Mathematical Analysis of Infectious Diseases

Mathematical Analysis of Infectious Diseases

1st Edition - June 10, 2022

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  • Editors: Praveen Agarwal, Juan Nieto, Delfim Torres
  • 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

  • 1. Spatiotemporal Dynamics Of The First Wave Of The Covid-19 Epidemic In Brazil

    Marat Rafikov, J.M.V. Grzybowski and Roberto Valmir Da Silva

    2. Transport And Optimal Control Of Vaccination Dynamics For Covid-19

    Delfim F. M. Torres, Mohamed Abdelaziz Zaitri and Mohand Ouamer Bibi

    3. COVID-19’s Pandemic: A New Way Of Thinking Through Linear Combinations Of Proportions

    Cristiana J. Silva, Juliana Dias Reis, Adelaide Freitas and Sara Escudeiro

    4. Stochastic Sica Epidemic Model With Jump L\'Evy Processes

    Delfim F. M. Torres, Houssine Zine and Jaouad Dananeb

    5. Examining The Correlation Between The Weather Conditions And Covid-19 Pandemic In Galicia

    Luca Piccotti Sr., Guido Ignacio Novoa Flores and Juan J. Nieto

    6. A Fractional-Order Malaria Model With Temporary Immunity

    Ram Singh and Attiq Ul Rehman

    7. Parameter Identification In Epidemiological Models

    Ana Carpio and Emile Pierret

    8. Lyapunov Functions And Stability Analysis Of Fractional-Order Systems

    Adnane Boukhouima, Houssine Zineb, El Mehdi Lotfia, Marouane Mahroufa, Delfim F. M. Torres and Noura Yousfi

    9. Some Key Concepts Of Mathematical Epidemiology

    Jaafar El Karkri and Mohammed Benmir

    10. Analytical Solutions And Parameter Estimation Of The Sir Epidemic Model

    Dimiter Prodanov

    11. Global Stability of a Diffusive SEIR Epidemic Model with Distributed Delay

    Abdesslem Lamrani Alaoui, Moulay Rchid Sidi Ammi, Mouhcine Tilioua and Delfim F. M. Torres

    12. Application Of Fractional Order Differential Equations In Modeling Viral Disease Transmission

    Shahram Rezapour and Hakimeh Mohammadi

    13. Role Of Immune Effector Responses During Hcv Infection: A Mathematical Study

    Fahad Al Basir and Amar Nath Chatterjee

    14. Modeling The Impact Of Isolation During An Outbreak Of Ebola Virus Disease

    Amira Rachah

    15. Application Of The Stochastic Arithmetic To Validate The Results Of Nonlinear Fractional Model Of Hiv Infection For Cd8+T-Cells

    Samad Noeiaghdam and Denis Sidorov

    16. Existence Of Solutions Of Modified Fractional Integral Equation Models For Endemic Infectious Diseases

    Hemant Kumar Nashine, Rabha W. Ibrahim and Reena Jain

    17. Numerical solution of a fractional epidemic model via general Lagrange scaling functions with bibliometric analysis

    Yadollah Ordokhani and Sedigheh Sabermahani

Product details

  • No. of pages: 300
  • Language: English
  • Copyright: © Academic Press 2022
  • Published: June 10, 2022
  • Imprint: Academic Press
  • 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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