Mathematical Analysis of Infectious Diseases

Mathematical Analysis of Infectious Diseases

1st Edition - June 1, 2022

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  • Editors: Praveen Agarwal, Juan Nieto, Delfim Torres
  • eBook ISBN: 9780323904582
  • Paperback ISBN: 9780323905046

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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.

Key Features

  • Offers analytical and numerical techniques for virus models
  • Discusses mathematical modeling and its applications in treating infectious diseases or analyzing their spreading rates
  • Covers the application of differential equations for analyzing disease problems
  • Examines probability distribution and bio-mathematical applications


Epidemiologists, epidemic modelers, virologists, infectious disease and public health researchers, mathematical modelers for infectious disease biomathematicians, government agencies working on infectious disease prevention, control, and response. Graduate students studying biological sciences, infectious diseases, public health particularly epidemiology, mathematical and epidemiological modeling

Table of Contents

  • 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

Product details

  • No. of pages: 344
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: June 1, 2022
  • Imprint: Academic Press
  • eBook ISBN: 9780323904582
  • Paperback ISBN: 9780323905046

About the Editors

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 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 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

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