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Mathematics
Special Issues
Models in Population Dynamics, Ecology and Evolution
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Models in Population Dynamics, Ecology and Evolution

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

Deadline for manuscript submissions: 31 October 2025 | Viewed by 522

Special Issue Editors

Prof. Dr. Sergei Petrovskii

E-Mail Website
Guest Editor
School of Computing and Mathematical Sciences, University of Leicester, Leicester, UK
Interests: mathematical ecology; climate change; mass extinctions; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals
Dr. Maíra Aguiar

E-Mail Website
Guest Editor
Mathematical and Theoretical Biology (MTB) Group, Basque Center for Applied Mathematics (BCAM), Bilbao, Spain
Interests: epidemiological dynamics of multi-strain infectious diseases; interplay between pathogen serotypes and cross-immunity; epidemiological dynamics of vaccine preventable diseases; epidemiological dynamics of vector-pathogen-host interaction; within-host dynamics focusing on immune responses; complex dynamics, empirical data analysis and public health intervention measures

Special Issue Information

Dear Colleagues,

We are pleased to invite you to contribute to the Special Issue “Models in Population Dynamics, Ecology and Evolution”. The Special Issue is broadly based on the conference on Models in Population Dynamics, Ecology, and Evolution - MPDEE’25 (https://www.bcamath.org/events/mpdee25/en/) that took place in Bilbao, Spain, from 5 to 9 May, 2025.

The meeting considered applications of mathematical modelling to explore processes and mechanisms in various biological systems ranging from bacteria to the human society. A special focus was on the interplay between ecology and evolution across time and space, particularly under the effect of climate change. MPDEE’25 also explored similarities between modelling techniques traditionally applied in ecology and evolution and those used in other life sciences aiming to enhance interdisciplinary approaches and to stimulate further advances in population dynamics, ecology and evolution.

This Special Issue reflects the conference’s main themes and serves as a publication outlet for work presented at the event. Submissions from conference participants are welcome, but the Special Issue is also open to all researchers whose work fits within the scope, regardless of their participation in MPDEE’25.

Prof. Dr. Sergei Petrovskii
Dr. Maíra Aguiar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modelling
  • biological systems
  • ecology
  • evolution
  • population dynamics
  • climate change
  • modelling techniques
  • life sciences
  • theoretical biology
  • theory–empirical integration
  • spatial and temporal dynamics

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Published Papers (1 paper)

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Research

25 pages, 14199 KiB  
Article
A Nonlinear Cross-Diffusion Model for Disease Spread: Turing Instability and Pattern Formation
by Ravi P. Gupta, Arun Kumar and Shristi Tiwari
Mathematics 2025, 13(15), 2404; https://doi.org/10.3390/math13152404 - 25 Jul 2025
Viewed by 329
Abstract
In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of [...] Read more.
In this article, we propose a novel nonlinear cross-diffusion framework to model the distribution of susceptible and infected individuals within their habitat using a reduced SIR model that incorporates saturated incidence and treatment rates. The study investigates solution boundedness through the theory of parabolic partial differential equations, thereby validating the proposed spatio-temporal model. Through the implementation of the suggested cross-diffusion mechanism, the model reveals at least one non-constant positive equilibrium state within the susceptible–infected (SI) system. This work demonstrates the potential coexistence of susceptible and infected populations through cross-diffusion and unveils Turing instability within the system. By analyzing codimension-2 Turing–Hopf bifurcation, the study identifies the Turing space within the spatial context. In addition, we explore the results for Turing–Bogdanov–Takens bifurcation. To account for seasonal disease variations, novel perturbations are introduced. Comprehensive numerical simulations illustrate diverse emerging patterns in the Turing space, including holes, strips, and their mixtures. Additionally, the study identifies non-Turing and Turing–Bogdanov–Takens patterns for specific parameter selections. Spatial series and surfaces are graphed to enhance the clarity of the pattern results. This research provides theoretical insights into the implications of cross-diffusion in epidemic modeling, particularly in contexts characterized by localized mobility, clinically evident infections, and community-driven isolation behaviors. Full article
(This article belongs to the Special Issue Models in Population Dynamics, Ecology and Evolution)
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