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Mathematics
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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: 30 April 2026 | Viewed by 2881

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 250 words) can be sent to the Editorial Office for assessment.

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 (4 papers)

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Research

34 pages, 1678 KB  
Article
An Age-Distributed Immuno-Epidemiological Model with Information-Based Vaccination Decision
by Samiran Ghosh, Malay Banerjee and Vitaly Volpert
Mathematics 2026, 14(1), 162; https://doi.org/10.3390/math14010162 - 31 Dec 2025
Viewed by 316
Abstract
An age-distributed immuno-epidemiological model with information-based vaccination proposed in this work represents a system of integro-differential equations with compartments for the numbers of susceptible individuals, infected individuals, vaccinated individuals, and recovered individuals. This model describes the influence of vaccination decisions on epidemic progression [...] Read more.
An age-distributed immuno-epidemiological model with information-based vaccination proposed in this work represents a system of integro-differential equations with compartments for the numbers of susceptible individuals, infected individuals, vaccinated individuals, and recovered individuals. This model describes the influence of vaccination decisions on epidemic progression in different age groups. In a particular case of the model without age distribution, we determine the basic reproduction number and the final size of epidemic, that is, the limiting number of susceptible individuals at asymptotically large time. Moreover, we study the existence and uniqueness of a positive solution for the age-structured model. Numerical simulations show that the information-based vaccination acceptance can significantly influence the epidemic progression. Though the initial stage of epidemic progression is the same for all memory kernels, as the epidemic progresses and more information about the disease becomes available, further epidemic progression strongly depends on the memory effect. A short-range memory kernel appears to be more effective in restraining the epidemic outbreaks because it allows for more responsive and adaptive vaccination decisions based on the most recent information about the disease. Additionally, the simulation results suggest that relying on either a responsive vaccination approach or a highly effective vaccine alone may be insufficient to significantly reduce the epidemic size and prevent large outbreaks. Both factors are necessary to achieve substantial epidemic control. Moreover, the impacts of the age-dependent initial susceptible population and the age-dependent memory kernel are studied through numerical simulation of the age-dependent model. Full article
(This article belongs to the Special Issue Models in Population Dynamics, Ecology and Evolution)
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32 pages, 6353 KB  
Article
Multiscale Dynamics of MMC Chemotherapy in Bladder Cancer: The SPVF Approach
by Marom Yosef, Svetlana Bunimovich-Mendrazitsky and OPhir Nave
Mathematics 2025, 13(24), 3974; https://doi.org/10.3390/math13243974 - 13 Dec 2025
Viewed by 325
Abstract
Mitomycin-C (MMC) is the leading chemotherapeutic agent for the treatment of non-muscle invasive bladder cancer (NMIBC), but recurrence rates remain high due to poorly understood interactions between the tumor, immune system, and drugs. We present a five-equation mathematical model that explicitly tracks MMC, [...] Read more.
Mitomycin-C (MMC) is the leading chemotherapeutic agent for the treatment of non-muscle invasive bladder cancer (NMIBC), but recurrence rates remain high due to poorly understood interactions between the tumor, immune system, and drugs. We present a five-equation mathematical model that explicitly tracks MMC, tumor cells, dendritic cells (DCs), effector T cells, and regulatory T cells (Tregs). The model incorporates clinically realistic treatment regimens (6-week induction followed by maintenance therapy), including DC activation by tumor debris, dual DC activation of effector and Treg cells, and reversal of MMC-induced immunosuppression. The resulting nonlinear system exhibits hidden multiscale dynamics. We apply the singular perturbed vector field (SPVF) method to identify fast–slow hierarchies, decompose the system, and conduct stability analysis. Our results reveal stable equilibria corresponding to either tumor eradication or persistence, with a critical dependence on the initial tumor size and growth rate. Modeling shows that increased DC production paradoxically contributes to treatment failure by enhancing Treg activity—a non-monotonic immune response that challenges conventional wisdom. These results shed light on the mechanisms of NMIBC evolution and highlight the importance of balanced immunomodulation in the development of therapeutic strategies. Full article
(This article belongs to the Special Issue Models in Population Dynamics, Ecology and Evolution)
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16 pages, 843 KB  
Article
Mathematical Modeling and Intensive Simulations Assess Chances for Recovery of the Collapsed Azov Pikeperch Population
by Yuri V. Tyutyunov and Inna Senina
Mathematics 2025, 13(19), 3232; https://doi.org/10.3390/math13193232 - 9 Oct 2025
Viewed by 616
Abstract
The main objective of the study is to evaluate the recovery potential of the collapsed semi-anadromous pikeperch population (Sander lucioperca L.) in the Azov Sea during 2021–2030. We use a Ricker-based age-structured model that accounts for the effects of salinity and temperature [...] Read more.
The main objective of the study is to evaluate the recovery potential of the collapsed semi-anadromous pikeperch population (Sander lucioperca L.) in the Azov Sea during 2021–2030. We use a Ricker-based age-structured model that accounts for the effects of salinity and temperature on reproduction. In earlier work, the model predicted and explained the pikeperch stock collapse as the consequence of salinity and temperature exceeding the species’ tolerance limits. To assess the probability of stock recovery, we conducted a long-term retrospective validation and ran Monte Carlo projections under alternative climate scenarios with supplemental management actions. The results confirm that the dynamics of the pikeperch population in the Azov Sea are essentially environment-driven and negatively impacted by the large positive anomalies in both water temperature and salinity. Simulations suggest that either a substantial and persistent artificial restocking of juvenile recruits, or mostly unlikely scenarios of simultaneous reduction in salinity and temperature combined with additional restocking can provide conditions for the stock restoration within the decade considered. Based on these projections, we recommend a suite of urgent restoration measures to create the conditions required for future stock recovery. Full article
(This article belongs to the Special Issue Models in Population Dynamics, Ecology and Evolution)
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25 pages, 14199 KB  
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 998
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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