Travelling Waves in Gene Expression: A Mathematical Model of Cell-State Dynamics in Melanoma

by Charlotte Taylor Barca; Rotem Leshem; Vishaka Gopalan; Sarah Woolner; Kerrie L Marie; Gareth Wyn Jones; Oliver E Jensen

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Melanoma is a form of skin cancer, made particularly aggressive by the ability of certain cells (melanocytes) to switch between states that confer different phenotypes. This behaviour can lead to therapy resistance and evasion of the body’s immune response. Understanding the mechanisms leading to cell-state transitions, and the spatial patterns of cell states in a tumour, is essential to the development and improvement of therapies or predictive biomarkers. We use a low-order mathematical model of a fundamental gene regulatory network in a population of melanoma cells to identify possible states, and the conditions under which the whole cell population can be driven into a single state.

Image Description: A snapshot of the cell monolayer simulation and the melanoma gene regulatory network.

An Agent-Based Modelling Approach to Investigate the Impact of Sex and Gender on Tuberculosis Transmission: A Case Study of Kampala, Uganda

by James W. G. Doran, Dennis Mujuni, Kit Gallagher, Christian A. Yates, and Ruth Bowness.

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This study shows mathematical models can reveal why men have a higher burden of tuberculosis (TB) than women in high‑incidence settings like Kampala. By building an agent‑based model that simulates people’s social contacts and disease progression, we show both biological and behavioural differences impact TB incidence. The model shows sex-specific within‑host factors, like men’s higher likelihood of progression to active disease, have the largest influence on case numbers. Meanwhile, gender-specific between-host factors, especially same-sex mixing and longer male diagnosis delays, drive the above-one male‑to‑female case ratio. This study offers a proof‑of‑concept framework that could support public health planning, after further validation.

...where everyone got together to talk MathBio in Graz, Austria.

This year the SMB meeting was held together with the European Society for Mathematical and Theoretical Biology. In between hiking some hills and enjoying the local pumpkin seed oil the attendees stopped to speak about their work on women’s health, and social determination of measles, and a precious baseball card collection.

Featured Speakers:

[00:47] Philip Gerlee — Chalmers University of Technology & University of Gothenburg, Sweden

[09:26] Alex Johnson — North Carolina State University, USA

[13:21] Bhavana Murankar — North Carolina State University, USA

[19:11] Dan Mark Orapa — University of the Philippines, Philippines

[24:00] Volkan Ozcoban — University of Melbourne, Australia

[34:52] Angela Peace — Virginia Tech, USA

[38:33] Jorge Velasco Hernandez — National Autonomous University of Mexico, Mexico

[45:49] Mohammed Zahid — The University of Texas MD Anderson Cancer Center, USA

Learn more about the new SMB webinar series MathBioNexus: https://www.smb.org/mathbionexus

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
• Bluesky: @smbmathbiology.bsky.social 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

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Climate-Informed Predictive Optimal Control of Desert Locust Dynamics Under Machine-Learning Climate Forcing

by Dejen K. Mamo, Mathew N. Kinyanjui & Nourridine Siewe.

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Desert locusts swarm when the weather cooperates: rain greens the desert and warmth speeds their growth. Can better forecasts make control smarter? Instead of describing the seasons with a smooth sine wave, we trained two machine-learning models on decades of records from Amibara, Ethiopia — one for temperature, one for rainfall — and fed their forecasts into a population model tracking eggs, hoppers, bands, adults and swarms alongside the vegetation they strip. We then computed the treatment schedule that holds locusts lowest and vegetation highest for the least effort. Treating young and adult locusts together beat either alone, cutting the management burden by over 95%, and that ranking held when we deliberately corrupted the forecasts.

Image Description: Machine-learning forecasts of temperature and rainfall drive a stage- and phase-structured desert locust population model; the optimal control problem then schedules juvenile and adult treatment to jointly minimise locust abundance and vegetation loss.

The Bulletin of Mathematical Biology and the Society for Mathematical Biology: Strengthening our Shared Community

by Matthew J. Simpson, Reinhard C. Laubenbacher & Jennifer A. Flegg.

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The Bulletin of mathematical biology (BMB) is the official journal of the Society for Mathematical Biology (SMB). We write this Editorial in our respective capacities as the current Editor-in-Chief of BMB (Simpson), President of the SMB and former Editor-in-Chief of BMB (Laubenbacher), and Chair of the SMB Publications Committee (Flegg). This Editorial follows the joint ECMTB–SMB meeting held from 13–17 July 2026 in Graz, Austria. Organised jointly by the SMB and the European Society for Mathematical and Theoretical Biology (ESMTB), the meeting brought together almost 1300 participants from around the world. As with all recent annual meetings, during the 2026 meeting we took several opportunities to highlight the close relationship between BMB and the SMB. Nevertheless, a number of SMB members and BMB authors told us that they had not previously realised that BMB is the official journal of the Society. These conversations motivate us to explain what this relationship means, why it matters, and how members of our community can help strengthen it.

Multiscale Analysis of a Kinetic Equation for Mechanotaxis

by Benoît Perthame, Francesco Salvarani, Shugo Yasuda.

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How do billions of individual cells coordinate to form the complex, beautiful patterns seen in nature? The answer lies in how they physically "feel" and navigate the surfaces beneath them. Bridging microscopic physics and macroscopic biology, our study introduces a mathematical framework for mechanotaxis: cells actively modify the substrate, which then feeds back on their mobility through friction. We show how this feedback can trigger self-organization, producing stripes and spots like those in bacterial colonies. Because cell motion on surfaces is central to development, cancer, wound healing, and tissue engineering, this framework offers a new way to understand how collective behavior emerges from individual rules.

Image Description: Mechanical feedback between cells and their substrate can generate diverse population-level patterns. Cells locally modify the substrate, which in turn alters their mobility and spatial organization. Our multiscale model connects these cell-scale interactions to collective behavior and shows how the strength of substrate modification can produce periodic patterns, phase-separated states, or localized clusters.

Mathematical Modelling of the Mitochondrial Dicarboxylate Carrier (SLC25A10)

by Ramin Nashebi, Yingying Lyu, Elías Vera-Sigüenza, Daniel A. Tennant & Fabian Spill

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SLC25A10 is a mitochondrial transport protein that exchanges succinate, malate, and phosphate across the inner mitochondrial membrane. We developed a mathematical model of its “ping-pong” transport mechanism and tested it against published measurements from mitochondria and proteoliposomes. The model predicts two transport stages: an early phase in which matrix phosphate supports rapid succinate and malate uptake while phosphate exits, followed by a slower phase dominated by malate–succinate redistribution after phosphate depletion. It also suggests that mitochondrial shape affects transport, with swelling increasing early flux and condensation reducing it. These results help explain how SLC25A10 responds to changing metabolic conditions.

Image Description: Graphical summary of the SLC25A10 mathematical transport model and its biological implications.

Metal-Ion-Mediated Amyloid-Aggregation in Alzheimer’s Disease: A Mathematical Model of Chelation and Inhibitory Therapies

by Shantia Yarahmadian et al.

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We develop a novel, comprehensive, and rigorously validated mathematical framework to investigate the kinetics of amyloid-(A) aggregation in the presence of biologically relevant metal ions, chelating agents, and inhibitor drugs. Building upon and extending existing aggregation models, our approach integrates metal-assisted aggregation, A-assembly, and therapeutic interventions within a unified and mechanistically consistent formulation.

When Strain Meets Stress: Threshold Dynamics and Regime Shifts in Wolbachia-Based Mosquito Population Replacement

by Suddhyashil Sarkar, Ayan Paul & Joydeb Bhattacharyya.

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Wolbachia-based mosquito population replacement is a promising biocontrol strategy to reduce arboviral disease transmission by introducing Wolbachia-infected mosquitoes into wild populations. The success of this approach depends on the strain-specific characteristics of the Wolbachia symbiont and the mosquito host. This study presents a mathematical modelling framework to evaluate how Wolbachia strains and mosquito hosts influence the success of population replacement. The model incorporates key biological factors, including incomplete cytoplasmic incompatibility (CI), imperfect maternal transmission (MT), fitness costs, immigration, and potential loss of Wolbachia from mosquitoes. Analytical and numerical simulations demonstrate that strain-specific differences significantly impact the establishment, spread, and long-term persistence of Wolbachia in mosquito populations. Results indicate that high CI and MT levels, combined with low fitness costs and minimal immigration, facilitate successful Wolbachia establishment. To account for environmental stress, the model is extended to a stochastic framework incorporating environmental noise. Analysis reveals that stochasticity can shift invasion thresholds, destabilize equilibria, and induce noise-driven transitions between coexistence states. Numerical simulations show that low noise levels allow deterministic thresholds to remain predictive, whereas stronger fluctuations can undermine replacement success despite favourable deterministic conditions. A stochastic optimal control formulation further indicates that higher and more prolonged releases are necessary in noisy environments to ensure replacement. Collectively, these findings highlight how both strain traits and environmental stress shape the deterministic and stochastic thresholds governing the success of Wolbachia-based mosquito population replacement.

....where we talk about a paper studying: parameters for glow in the dark cells.

Veronica Ciocanel is an Assistant Professor in Math (primary) and Biology (joint) at Duke University. In her research, she applies techniques from dynamical systems and data-driven modeling to questions in cell and developmental biology.

Find out more about Veronica’s work on her website: https://sites.math.duke.edu/~ciocanel/

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
• Bluesky: @smbmathbiology.bsky.social 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

Apple Link      Spotify Link     Read the full transcript