**Close Encounters of the Cell Kind: The Impact of Contact Inhibition on Tumour Growth and Cancer Models.**

Abstract
Cancer is a complex phenomenon, and the sheer variation in behaviour across different types renders it difficult to ascertain underlying biological mechanisms. Experimental approaches frequently yield conflicting results for myriad reasons, and mathematical modelling of cancer is a vital tool to explore what we cannot readily measure, and ultimately improve treatment and prognosis. Like experiments, models are underpinned by certain biological assumptions, variation of which can lead to divergent predictions. An outstanding and important question concerns contact inhibition of proliferation (CIP), the obs...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Grimes DR, Fletcher AG **Tags: **Bull Math Biol **Source Type: **research

**Statistically consistent and computationally efficient inference of ancestral DNA sequences in the TKF91 model under dense taxon sampling.**

Abstract
In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and whose branchings indicate past speciation events. Phylogenetic analyses often rely on molecular sequences, such as DNA sequences, collected from the species of interest, and it is common in this context to employ statistical approaches based on stochastic models of sequence evolution on a tree. For tractability, such models necessarily make simplifying assumptions about the evolutionary mechanisms involved. In particular, commo...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Fan WT, Roch S **Tags: **Bull Math Biol **Source Type: **research

**A Current Perspective on Wound Healing and Tumour-Induced Angiogenesis.**

Abstract
Angiogenesis, or capillary growth from pre-existing vasculature, is an essential component of several physiological processes, both vital and pathological. These include dermal wound healing and tumour growth that together pose some of the most significant challenges to healthcare systems worldwide. Over the last few decades, mathematical modelling has proven to be a valuable tool for unravelling the complex network of interactions that underlie such processes. Moreover, theoretical frameworks that describe some of the mechanical and chemical aspects of angiogenesis inherent in wound healing and tumour gr...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Flegg JA, Menon SN, Byrne HM, McElwain DLS **Tags: **Bull Math Biol **Source Type: **research

**Approximations of Cumulants of the Stochastic Power Law Logistic Model.**

ll I
Abstract
Asymptotic approximations of the first three cumulants of the quasi-stationary distribution of the stochastic power law logistic model are derived. The results are based on a system of ODEs for the first three cumulants. We deviate from the classical moment closure approach by determining approximations without closing the system of equations. The approximations are explicit in the model's parameters, conditions for validity of the approximations are given, magnitudes of approximation errors are given, and spurious solutions are easily detected and eliminated. In these ways, we provide improvements o...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Nåsell I **Tags: **Bull Math Biol **Source Type: **research

**A Hybrid Model of Cartilage Regeneration Capturing the Interactions Between Cellular Dynamics and Porosity.**

Abstract
To accelerate the development of strategies for cartilage tissue engineering, models are necessary to investigate the interactions between cellular dynamics and the local microenvironment. We use a discrete framework to capture the individual behavior of cells, modeling experiments where cells are seeded in a porous scaffold or hydrogel and over the time course of a month, the scaffold slowly degrades while cells divide and synthesize extracellular matrix constituents. The movement of cells and the ability to proliferate is a function of the local porosity, defined as the volume fraction of fluid in the s...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Cassani S, Olson SD **Tags: **Bull Math Biol **Source Type: **research

**Mathematical Modelling of Auxin Transport in Plant Tissues: Flux Meets Signalling and Growth.**

Abstract
Plant hormone auxin has critical roles in plant growth, dependent on its heterogeneous distribution in plant tissues. Exactly how auxin transport and developmental processes such as growth coordinate to achieve the precise patterns of auxin observed experimentally is not well understood. Here we use mathematical modelling to examine the interplay between auxin dynamics and growth and their contribution to formation of patterns in auxin distribution in plant tissues. Mathematical models describing the auxin-related signalling pathway, PIN and AUX1 dynamics, auxin transport, and cell growth in plant tissues...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Allen HR, Ptashnyk M **Tags: **Bull Math Biol **Source Type: **research

**Additional Analytical Support for a New Method to Compute the Likelihood of Diversification Models.**

Abstract
Molecular phylogenies have been increasingly recognized as an important source of information on species diversification. For many models of macroevolution, analytical likelihood formulas have been derived to infer macroevolutionary parameters from phylogenies. A few years ago, a general framework to numerically compute such likelihood formulas was proposed, which accommodates models that allow speciation and/or extinction rates to depend on diversity. This framework calculates the likelihood as the probability of the diversification process being consistent with the phylogeny from the root to the tips. H...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Laudanno G, Haegeman B, Etienne RS **Tags: **Bull Math Biol **Source Type: **research

**Optimal Virulence, Diffusion and Tradeoffs.**

Abstract
In this work we propose a variant of a classical SIR epidemiological model where pathogens are characterized by a (phenotypic) mutant trait x. Imposing that the trait x mutates according to a random walk process and that it directly influences the epidemiological components of the pathogen, we studied its evolutionary development by interpreting the tenet of maximizing the basic reproductive number of the pathogen as an optimal control problem. Pontryagin's maximum principle was used to identify the possible optimal evolutionary strategies of the pathogen. Qualitatively, three types of optimal evolutionar...

**Source: **Bulletin of Mathematical Biology - January 22, 2020 **Category: **Bioinformatics **Authors: **Silva EJAD, Castilho C **Tags: **Bull Math Biol **Source Type: **research

**Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.**

Abstract
Invasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity, an alternative hypothesis presents itself: could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the c...

**Source: **Bulletin of Mathematical Biology - January 17, 2020 **Category: **Bioinformatics **Authors: **Strobl MAR, Krause AL, Damaghi M, Gillies R, Anderson ARA, Maini PK **Tags: **Bull Math Biol **Source Type: **research

**A Next-Generation Approach to Calculate Source-Sink Dynamics in Marine Metapopulations.**

Abstract
In marine systems, adult populations confined to isolated habitat patches can be connected by larval dispersal. Source-sink theory provides effective tools to quantify the effect of specific habitat patches on the dynamics of connected populations. In this paper, we construct the next-generation matrix for a marine metapopulation and demonstrate how it can be used to calculate the source-sink dynamics of habitat patches. We investigate the effect of environmental variables on the source-sink dynamics and demonstrate how the next-generation matrix can provide useful biological insight into transient as wel...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Harrington PD, Lewis MA **Tags: **Bull Math Biol **Source Type: **research

**The Timing and Nature of Behavioural Responses Affect the Course of an Epidemic.**

Abstract
During an epidemic, the interplay of disease and opinion dynamics can lead to outcomes that are different from those predicted based on disease dynamics alone. Opinions and the behaviours they elicit are complex, so modelling them requires a measure of abstraction and simplification. Here, we develop a differential equation model that couples SIR-type disease dynamics with opinion dynamics. We assume a spectrum of opinions that change based on current levels of infection as well as interactions that to some extent amplify the opinions of like-minded individuals. Susceptibility to infection is based on the...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Tyson RC, Hamilton SD, Lo AS, Baumgaertner BO, Krone SM **Tags: **Bull Math Biol **Source Type: **research

**Inside Dynamics of Integrodifference Equations with Mutations.**

Abstract
The method of inside dynamics provides a theory that can track the dynamics of neutral gene fractions in spreading populations. However, the role of mutations has so far been absent in the study of the gene flow of neutral fractions via inside dynamics. Using integrodifference equations, we develop a neutral genetic mutation model by extending a previously established scalar inside dynamics model. To classify the mutation dynamics, we define a mutation class as the set of neutral fractions that can mutate into one another. We show that the spread of neutral genetic fractions is dependent on the leading ed...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Marculis NG, Lewis MA **Tags: **Bull Math Biol **Source Type: **research

**Most Parsimonious Likelihood Exhibits Multiple Optima for Compatible Characters.**

Abstract
Maximum likelihood estimators are a popular method for scoring phylogenetic trees to best explain the evolutionary histories of biomolecular sequences. In 1994, Steel showed that, given an incompatible set of binary characters and a fixed tree topology, there exist multiple sets of branch lengths that are optima of the maximum average likelihood estimator. Since parsimony techniques-another popular method of scoring evolutionary trees-tend to exhibit favorable behavior on data compatible with the tree, Steel asked if the same is true for likelihood estimators, or if multiple optima can occur for compatibl...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Matsieva J, St John K **Tags: **Bull Math Biol **Source Type: **research

**Coinfection, Altered Vector Infectivity, and Antibody-Dependent Enhancement: The Dengue-Zika Interplay.**

Abstract
Although dengue and Zika cocirculation has increased within the past 5 years, very little is known about its epidemiological consequences. To investigate the effect of dengue and Zika cocirculation on the spread of both pathogens, we create a deterministic dengue and Zika coinfection model, the first to incorporate altered infectivity of mosquitoes (due to coinfection). The model also addresses increased infectivity due to antibody-dependent enhancement (ADE) within the human population. Central to our analysis is the derivation and interpretation of the basic reproductive number and invasion reprodu...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Olawoyin O, Kribs C **Tags: **Bull Math Biol **Source Type: **research

**The Optimal Age of Vaccination Against Dengue with an Age-Dependent Biting Rate with Application to Brazil.**

Abstract
In this paper we introduce a single serotype transmission model, including an age-dependent mosquito biting rate, to find the optimal vaccination age against dengue in Brazil with Dengvaxia. The optimal vaccination age and minimal lifetime expected risk of hospitalisation are found by adapting a method due to Hethcote (Math Biosci 89:29-52). Any number and combination of the four dengue serotypes DENv1-4 is considered. Successful vaccination against a serotype corresponds to a silent infection. The effects of antibody-dependent enhancement (ADE) and permanent cross-immunity after two heterologous infectio...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Maier SB, Massad E, Amaku M, Burattini MN, Greenhalgh D **Tags: **Bull Math Biol **Source Type: **research

**Overcoming Drug Resistance to BRAF Inhibitor.**

Abstract
One of the most frequently found mutations in human melanomas is in the B-raf gene, making its protein BRAF a key target for therapy. However, in patients treated with BRAF inhibitor (BRAFi), although the response is very good at first, relapse occurs within 6 months, on the average. In order to overcome this drug resistance to BRAFi, various combinations of BRAFi with other drugs have been explored, and some are being applied clinically, such as a combination of BRAF and MEK inhibitors. Experimental data for melanoma in mice show that under continuous treatment with BRAFi, the pro-cancer MDSCs and c...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Friedman A, Siewe N **Tags: **Bull Math Biol **Source Type: **research

**A Stochastic Model of DNA Double-Strand Breaks Repair Throughout the Cell Cycle.**

Abstract
Cell cycle phase is a decisive factor in determining the repair pathway of DNA double-strand breaks (DSBs) by non-homologous end joining (NHEJ) or homologous recombination (HR). Recent experimental studies revealed that 53BP1 and BRCA1 are the key mediators of the DNA damage response (DDR) with antagonizing roles in choosing the appropriate DSB repair pathway in G1, S, and G2 phases. Here, we present a stochastic model of biochemical kinetics involved in detecting and repairing DNA DSBs induced by ionizing radiation during the cell cycle progression. A three-dimensional stochastic process is defined to mo...

**Source: **Bulletin of Mathematical Biology - January 14, 2020 **Category: **Bioinformatics **Authors: **Mohseni-Salehi FS, Zare-Mirakabad F, Sadeghi M, Ghafouri-Fard S **Tags: **Bull Math Biol **Source Type: **research

**On the Regional Control of a Reaction-Diffusion System SIR.**

Abstract
This paper presents a study of regional optimal control strategies of a spatiotemporal SIR epidemic model which is formulated from existing SIR epidemic models by including a diffusion term. Our main objective is to characterize the two optimal controls that minimize the number of infected individuals, the corresponding vaccination and treatment costs. For that matter, we prove the existence of a pair of control and provide a characterization of optimal controls in terms of state and adjoint functions. Finally, we present numerical simulations on data concerning the evolution of the zoonotic Ebola virus i...

**Source: **Bulletin of Mathematical Biology - December 23, 2019 **Category: **Bioinformatics **Authors: **El Alami Laaroussi A, Rachik M **Tags: **Bull Math Biol **Source Type: **research

**Control of Intracellular Molecular Networks Using Algebraic Methods.**

Abstract
Many problems in biology and medicine have a control component. Often, the goal might be to modify intracellular networks, such as gene regulatory networks or signaling networks, in order for cells to achieve a certain phenotype, what happens in cancer. If the network is represented by a mathematical model for which mathematical control approaches are available, such as systems of ordinary differential equations, then this problem might be solved systematically. Such approaches are available for some other model types, such as Boolean networks, where structure-based approaches have been developed, as well...

**Source: **Bulletin of Mathematical Biology - December 23, 2019 **Category: **Bioinformatics **Authors: **Sordo Vieira L, Laubenbacher RC, Murrugarra D **Tags: **Bull Math Biol **Source Type: **research

**The Effect of Movement Behavior on Population Density in Patchy Landscapes.**

Abstract
Many biological populations reside in increasingly fragmented landscapes, where habitat quality may change abruptly in space. Individuals adjust their movement behavior to local habitat quality and show preferences for some habitat types over others. Several recent publications explore how such individual movement behavior affects population-level dynamics in a framework of reaction-diffusion systems that are coupled through discontinuous boundary conditions. While most of those works are based on linear analysis, we study positive steady states of the nonlinear equations. We prove existence, uniqueness a...

**Source: **Bulletin of Mathematical Biology - December 23, 2019 **Category: **Bioinformatics **Authors: **Zaker N, Ketchemen L, Lutscher F **Tags: **Bull Math Biol **Source Type: **research

**Modeling Antibiotic Use Strategies in Intensive Care Units: Comparing De-escalation and Continuation.**

Abstract
Antimicrobial de-escalation refers to the treatment mechanism of switching from empiric antibiotics with good coverage to alternatives based on laboratory susceptibility test results, with the aim of avoiding unnecessary use of broad-spectrum antibiotics. In a previous study, we have developed multi-strain and multi-drug models in an intensive care unit setting, to evaluate the benefits and trade-offs of de-escalation in comparison with the conventional strategy called antimicrobial continuation. Our simulation results indicated that for a large portion of credible parameter combinations, de-escalation re...

**Source: **Bulletin of Mathematical Biology - December 23, 2019 **Category: **Bioinformatics **Authors: **Huo X **Tags: **Bull Math Biol **Source Type: **research

**Surfing the Hyperbola Equations of the Steady-State Farquhar-von Caemmerer-Berry C3 Leaf Photosynthesis Model: What Can a Theoretical Analysis of Their Oblique Asymptotes and Transition Points Tell Us?**

Abstract
The asymptotes and transition points of the net CO2 assimilation (A/Ci) rate curves of the steady-state Farquhar-von Caemmerer-Berry (FvCB) model for leaf photosynthesis of C3 plants are examined in a theoretical study, which begins from the exploration of the standard equations of hyperbolae after rotating the coordinate system. The analysis of the A/Ci quadratic equations of the three limitation states of the FvCB model-abbreviated as Ac, Aj and Ap-allows us to conclude that their oblique asymptotes have a common slope that depends only on the mesophyll conductance to CO2 diffusion (gm). The limiting va...

**Source: **Bulletin of Mathematical Biology - December 23, 2019 **Category: **Bioinformatics **Authors: **Miranda-Apodaca J, Marcos-Barbero EL, Morcuende R, Arellano JB **Tags: **Bull Math Biol **Source Type: **research

**Predicting Pattern Formation in Multilayer Networks.**

Abstract
We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactions among oscillators in sustaining differences in both the phase and amplitude of oscillations leading to the formation of asynchronous patterns. Finally, we demonstrate the generalizability of our model's predictions through comparison with a more realistic multilayer model. Overall, our mod...

**Source: **Bulletin of Mathematical Biology - December 20, 2019 **Category: **Bioinformatics **Authors: **Hayes SM, Anderson KE **Tags: **Bull Math Biol **Source Type: **research

**Current Trends in Mathematical Epidemiology.**

PMID: 31724112 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - November 14, 2019 **Category: **Bioinformatics **Authors: **Arino J, Watmough J **Tags: **Bull Math Biol **Source Type: **research

**Transmission Dynamics and Control Mechanisms of Vector-Borne Diseases with Active and Passive Movements Between Urban and Satellite Cities.**

Abstract
A metapopulation model which explicitly integrates vector-borne and sexual transmission of an epidemic disease with passive and active movements between an urban city and a satellite city is formulated and analysed. The basic reproduction number of the disease is explicitly determined as a combination of sexual and vector-borne transmission parameters. The sensitivity analysis reveals that the disease is primarily transmitted via the vector-borne mode, rather than via sexual transmission, and that sexual transmission by itself may not initiate or sustain an outbreak. Also, increasing the population moveme...

**Source: **Bulletin of Mathematical Biology - October 23, 2019 **Category: **Bioinformatics **Authors: **Harvim P, Zhang H, Georgescu P, Zhang L **Tags: **Bull Math Biol **Source Type: **research

**Modelling Biological Evolution: Developing Novel Approaches.**

PMID: 31617043 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - October 15, 2019 **Category: **Bioinformatics **Authors: **Morozov A **Tags: **Bull Math Biol **Source Type: **research

**Catch Me If You Can: A Spatial Model for a Brake-Driven Gene Drive Reversal.**

rre F
Abstract
Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may, however, have to be stopped. "Antidotes" (brakes) have been suggested, but have been so far only studied in well-mixed populations. Here, we consider a reaction-diffusion system modeling the release of a gene drive (of fitness [Formula: see text]) and a brake (fitness [Formula: see text], [Formula: see text]) in a wild-type population (fitness 1). We prov...

**Source: **Bulletin of Mathematical Biology - October 12, 2019 **Category: **Bioinformatics **Authors: **Girardin L, Calvez V, Débarre F **Tags: **Bull Math Biol **Source Type: **research

**A Population Dynamics Model of Mosquito-Borne Disease Transmission, Focusing on Mosquitoes' Biased Distribution and Mosquito Repellent Use.**

We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the model clearly shows the existence of thresholds for mosquito repellent efficacy and its utilization rate in the human population with respect to the elimination of mosquito-borne diseases. Further, the results imply that the suppression of mosquito-borne diseases becomes more difficult when the mosquitoe...

**Source: **Bulletin of Mathematical Biology - October 8, 2019 **Category: **Bioinformatics **Authors: **Aldila D, Seno H **Tags: **Bull Math Biol **Source Type: **research

**Turing Instability and Colony Formation in Spatially Extended Rosenzweig-MacArthur Predator-Prey Models with Allochthonous Resources.**

Abstract
While it is somewhat well known that spatial PDE extensions of the Rosenzweig-MacArthur predator-prey model do not admit spatial pattern formation through the Turing mechanism, in this paper we demonstrate that the addition of allochthonous resources into the system can result in spatial patterning and colony formation. We study pattern formation, through Turing and Turing-Hopf mechanisms, in two distinct spatial Rosenzweig-MacArthur models generalized to include allochthonous resources. Both models have previously been shown to admit heterogeneous spatial solutions when prey and allochthonous resources a...

**Source: **Bulletin of Mathematical Biology - October 8, 2019 **Category: **Bioinformatics **Authors: **Zhou Z, Van Gorder RA **Tags: **Bull Math Biol **Source Type: **research

**Modelling the Host Immune Response to Mature and Immature Dengue Viruses.**

Abstract
Immature dengue virions contained in patient blood samples are essentially not infectious because the uncleaved surface protein prM renders them incompetent for membrane fusion. However, the immature virions regain full infectivity when they interact with anti-prM antibodies, and once opsonised virion fusion into Fc receptor-expressing cells is facilitated. We propose a within-host mathematical model for the immune response which takes into account the dichotomy between mature infectious and immature noninfectious dengue virions. The model accounts for experimental observations on the different interactio...

**Source: **Bulletin of Mathematical Biology - September 20, 2019 **Category: **Bioinformatics **Authors: **Borisov M, Dimitriu G, Rashkov P **Tags: **Bull Math Biol **Source Type: **research

**Compensatory Foraging in Stoichiometric Producer-Grazer Models.**

Abstract
Nutritional constraints are common as food resources are rarely optimally suited for grazing species. Elemental mismatches between trophic levels can influence population growth and foraging behaviors. Grazing species, such as Daphnia, utilize optimal foraging techniques, such as compensatory feeding. Here, we develop two stoichiometric producer-grazer models, a base model that incorporates a fixed energetic foraging cost and an optimal foraging model where energetic foraging costs depend on food nutritional content. A variable energetic foraging cost results in cell quota-dependent predation behaviors. A...

**Source: **Bulletin of Mathematical Biology - September 20, 2019 **Category: **Bioinformatics **Authors: **Peace A, Wang H **Tags: **Bull Math Biol **Source Type: **research

**Revealing Evolutionarily Optimal Strategies in Self-Reproducing Systems via a New Computational Approach.**

Abstract
Modelling the evolution of complex life history traits and behavioural patterns observed in the natural world is a challenging task. Here, we develop a novel computational method to obtain evolutionarily optimal life history traits/behavioural patterns in population models with a strong inheritance. The new method is based on the reconstruction of evolutionary fitness using underlying equations for population dynamics and it can be applied to self-reproducing systems (including complicated age-structured models), where fitness does not depend on initial conditions, however, it can be extended to some freq...

**Source: **Bulletin of Mathematical Biology - September 20, 2019 **Category: **Bioinformatics **Authors: **Sandhu SK, Morozov A, Kuzenkov O **Tags: **Bull Math Biol **Source Type: **research

**An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination.**

Abstract
We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability ...

**Source: **Bulletin of Mathematical Biology - September 12, 2019 **Category: **Bioinformatics **Authors: **Magal P, Webb GF, Wu Y **Tags: **Bull Math Biol **Source Type: **research

**Resilience Analysis for Competing Populations.**

aga D
Abstract
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime shifts, characterizing the influence of the system parameters on resilience is the first step toward controlling the system to avoid undesirable critical transitions. In this paper, we apply tools of qualitative theory of differential equations to study the resilience of competing populations as modeled by the classical Lotka-Volterra system. Within the high interspec...

**Source: **Bulletin of Mathematical Biology - August 30, 2019 **Category: **Bioinformatics **Authors: **César Fassoni A, Carvalho Braga D **Tags: **Bull Math Biol **Source Type: **research

**Antibody-Mediated Immobilization of Virions in Mucus.**

Abstract
Antibodies have been shown to hinder the movement of herpes simplex virus virions in cervicovaginal mucus, as well as other viruses in other mucus secretions. However, it has not been possible to directly observe the mechanisms underlying this phenomenon, so the nature of virion-antibody-mucin interactions remain poorly understood. In this work, we analyzed thousands of virion traces from single particle tracking experiments to explicate how antibodies must cooperate to immobilize virions for relatively long time periods. First, using a clustering analysis, we observed a clear separation between two class...

**Source: **Bulletin of Mathematical Biology - August 29, 2019 **Category: **Bioinformatics **Authors: **Jensen MA, Wang YY, Lai SK, Forest MG, McKinley SA **Tags: **Bull Math Biol **Source Type: **research

**How Spatial Heterogeneity Affects Transient Behavior in Reaction-Diffusion Systems for Ecological Interactions?**

Abstract
Most studies of ecological interactions study asymptotic behavior, such as steady states and limit cycles. The transient behavior, i.e., qualitative aspects of solutions as and before they approach their asymptotic state, may differ significantly from asymptotic behavior. Understanding transient dynamics is crucial to predicting ecosystem responses to perturbations on short timescales. Several quantities have been proposed to measure transient dynamics in systems of ordinary differential equations. Here, we generalize these measures to reaction-diffusion systems in a rigorous way and prove various relatio...

**Source: **Bulletin of Mathematical Biology - August 23, 2019 **Category: **Bioinformatics **Authors: **Wang X, Efendiev M, Lutscher F **Tags: **Bull Math Biol **Source Type: **research

**Multiple Scale Homogenisation of Nutrient Movement and Crop Growth in Partially Saturated Soil.**

Abstract
In this paper, we use multiple scale homogenisation to derive a set of averaged macroscale equations that describe the movement of nutrients in partially saturated soil that contains growing potato tubers. The soil is modelled as a poroelastic material, which is deformed by the growth of the tubers, where the growth of each tuber is dependent on the uptake of nutrients via a sink term within the soil representing root nutrient uptake. Special attention is paid to the reduction in void space, resulting change in local water content and the impact on nutrient diffusion within the soil as the tubers increase...

**Source: **Bulletin of Mathematical Biology - August 22, 2019 **Category: **Bioinformatics **Authors: **Duncan SJ, Daly KR, McKay Fletcher DM, Ruiz S, Sweeney P, Roose T **Tags: **Bull Math Biol **Source Type: **research

**Lift and Drag Acting on the Shell of the American Horseshoe Crab (Limulus polyphemus).**

This study provides a preliminary foundation for assessing the relationship between documented morphological variation and potential environmental variation for distinct populations of horseshoe crabs along the Atlantic Coast. It also motivates future studies which could consider the stability of the horseshoe crab in unsteady, oscillating flows.
PMID: 31435839 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - August 21, 2019 **Category: **Bioinformatics **Authors: **Davis AL, Hoover AP, Miller LA **Tags: **Bull Math Biol **Source Type: **research

**Within-Host Viral Dynamics in a Multi-compartmental Environment.**

Abstract
The discrepancy in the turnover of cells and virus in different organs or viral reservoirs necessitates the investigation of multiple compartments within a host. Establishing a multi-compartmental structure that describes the complexity of various organs, where viral infection comprehensively proceeds, provides a modeling framework for exploring the effect of spatial heterogeneity on viral dynamics. To successfully suppress within-host viral replication, it is imperative to determine drug administration during therapy, particularly for a combination of antiretroviral drugs. The proposed model provides qua...

**Source: **Bulletin of Mathematical Biology - August 20, 2019 **Category: **Bioinformatics **Authors: **Chen SS, Cheng CY, Rong L **Tags: **Bull Math Biol **Source Type: **research

**Invasion Dynamics in an Intraguild Predation System with Predator-Induced Defense.**

In this study, adaptive predator-induced and fitness-dependent defense of the intermediate predator is included into the model. In contrast to previous studies, this is done without an artificial bounding term. Numerical bifurcation software is used to show that adaptive defense mechanisms can significantly enhance parameter regimes leading to coexistence. Two different adaptation parameters are distinguished and linked to adaptations under different environmental conditions. The results indicate that the form of the reactivity-accuracy trade-off depends on the state of the environment. Finally, it is shown that an impact ...

**Source: **Bulletin of Mathematical Biology - August 20, 2019 **Category: **Bioinformatics **Authors: **Köhnke MC **Tags: **Bull Math Biol **Source Type: **research

**Analytical Solution and Exposure Analysis of a Pharmacokinetic Model with Simultaneous Elimination Pathways and Endogenous Production: The Case of Multiple Dosing Administration.**

Abstract
In this paper, a typical pharmacokinetic (PK) model is studied for the case of multiple intravenous bolus-dose administration. This model, of one-compartment structure, not only exhibits simultaneous first-order and Michaelis-Menten elimination, but also involves a constant endogenous production. For the PK characterization of the model, we have established the closed-form solution of concentrations over time, the existence and local stability of the steady state. Using analytical approaches and the concept of corrected concentration, we have shown that the area under the curve ([Formula: see text]) at st...

**Source: **Bulletin of Mathematical Biology - August 16, 2019 **Category: **Bioinformatics **Authors: **Wu X, Nekka F, Li J **Tags: **Bull Math Biol **Source Type: **research

**Correction to: A Multi-stage Representation of Cell Proliferation as a Markov Process.**

Abstract
Equations (9) and (10) were transcribed incorrectly.
PMID: 31396787 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - August 8, 2019 **Category: **Bioinformatics **Authors: **Yates CA, Ford MJ, Mort RL **Tags: **Bull Math Biol **Source Type: **research

**A Spatially Resolved and Quantitative Model of Early Atherosclerosis.**

Abstract
Atherosclerosis is a major burden for all societies, and there is a great need for a deeper understanding of involved key inflammatory, immunological and biomechanical processes. A decisive step for the prevention and medical treatment of atherosclerosis is to predict what conditions determine whether early atherosclerotic plaques continue to grow, stagnate or become regressive. The driving biological and mechanobiological mechanisms that determine the stability of plaques are yet not fully understood. We develop a spatially resolved and quantitative mathematical model of key contributors of early atheros...

**Source: **Bulletin of Mathematical Biology - August 7, 2019 **Category: **Bioinformatics **Authors: **Thon MP, Myerscough MR, Gee MW **Tags: **Bull Math Biol **Source Type: **research

**A Mathematical Model for the Effect of Low-Dose Radiation on the G2/M Transition.**

Abstract
We develop a mathematical model to study the immediate effect of low-dose radiation on the G2 checkpoint and the G2/M transition of the cell cycle via a radiation pathway (the ATM-Chk2 pathway) of an individual mammalian cell. The model consists of a system of nonlinear differential equations describing the dynamics of a network of regulatory proteins that play key roles in the G2/M transition, cell cycle oscillations, and the radiation pathway. We simulate the application of a single pulse of low-dose radiation at different intensities ([Formula: see text] 0-0.4 Gy) and times during the latter ...

**Source: **Bulletin of Mathematical Biology - August 7, 2019 **Category: **Bioinformatics **Authors: **Contreras C, Carrero G, de Vries G **Tags: **Bull Math Biol **Source Type: **research

**On the Three Properties of Stationary Populations and Knotting with Non-stationary Populations.**

Abstract
A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is nonzero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these important properties is that SPI can be applied to partition a population into stationary and non-stationary components. These propert...

**Source: **Bulletin of Mathematical Biology - August 2, 2019 **Category: **Bioinformatics **Authors: **Rao ASRS, Carey JR **Tags: **Bull Math Biol **Source Type: **research

**A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics.**

Abstract
Mathematical models that are based on differential equations require detailed knowledge about the parameters that are included in the equations. Some of the parameters can be measured experimentally while others need to be estimated. When the models become more sophisticated, such as in the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), several strategies can be tried. It is possible to use parameter estimation on an analytical approximation of the solution to the multiscale model equations, namely the long-term approximation, but this limits ...

**Source: **Bulletin of Mathematical Biology - July 23, 2019 **Category: **Bioinformatics **Authors: **Reinharz V, Churkin A, Lewkiewicz S, Dahari H, Barash D **Tags: **Bull Math Biol **Source Type: **research

**On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg-Marquardt Algorithm with Broyden's Rank-one Updates for the Jacobian Operator.**

Abstract
Rigorously calibrating dynamic models with time-series data can pose roadblocks. Oftentimes, the problem is ill-posed and one has to rely on appropriate regularization techniques to ensure stable parameter estimation from which forward projections with quantified uncertainty could be generated. If the inversion procedure is cast as nonlinear least squares constrained by a system of nonlinear differential equations, then the system has to be solved numerically at every step of the iterative process and the corresponding parameter-to-data map cannot be used to evaluate the Fréchet derivative analytic...

**Source: **Bulletin of Mathematical Biology - July 23, 2019 **Category: **Bioinformatics **Authors: **Smirnova A, Sirb B, Chowell G **Tags: **Bull Math Biol **Source Type: **research

**Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to.**

Abstract
The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735-1741, 1977; Norton in Can Res 48:7067-7071, 1988; Hahnfeldt et al. in Can Res 59:4770-4775, 1999; Anderson et al. in Comput Math Methods Med 2:129-154, 2000. https://doi.org/10.1080/10273660008833042 ; Michor et al. in...

**Source: **Bulletin of Mathematical Biology - July 23, 2019 **Category: **Bioinformatics **Authors: **Brady R, Enderling H **Tags: **Bull Math Biol **Source Type: **research

**Multistationarity in the Space of Total Concentrations for Systems that Admit a Monomial Parametrization.**

Abstract
We apply tools from real algebraic geometry to the problem of multistationarity of chemical reaction networks. A particular focus is on the case of reaction networks whose steady states admit a monomial parametrization. For such systems, we show that in the space of total concentrations multistationarity is scale invariant: If there is multistationarity for some value of the total concentrations, then there is multistationarity on the entire ray containing this value (possibly for different rate constants)-and vice versa. Moreover, for these networks it is possible to decide about multistationarity indepe...

**Source: **Bulletin of Mathematical Biology - July 22, 2019 **Category: **Bioinformatics **Authors: **Conradi C, Iosif A, Kahle T **Tags: **Bull Math Biol **Source Type: **research

**Analysis of a Length-Structured Density-Dependent Model for Fish.**

We present a length-structured matrix model for fish populations in which the probability that a fish grows into the next length class is a decreasing nonlinear function of the total biomass of the population. We present mathematical results classifying the dynamics that this density-dependent model predicts. We illustrate these results with numerical simulations for an invasive white perch population and show how the mathematical results can be used to predict the persistence and/or boundedness of the population as well as an equilibrium structure that is dominated by small fish. We illustrate the results with management ...

**Source: **Bulletin of Mathematical Biology - July 22, 2019 **Category: **Bioinformatics **Authors: **Callahan J, Eager E, Rebarber R, Strawbridge E, Yuan S **Tags: **Bull Math Biol **Source Type: **research