Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

1. Front Matter

   Pages i-xi

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2. Mathematical Modeling of Thrombin Generation and Wave Propagation: From Simple to Complex Models and Backwards

   • Alexey Tokarev, Nicolas Ratto, Vitaly Volpert

   Pages 1-22

3. Optimal Control of a Delayed Hepatitis B Viral Infection Model with DNA-Containing Capsids and Cure Rate

   • Adil Meskaf, Karam Allali

   Pages 23-33

4. Dynamics of a Generalized Model for Ebola Virus Disease

   • Zineb El Rhoubari, Hajar Besbassi, Khalid Hattaf, Noura Yousfi

   Pages 35-46

5. Bifurcations in a Mathematical Model for Study of the Human Population and Natural Resource Exploitation

   • I. M. Cholo Camargo, G. Olivar Tost, I. Dikariev

   Pages 47-58

6. Mathematical Analysis of the Dynamics of HIV Infection with CTL Immune Response and Cure Rate

   • Sanaa Harroudi, Karam Allali

   Pages 59-70

7. Qualitative Analysis of a PDE Model of Telomere Loss in a Proliferating Cell Population in the Light of Suns and Stars

   • Y. Elalaoui, L. Alaoui

   Pages 71-85

8. The Threshold of a Stochastic SIQR Epidemic Model with Lévy Jumps

   • Driss Kiouach, Yassine Sabbar

   Pages 87-105

9. Global Dynamics of a Generalized Chikungunya Virus

   • Hajar Besbassi, Zineb El Rhoubari, Khalid Hattaf, Noura Yousfi

   Pages 107-117

10. Differential Game Model for Sustainability Multi-Fishery

    • Nadia Raissi, Chata Sanogo, Mustapha Serhani

    Pages 119-137

11. Towards a Thermostatistics of the Evolution of Protein Domains Through the Formation of Families and Clans

    • Rubem P. Mondaini, Simão C. de Albuquerque Neto

    Pages 139-152

12. Analysis of Tumor/Effector Cell Dynamics and Decision Support in Therapy

    • S. Sabir, N. Raissi

    Pages 153-164

13. Optimal Control of an HIV Infection Model with Logistic Growth, CTL Immune Response and Infected Cells in Eclipse Phase

    • Jaouad Danane, Karam Allali

    Pages 165-176

14. Khinchin–Shannon Generalized Inequalities for “Non-additive” Entropy Measures

    • Rubem P. Mondaini, Simão C. de Albuquerque Neto

    Pages 177-190

15. Application of the Markov Chains in the Prediction of the Mortality Rates in the Generalized Stochastic Milevsky–Promislov Model

    • Piotr S̀liwka

    Pages 191-208

16. Modelling the Role of Vector Transmission of Aphid Bacterial Endosymbionts and the Protection Against Parasitoid Wasps

    • Sharon Zytynska, Ezio Venturino

    Pages 209-230

17. The Incorporation of Fractal Kinetics in the PK Modeling of Chemotherapeutic Drugs with Nonlinear Concentration-Time Profiles

    • Tahmina Akhter, Sivabal Sivaloganathan

    Pages 231-254

18. Mathematical Modeling of Inflammatory Processes

    • O. Kafi, A. Sequeira

    Pages 255-269

19. Modeling the Memory and Adaptive Immunity in Viral Infection

    • Adnane Boukhouima, Khalid Hattaf, Noura Yousfi

    Pages 271-297

20. Optimal Temporary Vaccination Strategies for Epidemic Outbreaks

    • K. Muqbel, A. Dénes, G. Röst

    Pages 299-307

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018. The topics covered include applications of mathematical modeling in hepatitis B, HIV and Chikungunya infections; tumor cell dynamics; inflammatory processes; chemotherapeutic drug effects; and population dynamics. Also discussing the application of techniques like the generalized stochastic Milevsky-Promislov model, numerical simulations and convergence of discrete and continuous models, it is an invaluable resource on interdisciplinary research in mathematical biology for students, researchers, and professionals.


Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideasand techniques, promoting truly international cooperation for problem discussion. The 2018 edition of BIOMAT International Symposium received contributions by authors from seventeen countries: Algeria, Brazil, Cameroon, Canada, Chad, Colombia, France, Germany, Hungary, Italy, Mali, Morocco, Nigeria, Poland, Portugal, Russia, and Senegal. Selected papers presented at the 2017 edition of this Symposium were also published by Springer, in the volume “Trends in Biomathematics: Modeling, Optimization and Computational Problems” (978-3-319-91091-8).

• Mathematical modeling
• Infection dynamics
• Infection model
• Tumor cell dynamics
• Chikungunya dynamics
• Khinchin-Shannon inequalities
• Milevsky-Promislov model
• Numerical simulation
• partial differential equations

• Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Brazil

  Rubem P. Mondaini

Rubem P. Mondaini is President of the BIOMAT Consortium/International Institute for Interdisciplinary Sciences and a Full Professor of Mathematical Biology and Biological Physics at the Federal University of Rio de Janeiro, Brazil. He holds a PhD in Theoretical Physics from the Brazilian Centre for Physical Research, Brazil.  His research activities abroad include a period as a Visiting Scientist at the International Centre for Theoretical Physics (ICTP), Trieste, Italy (1978) and as a Senior Postdoc at the Department of Mathematics of King's College, University of London, UK (1986).  He was also a Visiting Professor at the Centre of Physics of Condensed Matter, Lisbon, Portugal (1986) and at the Department of Chemical Engineering of Princeton University (2008).  He has been the Chairman of the Annual BIOMAT Conferences since their inception during the BIOMAT 2001 Symposium in Rio de Janeiro, Brazil.

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