Applications of Differential Equations and Mathematical Modelling in Mathematical Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E3: Mathematical Biology".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 208

Special Issue Editors


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Guest Editor
1. Department of Mathematics, Instituto Superior de Engenharia de Lisboa—ISEL, Rua Conselheiro Emídio Navarro 1, 1949-014 Lisbon, Portugal
2. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193 Aveiro, Portugal
Interests: dynamical systems; chaos theory; differential equations; applied mathematics

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Guest Editor
1. ISEL-Engineering Superior Institute of Lisbon, Department of Mathematics, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
2. Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
Interests: differential equations; nonlinear dynamics; complex systems; chaos; mathematical biology

Special Issue Information

Dear Colleagues,

The use of mathematics for modelling is essential in many scientific areas. The complexity of real-world systems and the growing availability of biological data make the close interaction between scientists of different disciplines crucial for realism and significance of the obtained theoretical results. Mathematical biology is a particularly vibrant field, utilising mathematical, statistical and computer-based methods to investigate a wide range of biological problems in areas such as epidemiology, virology, complex ecosystems, genetics, cancer dynamics, and many others. In this Special Issue, the theory of differential equations stands out as indispensable for modelling and understanding biological phenomena, regarding its conceptual richness and applicability. By disclosing the compelling aspects of combining mathematics with real-world problems, this Special Issue is likely to attract a wide audience by its importance and interdisciplinarity.

Prof. Dr. Cristina Januário
Prof. Dr. Jorge Duarte
Guest Editors

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Keywords

  • differential equations
  • mathematical biology
  • nonlinear models

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Published Papers (1 paper)

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Research

29 pages, 5273 KiB  
Article
Ion Channel Memory Drives Cardiac Early Afterdepolarizations in Fractional Models
by Noemi Zeraick Monteiro, Rodrigo Weber dos Santos and Sandro Rodrigues Mazorche
Mathematics 2025, 13(10), 1585; https://doi.org/10.3390/math13101585 - 12 May 2025
Viewed by 149
Abstract
Understanding how past factors influence ion channel kinetics is essential for understanding complex phenomena in cardiac electrophysiology, such as early afterdepolarizations (EADs), which are abnormal depolarizations during the action potential plateau associated with life-threatening arrhythmias. We developed a mathematical framework that extends Hodgkin-Huxley [...] Read more.
Understanding how past factors influence ion channel kinetics is essential for understanding complex phenomena in cardiac electrophysiology, such as early afterdepolarizations (EADs), which are abnormal depolarizations during the action potential plateau associated with life-threatening arrhythmias. We developed a mathematical framework that extends Hodgkin-Huxley type equations with gamma Mittag-Leffler distributed delays, using tools from Fractional Calculus. Traditional memoryless two-variable models fail to reproduce EADs. Our approach modifies FitzHugh-Nagumo, Mitchell-Schaeffer, and Karma cardiac models, enabling the generation of EADs in each of them. We analyze the emergence of these oscillations by discussing the fractional parameters and the mean and variance of the memory kernels. Stability observations are also presented. Full article
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