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Bulletin of Mathematical Biology

S Sugaya, V M Kenkre
The process of transmission of infection in epidemics is analyzed by studying a pair of random walkers, the motion of each of which in two dimensions is confined spatially by the action of a quadratic potential centered at different locations for the two walks. The walkers are animals such as rodents in considerations of the Hantavirus epidemic, infected or susceptible. In this reaction-diffusion study, the reaction is the transmission of infection, and the confining potential represents the tendency of the animals to stay in the neighborhood of their home range centers...
October 12, 2018: Bulletin of Mathematical Biology
Eduard Campillo-Funollet, Chandrasekhar Venkataraman, Anotida Madzvamuse
In this study, we apply the Bayesian paradigm for parameter identification to a well-studied semi-linear reaction-diffusion system with activator-depleted reaction kinetics, posed on stationary as well as evolving domains. We provide a mathematically rigorous framework to study the inverse problem of finding the parameters of a reaction-diffusion system given a final spatial pattern. On the stationary domain the parameters are finite-dimensional, but on the evolving domain we consider the problem of identifying the evolution of the domain, i...
October 11, 2018: Bulletin of Mathematical Biology
Ankit Gupta, Mustafa Khammash
We consider the problem of estimating parameter sensitivities for stochastic models of multiscale reaction networks. These sensitivity values are important for model analysis, and the methods that currently exist for sensitivity estimation mostly rely on simulations of the stochastic dynamics. This is problematic because these simulations become computationally infeasible for multiscale networks due to reactions firing at several different timescales. However it is often possible to exploit the multiscale property to derive a "model reduction" and approximate the dynamics as a Piecewise deterministic Markov process, which is a hybrid process consisting of both discrete and continuous components...
October 9, 2018: Bulletin of Mathematical Biology
Shaimaa A Azoz, Daniel Coombs
The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth-death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time...
October 8, 2018: Bulletin of Mathematical Biology
Koyel Chakravarty, D C Dalal
The objective of the present study is to mathematically model the integrated kinetics of drug release in a polymeric matrix and its ensuing drug transport to the encompassing biological tissue. The model embodies drug diffusion, dissolution, solubilization, polymer degradation and dissociation/recrystallization phenomena in the polymeric matrix accompanied by diffusion, advection, reaction, internalization and specific/nonspecific binding in the biological tissue. The model is formulated through a system of nonlinear partial differential equations which are solved numerically in association with pertinent set of initial, interface and boundary conditions using suitable finite difference scheme...
October 8, 2018: Bulletin of Mathematical Biology
Manon Deville, Roberto Natalini, Clair Poignard
We propose a mathematical model to describe enzyme-based tissue degradation in cancer therapies. The proposed model combines the poroelastic theory of mixtures with the transport of enzymes or drugs in the extracellular space. The effect of the matrix-degrading enzymes on the tissue composition and its mechanical response are accounted for. Numerical simulations in 1D, 2D and axisymmetric (3D) configurations show how an injection of matrix-degrading enzymes alters the porosity of a biological tissue. We eventually exhibit numerically the main consequences of a matrix-degrading enzyme pretreatment in the framework of chemotherapy: the removal of the diffusive hindrance to the penetration of therapeutic molecules in tumors and the reduction of interstitial fluid pressure which improves transcapillary transport...
October 5, 2018: Bulletin of Mathematical Biology
Louise A Bowler, David J Gavaghan, Gary R Mirams, Jonathan P Whiteley
Distinct electrophysiological phenotypes are exhibited by biological cells that have differentiated into particular cell types. The usual approach when simulating the cardiac electrophysiology of tissue that includes different cell types is to model the different cell types as occupying spatially distinct yet coupled regions. Instead, we model the electrophysiology of well-mixed cells by using homogenisation to derive an extension to the commonly used monodomain or bidomain equations. These new equations permit spatial variations in the distribution of the different subtypes of cells and will reduce the computational demands of solving the governing equations...
October 5, 2018: Bulletin of Mathematical Biology
Justin Eilertsen, Santiago Schnell
As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis-Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis-Menten equations...
October 4, 2018: Bulletin of Mathematical Biology
Sangeeta Bhatia, Pedro Feijão, Andrew R Francis
Modellers of large-scale genome rearrangement events, in which segments of DNA are inverted, moved, swapped, or even inserted or deleted, have found a natural syntax in the language of permutations. Despite this, there has been a wide range of modelling choices, assumptions and interpretations that make navigating the literature a significant challenge. Indeed, even authors of papers that use permutations to model genome rearrangement can struggle to interpret each others' work, because of subtle differences in basic assumptions that are often deeply ingrained (and consequently sometimes not even mentioned)...
October 4, 2018: Bulletin of Mathematical Biology
Sha He, Sanyi Tang, Yanni Xiao, Robert A Cheke
The impact of air pollution on people's health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6 year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi'an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm...
October 2, 2018: Bulletin of Mathematical Biology
Venta Terauds, Jeremy Sumner
The calculation of evolutionary distance via models of genome rearrangement has an inherent combinatorial complexity. Various algorithms and estimators have been used to address this; however, many of these set quite specific conditions for the underlying model. A recently proposed technique, applying representation theory to calculate evolutionary distance between circular genomes as a maximum likelihood estimate, reduces the computational load by converting the combinatorial problem into a numerical one. We show that the technique may be applied to models with any choice of rearrangements and relative probabilities thereof; we then investigate the symmetry of circular genome rearrangement models in general...
September 27, 2018: Bulletin of Mathematical Biology
Alexander Erlich, Derek E Moulton, Alain Goriely
Biological growth is often driven by mechanical cues, such as changes in external pressure or tensile loading. Moreover, it is well known that many living tissues actively maintain a preferred level of mechanical internal stress, called the mechanical homeostasis. The tissue-level feedback mechanism by which changes in the local mechanical stresses affect growth is called a growth law within the theory of morphoelasticity, a theory for understanding the coupling between mechanics and geometry in growing and evolving biological materials...
September 21, 2018: Bulletin of Mathematical Biology
Santiago Schnell
The nature of scientific research in mathematical and computational biology allows editors and reviewers to evaluate the findings of a scientific paper. Replication of a research study should be the minimum standard for judging its scientific claims and considering it for publication. This requires changes in the current peer review practice and a strict adoption of a replication policy similar to those adopted in experimental fields such as organic synthesis. In the future, the culture of replication can be easily adopted by publishing papers through dynamic computational notebooks combining formatted text, equations, computer algebra and computer code...
September 19, 2018: Bulletin of Mathematical Biology
Hector Baños, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Pamela E Harris, Robert Krone, Colby Long, Allen Stewart, Robert Walker
Mixtures of group-based Markov models of evolution correspond to joins of toric varieties. In this paper, we establish a large number of cases for which these phylogenetic join varieties realize their expected dimension, meaning that they are nondefective. Nondefectiveness is not only interesting from a geometric point-of-view, but has been used to establish combinatorial identifiability for several classes of phylogenetic mixture models. Our focus is on group-based models where the equivalence classes of identified parameters are orbits of a subgroup of the automorphism group of the abelian group defining the model...
September 17, 2018: Bulletin of Mathematical Biology
Min K Roh
As mathematical models and computational tools become more sophisticated and powerful to accurately depict system dynamics, numerical methods that were previously considered computationally impractical started being utilized for large-scale simulations. Methods that characterize a rare event in biochemical systems are part of such phenomenon, as many of them are computationally expensive and require high-performance computing. In this paper, we introduce an enhanced version of the doubly weighted stochastic simulation algorithm (dwSSA) (Daigle et al...
September 17, 2018: Bulletin of Mathematical Biology
Majid Latif, Elebeoba E May
Bacterial biofilm formation is an organized collective response to biochemical cues that enables bacterial colonies to persist and withstand environmental insults. We developed a multiscale agent-based model that characterizes the intracellular, extracellular, and cellular scale interactions that modulate Escherichia coli MG1655 biofilm formation. Each bacterium's intracellular response and cellular state were represented as an outcome of interactions with the environment and neighboring bacteria. In the intracellular model, environment-driven gene expression and metabolism were captured using statistical regression and Michaelis-Menten kinetics, respectively...
September 14, 2018: Bulletin of Mathematical Biology
Maria E Orive, Robert D Holt, Michael Barfield
Populations subject to substantial environmental change that decreases absolute fitness (expected number of offspring per individual) to less than one must adapt to persist. The probability of adaptive evolutionary rescue may be influenced by factors intrinsic to the organism itself, or by features specific to the individual population and its environment. An important question (given the increasing prevalence of environmental change) is the predictability of evolutionary rescue. We used an individual-based simulation model and a related analytic model to examine population persistence, given a continuously changing environment that leads to a linear change in the optimum for a phenotypic trait under selection...
September 14, 2018: Bulletin of Mathematical Biology
Roger Cropp, John Norbury
Pollination interactions are common, and their maintenance is critical for many food crops upon which human populations depend. Pollination is a mutualism interaction; together with predation and competition, mutualism makes up the triumvirate of fundamental interactions that control population dynamics. Here we examine pollination interactions (nectar reward for gamete transport service) using a simple heuristic model similar to the Lotka-Volterra models that have underpinned our understanding of predation and competition so effectively since the 1920s...
September 12, 2018: Bulletin of Mathematical Biology
Ruriko Yoshida, Leon Zhang, Xu Zhang
Principal component analysis is a widely used method for the dimensionality reduction of a given data set in a high-dimensional Euclidean space. Here we define and analyze two analogues of principal component analysis in the setting of tropical geometry. In one approach, we study the Stiefel tropical linear space of fixed dimension closest to the data points in the tropical projective torus; in the other approach, we consider the tropical polytope with a fixed number of vertices closest to the data points. We then give approximative algorithms for both approaches and apply them to phylogenetics, testing the methods on simulated phylogenetic data and on an empirical dataset of Apicomplexa genomes...
September 11, 2018: Bulletin of Mathematical Biology
Damian Clancy
For a susceptible-infectious-susceptible infection model in a heterogeneous population, we derive simple and precise estimates of mean persistence time, from a quasi-stationary endemic state to extinction of infection. Heterogeneity may be in either individuals' levels of infectiousness or of susceptibility, as well as in individuals' infectious period distributions. Infectious periods are allowed to follow arbitrary non-negative distributions. We also obtain a new and accurate approximation to the quasi-stationary distribution of the process, as well as demonstrating the use of our estimates to investigate the effects of different forms of heterogeneity...
September 11, 2018: Bulletin of Mathematical Biology
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