A coupled spatial-network model: A mathematical framework for applications in epidemiology

by Hannah Kravitz, Christina Durón, and Moysey Brio

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A new compartmental modeling framework is proposed which couples population centers at the vertices, 1D travel routes on the edges, and a 2D continuum containing the rest of the population to simulate how an infection spreads through a population. The edge equations are coupled to the vertex ODEs through junction conditions, while the domain equations are coupled to the edges through boundary conditions. The model is illustrated on some example geometries, and a parameter study example is performed. The observed solutions exhibit exponential decay after a certain time has passed, and the cumulative infected population over the vertices, edges, and domain tends to a constant in time but varying in space, i.e., a steady state solution. 

Example implementation of the coupled spatial-network model.

Forecasting and Predicting Stochastic Agent-Based Model Data with Biologically-Informed Neural Networks

by John T Nardini

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Agent-based models (ABMs) are widely used to study biological systems, but heavy computational requirements limit our ability to predict their behavior. Differential equation (DE) models are often used as ABM surrogates, but they can provide poor predictions. We propose that biologically-informed neural networks (BINNs) can learn informative DE models that predict ABM behavior. We demonstrate how BINNs’ learned DE models can forecast future ABM data at new parameter values. We highlight the strong performance of this methodology in three case study ABMs that explore different rules on cell-cell interactions in collective migration. BINNs learn predictive and interpretable DE models even when other DE models are ill-posed or complex.

1) We explore several different ABM rules and summarize the ABM density over time. 2) BINN models can be trained to the ABM data. 3) We predict new ABM data by simulating the BINN's learned PDE model.

…where we talk about a paper studying who and when we should vaccinate.

After completing a DPhil in Statistics from the University of Oxford, focussing in epidemiology and phylogenetics, Matt now works as a data scientist for Italian football club Como 1907.

Matt was awarded the Lee A. Segel Prize for Best Student Paper published inThe Bulletin of Mathematical Biology for his paper Asymptotic Analysis of Optimal Vaccination Policies.

Join us to learn more about how this paper can help health professionals better assess the best way to distribute vaccines.

Find out more about Matt and his work on Linkedin:
linkedin.com/in/matthew-penn-732551232/

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• Twitter: @smb_mathbiology 
• Facebook: @smb.org 
• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

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…where we talk parasites, motorbikes, and digital twins.

Professor Reinhard Laubenbacher is: the Director of Laboratory for Systems Medicine at the University of Florida, an AAAS fellow (American Association for the Advancement of Science), and a scientist interested in using math to understand human disease and more specifically fungal infections in the lungs. When not at work, Reinhard and his wife enjoy motorbiking everywhere from the swamps of Florida, to the plains of Patagonia.

Find out more about Reinhard’s work on the following websites:

https://systemsmedicine.pulmonary.medicine.ufl.edu/

https://systemsmedicine.pulmonary.medicine.ufl.edu/profile/laubenbacher-reinhard/

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
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• The Bulletin of Mathematical Biology

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Harnessing flex point symmetry to estimate logistic tumor population growth

by Stefano Pasetto, Isha Harshe, Renee Brady-Nicholls, Robert A. Gatenby, Heiko Enderling

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Tumor growth dynamics are well-described mathematically by the S-shaped logistic function. Initially exponential growth decelerates as the tumor approaches its carrying capacity – the maximum tumor burden that can be sustained by the local and systemic (micro-)environment. The volume-to-carrying capacity ratio is a major determinant of response to (radio-)therapy; therefore, it is of high importance to estimate the carrying capacity from limited tumor volume measurements. The symmetry around the logistic growth flex point can be used to introduce ghost points symmetric to observed data points to double the available data to calibrate model parameters for an individual patient. With this approach, fewer data points are necessary to identify patient-specific carrying capacities, thereby potentiating shorter times to treatment decisions.

Relational Persistent Homology for Multispecies Data with Application to the Tumor Microenvironment

by Bernadette J. Stolz, Jagdeep Dhesi, Joshua A. Bull, Heather A. Harrington, Helen M. Byrne, Iris H. R. Yoon

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State-of-the-art data is exquisite in detail, often containing information on multiple species, e.g. cell types in imaging data. However, there are very few techniques equipped to analyse and quantify relations in such data. The paper by Stolz, Dhesi et al. proposes two topological approaches for multispecies data that can encode relations in spatial data. The authors showcase the methods on synthetic data of the tumour microenvironment which models the behaviour and interactions between tumour cells, macrophage subtypes, necrotic cells, and blood vessels. They demonstrate that relational topological features can extract biological insight, including dominant immune cell phenotype and parameter regimes of the data-generating model.

Relational persistent homology encodes spatial relations in multispecies data. We use synthetic images of the tumour microenvironment generated by an agent-based model as input to two different topological methods for encoding relations: Dowker persistent homology (top row) and multispecies witness persistent homology (bottom row). The topological features that we extract can classify the synthetic images according to dominant immune cell type and cluster qualitative behaviours of the model.

Assessing the Role of Patient Generation Techniques in Virtual Clinical Trial Outcomes

by Jana L. Gevertz and Joanna R. Wares

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Virtual clinical trials (VCTs) are a tool for understanding heterogeneous treatment responses. A number of techniques have been proposed to determine the set of model parametrizations ("virtual patients") that get included in a VCT. There is, however, no standard way to set the parameter prior distributions and to choose the criteria for including or excluding a parametrization sampled from the priors in the plausible population. In this work, we rigorously quantify the impact that VCT design choices have in a controlled setting using simulated patient data and a toy mathematical model. Our study provides a foundational understanding of how these choices influence the heterogeneity of virtual populations, and the predictions of a VCT.

Schematic of two methods for the generation of plausible patients for a virtual clinical trial.

...where we talk about infectious diseases, mentorship and mathematical tattoos.

Professor Stacey Smith? is an infectious disease modeler who appreciates the real world impacts that math biology can have. She leads educational and mentorship programming at the SMB and apparently never says no to anything SMB related. We caught Stacey at SMB 2024 in South Korea to talk about her research, life-changing transitions, and being a Whovian. 

Check out Stacey’s website for science, articles and Sci-Fi nerdiness: mysite.science.uottawa.ca/rsmith43/

And for those curious about the tattoo, read more about the Mandlebrot set: wikipedia.org/wiki/Mandelbrot_set

Find out more about SMB on: 

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…where we talk all things math bio at the annual meeting.

Science isn’t complete until it’s communicated, and what better place to do this than a scientific conference. This year, more than a thousand scientists were lucky enough to attend the SMB meeting in Seoul in Korea. This special episode gives a brief preview of some of the exciting research being done, as well as the people doing the work. Join us to hear from: 

• Fred Adler - Professor at the University of Utah, Utah, US 
• Kit Gallagher - Doctoral student at the University of Oxford, US & Moffitt Cancer Center, Florida, US
• Megan Greischer - Assistant Professor at Cornell University, New York, US
• Jona Kayser - Group leader at the Max Planck Institute for Physics and Medicine, Erlangen, Germany
• Bo-Moon Kim - Doctoral student at Kyoto University, Kyoto, Japan
• Breanne Sparta - Postdoctoral Researcher at UCLA, Los Angeles, US
• Rossana Vermiglio - Full professor at the University of Udine, Udine, Italy.

Find out more about SMB on: 

• Twitter: @smb_mathbiology 
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• Linkedin: @smb_mathbiology 
• The Bulletin of Mathematical Biology

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Statistical Mobility of Multicellular Colonies of Flagellated Swimming Cells

by Yonatan Ashenafi and Peter R. Kramer

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Eukaryotic cells, such as protozoa and sperm, use flagella—whip-like structures—for movement, helping them navigate, find food, interact, and evade predators. Researchers study flagellar propulsion through fluid dynamics and cellular responses. Recently, attention has shifted to multicellular colonies, where each cell has its own flagellum. In these colonies, misaligned flagella can cause unique movements, like rotating or spiraling. This paper presents a mathematical model to predict how flagellar behavior and colony structure affect movement, offering insights into the emergence of functional multicellularity.

Time-lapse composite schematic of a circular colony's planar motion. The colony consists of a dozen flagellated cells.