Bulletin of Mathematical Biology

Martina-Perez, Simon F.; Breinyn, Isaac B.; Cohen, Daniel J.; Baker, Ruth E.

doi: 10.1007/s11538-024-01319-8pmid: 38896328

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.

Baabdulla, Arwa Abdulla; Hillen, Thomas

doi: 10.1007/s11538-024-01322-zpmid: 38896363

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator–prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.

Bienvenu, François; Steel, Mike

doi: 10.1007/s11538-024-01316-xpmid: 38896355

In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is quantitative and specific to this problem; and a proof using branching process techniques that is less explicit, but also much more general, as it applies to any fixed patterns and can be extended to other trees and networks. In particular, it follows immediately from our second proof that the fraction of d-ary trees (resp. level-k networks) that contain a fixed d-ary tree (resp. level-k network) tends to 1 as the number of leaves grows.

Gross, Elizabeth; Krone, Robert; Martin, Samuel

doi: 10.1007/s11538-024-01314-zpmid: 38886260

Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal evolution or hybridization has occurred. Placing a Markov model of evolution on a phylogenetic network gives a model that is particularly amenable to algebraic study by representing it as an algebraic variety. In this paper, we give a formula for the dimension of the variety corresponding to a triangle-free level-1 phylogenetic network under a group-based evolutionary model. On our way to this, we give a dimension formula for codimension zero toric fiber products. We conclude by illustrating applications to identifiability.

Aliatimis, Georgios; Yoshida, Ruriko; Boyacı, Burak; Grant, James A.

doi: 10.1007/s11538-024-01327-8pmid: 38954147

Classification of gene trees is an important task both in the analysis of multi-locus phylogenetic data, and assessment of the convergence of Markov Chain Monte Carlo (MCMC) analyses used in Bayesian phylogenetic tree reconstruction. The logistic regression model is one of the most popular classification models in statistical learning, thanks to its computational speed and interpretability. However, it is not appropriate to directly apply the standard logistic regression model to a set of phylogenetic trees, as the space of phylogenetic trees is non-Euclidean and thus contradicts the standard assumptions on covariates. It is well-known in tropical geometry and phylogenetics that the space of phylogenetic trees is a tropical linear space in terms of the max-plus algebra. Therefore, in this paper, we propose an analogue approach of the logistic regression model in the setting of tropical geometry. Our proposed method outperforms classical logistic regression in terms of Area under the ROC Curve in numerical examples, including with data generated by the multi-species coalescent model. Theoretical properties such as statistical consistency have been proved and generalization error rates have been derived. Finally, our classification algorithm is proposed as an MCMC convergence criterion for Mr Bayes. Unlike the convergence metric used by Mr Bayes which is only dependent on tree topologies, our method is sensitive to branch lengths and therefore provides a more robust metric for convergence. In a test case, it is illustrated that the tropical logistic regression can differentiate between two independently run MCMC chains, even when the standard metric cannot.

Chambers, Keith L.; Watson, Michael G.; Myerscough, Mary R.

doi: 10.1007/s11538-024-01333-wpmid: 38980556

Atherosclerotic plaques are fatty deposits that form in the walls of major arteries and are one of the major causes of heart attacks and strokes. Macrophages are the main immune cells in plaques and macrophage dynamics influence whether plaques grow or regress. Macrophage proliferation is a key process in atherosclerosis, particularly in the development of mid-stage plaques, but very few mathematical models include proliferation. In this paper we reframe the lipid-structured model of Ford et al. (J Theor Biol 479:48–63, 2019. https://doi.org/10.1016/j.jtbi.2019.07.003) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable. Steady state analysis indicates that proliferation assists in reducing eventual necrotic core lipid content and spreads the lipid load of the macrophage population amongst the cells. The contribution of plaque macrophages from proliferation relative to recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (defined as having the same lipid content and cell numbers) recruitment-dominant plaque in the way lipid is distributed amongst the macrophages. The macrophage lipid distribution of an equivalent proliferation-dominant plaque is less skewed and exhibits a local maximum near the endogenous lipid content.

Landsittel, Joseph A.; Ermentrout, G. Bard; Stiefel, Klaus M.

doi: 10.1007/s11538-024-01330-zpmid: 38937322

We used computer simulations of growth, mating and death of cephalopods and fishes to explore the effect of different life-history strategies on the relative prevalence of alternative male mating strategies. Specifically, we investigated the consequences of single or multiple matings per lifetime, mating strategy switching, cannibalism, resource stochasticity, and altruism towards relatives. We found that a combination of single (semelparous) matings, cannibalism and an absence of mating strategy changes in one lifetime led to a more strictly partitioned parameter space, with a reduced region where the two mating strategies co-exist in similar numbers. Explicitly including Hamilton’s rule in simulations of the social system of a Cichlid led to an increase of dominant males, at the expense of both sneakers and dwarf males (“super-sneakers”). Our predictions provide general bounds on the viable ratios of alternative male mating strategies with different life-histories, and under possibly rapidly changing ecological situations.

Korsah, Maame Akua; Johnston, Stuart T.; Tiedje, Kathryn E.; Day, Karen P.; Flegg, Jennifer A.; Walker, Camelia R.

doi: 10.1007/s11538-024-01321-0pmid: 38888640

Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.

Yosprakob, Tharana; Shyntar, Alexandra; Iworima, Diepiriye G.; Edelstein-Keshet, Leah

doi: 10.1007/s11538-024-01325-wpmid: 38916694

Human pluripotent stem cells (hPSCs) hold promise for regenerative medicine to replace essential cells that die or become dysfunctional. In some cases, these cells can be used to form clusters whose size distribution affects the growth dynamics. We develop models to predict cluster size distributions of hPSCs based on several plausible hypotheses, including (0) exponential growth, (1) surface growth, (2) Logistic growth, and (3) Gompertz growth. We use experimental data to investigate these models. A partial differential equation for the dynamics of the cluster size distribution is used to fit parameters (rates of growth, mortality, etc.). A comparison of the models using their mean squared error and the Akaike Information criterion suggests that Models 1 (surface growth) or 2 (Logistic growth) best describe the data.

Pant, Binod; Safdar, Salman; Santillana, Mauricio; Gumel, Abba B.

doi: 10.1007/s11538-024-01324-xpmid: 38888744

The COVID-19 pandemic has not only presented a major global public health and socio-economic crisis, but has also significantly impacted human behavior towards adherence (or lack thereof) to public health intervention and mitigation measures implemented in communities worldwide. This study is based on the use of mathematical modeling approaches to assess the extent to which SARS-CoV-2 transmission dynamics is impacted by population-level changes of human behavior due to factors such as (a) the severity of transmission (such as disease-induced mortality and level of symptomatic transmission), (b) fatigue due to the implementation of mitigation interventions measures (e.g., lockdowns) over a long (extended) period of time, (c) social peer-pressure, among others. A novel behavior-epidemiology model, which takes the form of a deterministic system of nonlinear differential equations, is developed and fitted using observed cumulative SARS-CoV-2 mortality data during the first wave in the United States. The model fits the observed data, as well as makes a more accurate prediction of the observed daily SARS-CoV-2 mortality during the first wave (March 2020–June 2020), in comparison to the equivalent model which does not explicitly account for changes in human behavior. This study suggests that, as more newly-infected individuals become asymptomatically-infectious, the overall level of positive behavior change can be expected to significantly decrease (while new cases may rise, particularly if asymptomatic individuals have higher contact rate, in comparison to symptomatic individuals).