2,689 times. Dr. Agarwal is the recipient of several notable honors and awards. Dr. Agarwal provided significant service to Anand International College of Engineering, Jaipur. Under his leadership during 2010-20, Anand-ICE consistently progressed in the education and preparation of students, and in the new direction of academics, research, and development. His overall impact on the institute is considerable. Many scholars from different nations, including China, Uzbekistan, Thailand, and African Countries came to work under his guidance. The majority of these visiting post-doctoral scholars were sent to work under Dr. Agarwal by their employing institutions for at least one month.

Affiliations and expertise

Full Professor, Anand International College of Engineering, Jaipur India; Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE; Peoples Friendship University of Russia (RUDN University), Russian Federation

Juan J. Nieto

Juan José Nieto Roig is currently a Professor of Mathematical Analysis and Director of the Institute of Mathematics at the University of Santiago de Compostela where he has been affiliated since 1991. Dr. Nieto received his degree in Mathematics at the University of Santiago de Compostela in 1980. He was awarded a Fulbright scholarship and proceeded to the University of Texas at Arlington. He received his Ph.D. in Mathematics at the University of Santiago de Compostela in 1983. He is one of the most cited mathematicians in the world according to Web of Knowledge and appears in the Thompson Reuters Highly Cited Researchers list. He has also participated as editor in different mathematical journals including Editor in Chief of the journal, Nonlinear Analysis: Real World Applications from 2009 to 2012. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences.

Affiliations and expertise

Full Professor of Mathematical Analysis, Director of the Institute of Mathematics, CITMAga, University of Santiago de Compostela, Santiago de Compostela, Galicia, Spain

Delfim F.M. Torres

Dr. Delfim F. M. Torres is currently a Professor, Director of the R&D Unit CIDMA, and Director of the Doctoral Programme Consortium MAP-PDMA in Applied Mathematics at the University of Aveiro in Portugal where he also obtained a PhD in Mathematics in 2002 and Habilitation in Mathematics in 2011. Prof Torres as written numerous scientific articles and has co-authored 5 books. He is a Renowned and Acclaimed Mathematician, having been awarded the title of Highly Cited Researcher in Mathematics in 2015, 2016, 2017, and 2019. His main Research area is the calculus of variations and optimal control; optimization; fractional derivatives and integrals; dynamic equations on time scales; and mathematical biology

Affiliations and expertise

Full Professor, Director of the R&D Unit CIDMA, Department of Mathematics, University of Aveiro, Portugal