A Dual-age Structured Epidemiological Model with Waning Immunity and Reinfection

by R. M. Kovacevic, N. I. Stilianakis, V. M. Veliov

When is the right time for a booster? A new model that tracks two clocks at once. Many of the diseases we worry about most — COVID-19, influenza, RSV — share a common feature: immunity fades. After recovering or being vaccinated, our protection slowly erodes, increasing the likelihood of reinfection over time. Most mathematical models simplify this drastically, treating everyone who has recovered as identical and ignoring how recently, and how strongly, they were protected. Our study introduces a model that follows two personal "clocks" at once: how long it has been since someone last recovered (their immunity), and, if they are currently ill, how long the infection has been running.

Image Description: A Dual-age Structured Epidemiological Model with Waning Immunity and Reinfection.

…where we talk: an induction to MathBio, neuroscience in flies, and optimizing coffee breaks.

Lukas did a PhD at the University of Oxford and a postdoc at the Max Planck Institute of Neurobiology, where he discovered how single neurons implement basic arithmetic operations. Now he is an associate professor at the Medical University of Graz.

Learn more about Lukas’ work on his website: groschner-lab.org

Learn more about this year's Annual Meeting at: ecmtb2026.

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

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A new Insight into the threshold and oscillatory regimes in plant-pathogen models: A Nutrient-driven approach

by Dhruba Pariyar Damay, Angela Peace

This study examines how nutrient availability influences disease spread and how disease, in turn, affects nutrient dynamics. The work is motivated in part by root diseases, which occur largely below ground where transmission pathways are difficult to observe directly. Our results show that nutrient–disease feedbacks can strongly influence whether diseases become established, how outbreaks develop, and how nutrients are distributed between plants and the environment. By directly linking environmental nutrient conditions to disease transmission, this study provides new insight into the ecological processes governing plant disease and offers a foundation for improving predictions of disease risk and ecosystem responses in forest systems.

Image Description: Graphical abstract

An analytical framework for phenotypic selection of fitness-conferring genes

by Marc Sturrock, Anna Sturrock

Genetically identical cells differ in how much of any given protein they carry because gene expression is noisy. Under stress, such as when exposed to an antibiotic or a chemotherapy drug, the cells that happen to hold high levels of a useful survival protein outlast their less lucky neighbours, leaving the population transiently enriched for the survival phenotype without any genetic change. We derive an exact theory of when this happens. When stress kills cells outright, as in cancer chemotherapy, ordinary baseline noise is enough. When stress only slows growth, a cellular memory loop is required. Either way, this transient phenotypic resistance buys cells time during which permanent drug-resistance mutations can arise.

Image Description: An exact framework for the selective enrichment of fitness-conferring genes. Top: under growth-driven selection, a feedback loop linking growth to protein production enriches the survival gene relative to a neutral reference. Bottom: under death-driven selection, enrichment arises from ordinary gene-expression noise alone, with no feedback required.

Sustainable Coexistence with Infectious Diseases: A Behavioral Feedback Model Driven by Resource Accessibility under Static-Dynamic Optimal Control

by Yangyang Zhang, Huijun Liu, Sanyi Tang, Lili Liu

This study investigates the behavior-disease feedback mechanism and explores optimal control strategies balancing infection burden and intervention costs under the long-term management goal of coexisting with the virus. Simulations based on influenza data from Shanxi Province show that spontaneous, risk-driven behavioral adaptation alone can generate multi-peak epidemic waves. Static optimization reveals the behavioral threshold and public risk attention determine optimal intervention intensity and convergence. Dynamic optimization targeting the transmission rate alone or jointly with the behavioral threshold shows that early intervention during the rapid growth phase prevents repeated policy oscillations and epidemic rebounds.

Image Description: Balance the infection burden and intervention costs when facing the long-term management goal of coexisting with the virus

…where we talk: time at Los Alamos, modeling TB, and tips for international flights.

Dr. Kirschner was the first mathematics professor appointed in a medical school. She researches immune responses to infections using multiscale modeling. She served as Editor-in-Chief of the Journal of Theoretical Biology for 20 years and as president of SMB.

Learn more about Denise’s work on her website: http://malthus.micro.med.umich.edu

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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The Society is accepting nominations for the 2027 Society Prize Award cycle. Society members are encouraged to nominate candidates by submitting the required materials in PDF format via the Prize submission form. Contact SMB Secretary Brandilyn Stigler (secretary@smb.org) if you have any questions.

By Monday, 14 September 2026, the nominator must submit:

• Contact information for the nominators and nominee, including SMB Members IDs for both nominator and nominee
• A letter (no more than 4 pages) describing the nominee's qualifications and commenting on the nominee's scientific contributions for the society award.
• The nominee's curriculum vitae, including all publications.
• Two supporting letter

Submit Your Prize Nomination

Nominees may be affiliated with non-academic institutions, however, please note that Society membership is a requirement for the nominator and nominee. All applications must be complete and submitted by Monday, 23:59PM ET, 14 September 2026 in order to be considered.

Refining niche metric calculations: A modified weighting approach to Colwell and Futuyma’s method

by Kürşad Özkan, Serkan Özdemir, Bart Muys, Salih Doğan

This study resolves long-standing limitations of the Colwell & Futuyma (1971) method for calculating niche breadth and niche overlap. The original weighting factors collapse to zero when resource states are empty or uniformly used, making niche calculations undefined. We introduce modified weighting factors based on exponential transformations that always yield positive values, ensuring valid niche metric computation under any resource matrix structure. Testing with eight hypothetical matrices and an empirical mite community dataset demonstrated that the edj factor consistently produces ecologically meaningful results, correctly ranking specialists and generalists and resolving previously undefined niche overlap.

Image Description: This study introduces modified weighting factors based on exponential transformations to resolve the mathematical limitations of classical niche metrics (Colwell & Futuyma 1971; Hanski 1978). The classical weighting factors collapse to zero under certain resource matrix configurations, rendering niche breadth and overlap calculations undefined. The proposed modification ensures strictly positive weights while preserving the unit-sum constraint and full compatibility with the original framework. Validation across eight hypothetical matrices and an empirical dataset of 18 Raphignathoid mite species across six habitats in Türkiye demonstrates that the modified relative factor consistently produces ecologically coherent niche metrics, correctly ranking specialists and generalists and resolving previously undefined niche overlap estimates.

Ensemble Optimal Control for Managing Drug Resistance in Cancer Therapies

by Alessandro Scagliotti; Federico Scagliotti; Laura Deborah Locati; Federico Sottotetti

Cancer treatment often relies on the highest dose a patient can tolerate, but this may not be the best way to control tumors over time. This study uses mathematical modeling to explore a different approach: managing the balance between drug-sensitive and drug-resistant cancer cells. By simulating prostate cancer treated with androgen deprivation therapy, the authors show how treatment timing could be adapted rather than kept continuously high. The proposed “Off-On” adaptive therapy starts with observation and introduces treatment only when needed, aiming to keep the disease under long-term control. The work suggests that smarter schedules, not simply more drug, may improve chronic cancer management.

Image Description: Left: Ensemble optimal control approach. Center: On-Off Adaptive Therapy. Right: Off-On Adaptive Therapy.

Revisiting Turing's Chemical Basis of Morphogenesis

by John J. Tyson

Although Alan Turing’s 1952 paper on the chemical basis of morphogenesis is a classic of theoretical biology, it is notoriously difficult to read. His chemical examples are unusual, his linear stability analysis of the homogeneous steady state seems unnecessarily complex, and his numerical simulations are mysterious. To make Turing’s paper more accessible, I pose his reaction-diffusion equations in dimensionless form, place his linear stability analysis in the context of later approaches, revise his models in more chemically realistic terms, and provide help for computing Turing patterns in one- or two spatial dimensions. I also discuss how Turing’s stationary patterns relate to traveling waves in reaction-diffusion equations.