**Modeling the Effect of Memory in the Adaptive Immune Response.**

Abstract
It is well understood that there are key differences between a primary immune response and subsequent responses. Specifically, memory T cells that remain after a primary response drive the clearance of antigen in later encounters. While the existence of memory T cells is widely accepted, the specific mechanisms that govern their function are generally debated. In this paper, we develop a mathematical model of the immune response. This model follows the creation, activation, and regulation of memory T cells, which allows us to explore the differences between the primary and secondary immune responses. Thro...

**Source: **Bulletin of Mathematical Biology - September 14, 2020 **Category: **Bioinformatics **Authors: **Wyatt A, Levy D **Tags: **Bull Math Biol **Source Type: **research

**Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model.**

Abstract
We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where the expected sequence lengths tend to infinity, we show that no consistent distance estimation is possible from sequence lengths alone. More formally, we establish that the distributions of pairs of sequence lengths at different distances cannot be distinguished with probability going to one.
PMID: 32920679 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - September 13, 2020 **Category: **Bioinformatics **Authors: **Fan WL, Legried B, Roch S **Tags: **Bull Math Biol **Source Type: **research

**Epidemic Dynamics and Adaptive Vaccination Strategy: Renewal Equation Approach.**

Abstract
We use analytical methods to investigate a continuous vaccination strategy's effects on the infectious disease dynamics in a closed population and a demographically open population. The methodology and key assumptions are based on Breda et al. (J Biol Dyn 6(Sup2):103-117, 2012). We show that the cumulative force of infection for the closed population and the endemic force of infection in the demographically open population can be reduced significantly by combining two factors: the vaccine effectiveness and the vaccination rate. The impact of these factors on the force of infection can transform an endemic...

**Source: **Bulletin of Mathematical Biology - September 13, 2020 **Category: **Bioinformatics **Authors: **Nzokem A, Madras N **Tags: **Bull Math Biol **Source Type: **research

**Traveling Waves and Estimation of Minimal Wave Speed for a Diffusive Influenza Model with Multiple Strains.**

Abstract
Antiviral treatment remains one of the key pharmacological interventions against influenza pandemic. However, widespread use of antiviral drugs brings with it the danger of drug resistance evolution. To assess the risk of the emergence and diffusion of resistance, in this paper, we develop a diffusive influenza model where influenza infection involves both drug-sensitive and drug-resistant strains. We first analyze its corresponding reaction model, whose reproduction numbers and equilibria are derived. The results show that the sensitive strains can be eliminated by treatment. Then, we establish the exist...

**Source: **Bulletin of Mathematical Biology - September 13, 2020 **Category: **Bioinformatics **Authors: **Chen G, Fu X, Sun M **Tags: **Bull Math Biol **Source Type: **research

**Mathematical Biology: Expand, Expose, and Educate!**

This article examines the need to expand, expose, and educate others about mathematical biology. To support field expansion, we give several recommendations of ways to integrate mathematics applied curricula to attract broader student interest. With this exposure-whether it is led by an individual, a department, a university, or researchers in mathematical biology-each can help to promote a base knowledge and appreciation of the field. In order to encourage the next generation of researchers to consider mathematical biology, we highlight current interdisciplinary programs, share popular mathematical tools, and present some...

**Source: **Bulletin of Mathematical Biology - September 10, 2020 **Category: **Bioinformatics **Authors: **Lee S, Clinedinst L **Tags: **Bull Math Biol **Source Type: **research

**Learning Equations from Biological Data with Limited Time Samples.**

We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval e...

**Source: **Bulletin of Mathematical Biology - September 9, 2020 **Category: **Bioinformatics **Authors: **Nardini JT, Lagergren JH, Hawkins-Daarud A, Curtin L, Morris B, Rutter EM, Swanson KR, Flores KB **Tags: **Bull Math Biol **Source Type: **research

**Mathematical Biology Education: Changes, Communities, Connections, and Challenges.**

PMID: 32888094 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - September 4, 2020 **Category: **Bioinformatics **Authors: **Jungck JR, Robeva R, Gross LJ **Tags: **Bull Math Biol **Source Type: **research

**Optimal Control of the COVID-19 Pandemic with Non-pharmaceutical Interventions.**

e;a G
Abstract
The COVID-19 pandemic has forced societies across the world to resort to social distancing to slow the spread of the SARS-CoV-2 virus. Due to the economic impacts of social distancing, there is growing desire to relax these measures. To characterize a range of possible strategies for control and to understand their consequences, we performed an optimal control analysis of a mathematical model of SARS-CoV-2 transmission. Given that the pandemic is already underway and controls have already been initiated, we calibrated our model to data from the USA and focused our analysis on optimal controls from M...

**Source: **Bulletin of Mathematical Biology - September 4, 2020 **Category: **Bioinformatics **Authors: **Perkins TA, España G **Tags: **Bull Math Biol **Source Type: **research

**Detailed Balance [Formula: see text] Complex Balance [Formula: see text] Cycle Balance: A Graph-Theoretic Proof for Reaction Networks and Markov Chains.**

i B
Abstract
We further clarify the relation between detailed-balanced and complex-balanced equilibria of reversible chemical reaction networks. Our results hold for arbitrary kinetics and also for boundary equilibria. Detailed balance, complex balance, "formal balance," and the new notion of "cycle balance" are all defined in terms of the underlying graph. This fact allows elementary graph-theoretic (non-algebraic) proofs of a previous result (detailed balance = complex balance + formal balance), our main result (detailed balance = complex balance + cycle balance), and a corresponding result i...

**Source: **Bulletin of Mathematical Biology - September 3, 2020 **Category: **Bioinformatics **Authors: **Müller S, Joshi B **Tags: **Bull Math Biol **Source Type: **research

**The Case for Algebraic Biology: from Research to Education.**

Abstract
Though it goes without saying that linear algebra is fundamental to mathematical biology, polynomial algebra is less visible. In this article, we will give a brief tour of four diverse biological problems where multivariate polynomials play a central role-a subfield that is sometimes called algebraic biology. Namely, these topics include biochemical reaction networks, Boolean models of gene regulatory networks, algebraic statistics and genomics, and place fields in neuroscience. After that, we will summarize the history of discrete and algebraic structures in mathematical biology, from their early appeara...

**Source: **Bulletin of Mathematical Biology - August 20, 2020 **Category: **Bioinformatics **Authors: **Macauley M, Youngs N **Tags: **Bull Math Biol **Source Type: **research

**Effects of Latency on Estimates of the COVID-19 Replication Number.**

Abstract
There is continued uncertainty in how long it takes a person infected by the COVID-19 virus to become infectious. In this paper, we quantify how this uncertainty affects estimates of the basic replication number [Formula: see text], and thus estimates of the fraction of the population that would become infected in the absence of effective interventions. The analysis is general, and applies to all SEIR-based models, not only those associated with COVID-19. We find that when modeling a rapidly spreading epidemic, seemingly minor differences in how latency is treated can lead to vastly different estimates of...

**Source: **Bulletin of Mathematical Biology - August 20, 2020 **Category: **Bioinformatics **Authors: **Sadun L **Tags: **Bull Math Biol **Source Type: **research

**A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations.**

Abstract
We study traveling waves in a non-local cross-diffusion-type model, where organisms move along gradients in population densities. Such models are valuable for understanding waves of migration and invasion and how directed motion can impact such scenarios. In this paper, we demonstrate the emergence of traveling wave solutions, studying properties of both planar and radial wave fronts in one- and two-species variants of the model. We compute exact traveling wave solutions in the purely diffusive case and then perturb these solutions to analytically capture the influence directed motion has on these exact s...

**Source: **Bulletin of Mathematical Biology - August 11, 2020 **Category: **Bioinformatics **Authors: **Krause AL, Van Gorder RA **Tags: **Bull Math Biol **Source Type: **research

**A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns.**

Abstract
We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many species and more general kinds of dispersal. We first consider diffusive instabilities, determining that for directed motion along fecundity gradients, the model permits the Turing instability leading to colony formation and persistence provided there are three or more interacting species. We also prove that such patterning is not possible in the model under the Turing mechanism for two species under directed motion along fecundity gradients, confirmi...

**Source: **Bulletin of Mathematical Biology - August 11, 2020 **Category: **Bioinformatics **Authors: **Taylor NP, Kim H, Krause AL, Van Gorder RA **Tags: **Bull Math Biol **Source Type: **research

**On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility.**

Abstract
We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control, i.e., when releases are adjusted according to the wild population size estimates, lea...

**Source: **Bulletin of Mathematical Biology - August 9, 2020 **Category: **Bioinformatics **Authors: **Aronna MS, Dumont Y **Tags: **Bull Math Biol **Source Type: **research

**Basic Reproduction Numbers for a Class of Reaction-Diffusion Epidemic Models.**

We present a general numerical framework to compute such basic reproduction numbers; meanwhile, the numerical formulation provides useful insight into their characterizations. Using matrix analysis, we show that the basic reproduction numbers are the same for these PDE models and their associated ODE models in several important cases that include, among others, a single infected compartment, constant diffusion rates, uniform diffusion patterns among the infected compartments, and partial diffusion in the system.
PMID: 32772192 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - August 9, 2020 **Category: **Bioinformatics **Authors: **Yang C, Wang J **Tags: **Bull Math Biol **Source Type: **research

**Building Community-Based Approaches to Systemic Reform in Mathematical Biology Education.**

Abstract
Starting in the early 2000's, several reports were released recognizing the convergence of mathematics, biology and computer science, and calling for a rethinking of how undergraduates are prepared for careers in research and the science and technology workforce. This call for change requires careful consideration of the mathematical biology education system to identify key components and leverage points for change. This paper demonstrates the wide range of resources and approaches available to the mathematical biology education community to create systemic change by highlighting the efforts of four commu...

**Source: **Bulletin of Mathematical Biology - August 8, 2020 **Category: **Bioinformatics **Authors: **Akman O, Eaton CD, Hrozencik D, Jenkins KP, Thompson KV **Tags: **Bull Math Biol **Source Type: **research

**The de Rham-Hodge Analysis and Modeling of Biomolecules.**

Abstract
Biological macromolecules have intricate structures that underpin their biological functions. Understanding their structure-function relationships remains a challenge due to their structural complexity and functional variability. Although de Rham-Hodge theory, a landmark of twentieth-century mathematics, has had a tremendous impact on mathematics and physics, it has not been devised for macromolecular modeling and analysis. In this work, we introduce de Rham-Hodge theory as a unified paradigm for analyzing the geometry, topology, flexibility, and Hodge mode analysis of biological macromolecules. Geometric...

**Source: **Bulletin of Mathematical Biology - August 8, 2020 **Category: **Bioinformatics **Authors: **Zhao R, Wang M, Chen J, Tong Y, Wei GW **Tags: **Bull Math Biol **Source Type: **research

**Stoichiometric Modeling of Aboveground-Belowground Interaction of Herbaceous Plant and Two Herbivores.**

This study also explains the functional mechanism for the decline of species diversity in response to nitrogen enrichment.
PMID: 32770322 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - August 7, 2020 **Category: **Bioinformatics **Authors: **Rong X, Sun Y, Fan M, Wang H **Tags: **Bull Math Biol **Source Type: **research

**Getting a Grip on Variability.**

Abstract
Because science is a modeling enterprise, a key question for educators is: What kind of repertoire can initiate students into the practice of generating, revising, and critiquing models of the natural world? Based on our 20 years of work with teachers and students, we nominate variability as a set of connected key ideas that bridge mathematics and science and are fundamental for equipping youngsters for the posing and pursuit of questions about science. Accordingly, we describe a sequence for helping young students begin to reason productively about variability. Students first participate in random p...

**Source: **Bulletin of Mathematical Biology - August 6, 2020 **Category: **Bioinformatics **Authors: **Lehrer R, Schauble L, Wisittanawat P **Tags: **Bull Math Biol **Source Type: **research

**The Relation Between k-Circularity and Circularity of Codes.**

n L
Abstract
A code X is k-circular if any concatenation of at most k words from X, when read on a circle, admits exactly one partition into words from X. It is circular if it is k-circular for every integer k. While it is not a priori clear from the definition, there exists, for every pair [Formula: see text], an integer k such that every k-circular [Formula: see text]-letter code over an alphabet of cardinality n is circular, and we determine the least such integer k for all values of n and [Formula: see text]. The k-circular codes may represent an important evolution...

**Source: **Bulletin of Mathematical Biology - August 4, 2020 **Category: **Bioinformatics **Authors: **Fimmel E, Michel CJ, Pirot F, Sereni JS, Starman M, Strüngmann L **Tags: **Bull Math Biol **Source Type: **research

**A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer.**

Abstract
Oncolytic virotherapy is known as a new treatment to employ less virulent viruses to specifically target and damage cancer cells. This work presents a cellular automata model of oncolytic virotherapy with an application to pancreatic cancer. The fundamental biomedical processes (like cell proliferation, mutation, apoptosis) are modeled by the use of probabilistic principles. The migration of injected viruses (as therapy) is modeled by diffusion through the tissue. The resulting diffusion-reaction equation with smoothed point viral sources is discretized by the finite difference method and integrated by th...

**Source: **Bulletin of Mathematical Biology - July 31, 2020 **Category: **Bioinformatics **Authors: **Chen J, Weihs D, Vermolen FJ **Tags: **Bull Math Biol **Source Type: **research

**Characterizing Chemotherapy-Induced Neutropenia and Monocytopenia Through Mathematical Modelling.**

Abstract
In spite of the recent focus on the development of novel targeted drugs to treat cancer, cytotoxic chemotherapy remains the standard treatment for the vast majority of patients. Unfortunately, chemotherapy is associated with high hematopoietic toxicity that may limit its efficacy. We have previously established potential strategies to mitigate chemotherapy-induced neutropenia (a lack of circulating neutrophils) using a mechanistic model of granulopoiesis to predict the interactions defining the neutrophil response to chemotherapy and to define optimal strategies for concurrent chemotherapy/prophylactic gr...

**Source: **Bulletin of Mathematical Biology - July 31, 2020 **Category: **Bioinformatics **Authors: **Cassidy T, Humphries AR, Craig M, Mackey MC **Tags: **Bull Math Biol **Source Type: **research

**Modeling the 2014-2015 Ebola Virus Disease Outbreaks in Sierra Leone, Guinea, and Liberia with Effect of High- and Low-risk Susceptible Individuals.**

Abstract
Ebola virus disease (EVD) is a rare but fatal disease of humans and other primates caused by Ebola viruses. Study shows that the 2014-2015 EVD outbreak causes more than 10,000 deaths. In this paper, we propose and analyze a deterministic model to study the transmission dynamics of EVD in Sierra Leone, Guinea, and Liberia. Our analyses show that the model has two equilibria: (1) the disease-free equilibrium (DFE) which is locally asymptotically stable when the basic reproduction number ([Formula: see text]) is less than unity and unstable if it is greater than one, and (2) an endemic equilibrium (EE) which...

**Source: **Bulletin of Mathematical Biology - July 30, 2020 **Category: **Bioinformatics **Authors: **Lin Q, Musa SS, Zhao S, He D **Tags: **Bull Math Biol **Source Type: **research

**Agent-Based Modeling and Simulation in Mathematics and Biology Education.**

Abstract
With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.
PMI...

**Source: **Bulletin of Mathematical Biology - July 28, 2020 **Category: **Bioinformatics **Authors: **Bodine EN, Panoff RM, Voit EO, Weisstein AE **Tags: **Bull Math Biol **Source Type: **research

**The Case for Undergraduate Research Journals.**

Abstract
This note addresses the important role of undergraduate research journals in the undergraduate research experience. Peer review by professional researchers is identified as the most essential ingredient in establishing the relevance of these journals as venues for research dissemination. Included are examples of three such journals-Spora, SIAM Undergraduate Research Online, and the American Journal of Undergraduate Research-with demonstrated success in supporting the undergraduate research experience.
PMID: 32725432 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - July 28, 2020 **Category: **Bioinformatics **Authors: **Bendinskas KG, Caudill L, Melara LA **Tags: **Bull Math Biol **Source Type: **research

**Modeling and Dynamics Analysis of Zika Transmission with Limited Medical Resources.**

Abstract
Zika virus, a reemerging mosquito-borne flavivirus, posed a global public health emergency in 2016. Brazil is the most seriously affected country. Some measures have been implemented to control the Zika transmission, such as spraying mosquitoes, developing vaccines and drugs. However, because of the limited medical resources (LMRs) in the country, not every infected patient can be treated in time when infected with Zika virus. We aim to build a deterministic Zika model by introducing a piecewise smooth treatment recovery rate to research the effect of LMRs on the transmission and control of Zika. For the ...

**Source: **Bulletin of Mathematical Biology - July 23, 2020 **Category: **Bioinformatics **Authors: **Zhao H, Wang L, Oliva SM, Zhu H **Tags: **Bull Math Biol **Source Type: **research

**Connecting with Teachers through Modeling in Mathematical Biology.**

Abstract
In this work, we describe some effective teaching and research practices that can help to integrate mathematics and biology efficiently to enhance student learning at all levels. One of the successful approaches proposed is to employ mathematical modeling that can help transform pedagogical practices. In this regard, we introduce some modeling activities that have been shared with teachers through professional development programs and have been incorporated in the classrooms. We also present how engaging teachers in research experiences in mathematical modeling can help to transform their pedagogical prac...

**Source: **Bulletin of Mathematical Biology - July 22, 2020 **Category: **Bioinformatics **Authors: **Seshaiyer P, Lenhart S **Tags: **Bull Math Biol **Source Type: **research

**An Edge-Based Model of SEIR Epidemics on Static Random Networks.**

Abstract
Studies have been done using networks to represent the spread of infectious diseases in populations. For diseases with exposed individuals corresponding to a latent period, an SEIR model is formulated using an edge-based approach described by a probability generating function. The basic reproduction number is computed using the next generation matrix method and the final size of the epidemic is derived analytically. The SEIR model in this study is used to investigate the stochasticity of the SEIR dynamics. The stochastic simulations are performed applying continuous-time Gillespie's algorithm given Poisso...

**Source: **Bulletin of Mathematical Biology - July 16, 2020 **Category: **Bioinformatics **Authors: **Alota CP, Pilar-Arceo CPC, de Los Reyes V AA **Tags: **Bull Math Biol **Source Type: **research

**Inferring Metric Trees from Weighted Quartets via an Intertaxon Distance.**

Abstract
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these weights, and shown to exactly fit the same tree topology, but with edge weights rescaled by certain factors dependent on the associated split size. These distances are analogs for metric trees of similar ones recently introduced for topological trees that are based on induced unweighted rooted triples and quartets. The distances introduced here lead to new statistically con...

**Source: **Bulletin of Mathematical Biology - July 16, 2020 **Category: **Bioinformatics **Authors: **Yourdkhani S, Rhodes JA **Tags: **Bull Math Biol **Source Type: **research

**Modelling the Effect of Incubation and Latent Periods on the Dynamics of Vector-Borne Plant Viral Diseases.**

This study shows the relevance of the presence of two time delays, which may lead to system stabilization.
PMID: 32676825 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - July 16, 2020 **Category: **Bioinformatics **Authors: **Al Basir F, Adhurya S, Banerjee M, Venturino E, Ray S **Tags: **Bull Math Biol **Source Type: **research

**Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells.**

Abstract
Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article, we address pacemaker dynamics associated with the interaction of [Formula: see text] and [Formula: see text] fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Mor...

**Source: **Bulletin of Mathematical Biology - July 16, 2020 **Category: **Bioinformatics **Authors: **Fatoyinbo HO, Brown RG, Simpson DJW, van Brunt B **Tags: **Bull Math Biol **Source Type: **research

**Large River Effect or Frozen Kinetics: How Complex Nonlinear Living Systems Solve Optimization Problems.**

Abstract
In this paper, we introduce general idea of trajectories attraction in phase space, which is very common phenomenon for the processes in the Nature. We start from a rather general biological example of natural selection, where adaptation to the environmental conditions can be described as attraction of some population distribution in the phenotype space to a center of ecological niche. The niche is mathematically represented as the "survival coefficient" which in turn can be linked to a kind of energy potential. This link between biological and physical approaches may be very useful for solution...

**Source: **Bulletin of Mathematical Biology - July 14, 2020 **Category: **Bioinformatics **Authors: **Filippov A, Kovalev A, Gorb S **Tags: **Bull Math Biol **Source Type: **research

**Correction to: A Mathematical Model for the Kinetics of the MalFGK2 Maltose Transporter.**

EN
Abstract
The original version of this article unfortunately contained a mistake. The co-author Dr. Franck Duong Van Hoa first name and last name were misinterpreted in the original publication.
PMID: 32653954 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - July 11, 2020 **Category: **Bioinformatics **Authors: **Hiller RM, von Kügelgen J, Bao H, Duong Van Hoa F, Cytrynbaum EN **Tags: **Bull Math Biol **Source Type: **research

**High School Internship Program in Integrated Mathematical Oncology (HIP IMO): Five-Year Experience at Moffitt Cancer Center.**

We report here on the program structure, training deliverables, curriculum and outcomes. We hope to promote interdisciplinary educational activities early in a student's career.
PMID: 32648152 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - July 9, 2020 **Category: **Bioinformatics **Authors: **Enderling H, Altrock PM, Andor N, Basanta D, Brown JS, Gatenby RA, Marusyk A, Rejniak KA, Silva A, Anderson ARA **Tags: **Bull Math Biol **Source Type: **research

**Modeling Temperature-Dependent Sex Determination in Oviparous Species Using a Dynamical Systems Approach.**

Abstract
In many oviparous species, the incubation temperature of the egg determines the sex of the offspring. This is known as temperature-dependent sex determination (TSD). The probability of the hatched offspring being male or female varies across the incubation temperature range. This leads to the appearance of different TSD patterns in species such as FM pattern where females are predominately born at lower temperature and males at higher temperature, FMF pattern where the probability of female being born is higher at extreme temperatures and of the male being born is high at intermediate temperatures. We ana...

**Source: **Bulletin of Mathematical Biology - July 7, 2020 **Category: **Bioinformatics **Authors: **Verma N, Verma BK, Pushpavanam S **Tags: **Bull Math Biol **Source Type: **research

**A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers' Migration.**

Abstract
Metaecoepidemic models generalize metapopulation systems, combining local population dynamics with inter-patch migration coupled with an epidemic proliferation. A resource-consumer model is introduced with an ecosystem composed by two patches, in which consumers can freely move. A disease affects resources of the second patch. This situation corresponds to a grassland-herbivore environment, where one patch, managed in an extensive way, has a wider plant diversity, while the other one is highly fertilized leading to an important forage production. The latter is also subject to a fungal disease. Herbivores ...

**Source: **Bulletin of Mathematical Biology - July 7, 2020 **Category: **Bioinformatics **Authors: **Moulin T, Perasso A, Venturino E **Tags: **Bull Math Biol **Source Type: **research

**Collective Pulsing in Xeniid Corals: Part I-Using Computer Vision and Information Theory to Search for Coordination.**

Abstract
Xeniid corals (Cnidaria: Alcyonacea), a family of soft corals, include species displaying a characteristic pulsing behavior. This behavior has been shown to increase oxygen diffusion away from the coral tissue, resulting in higher photosynthetic rates from mutualistic symbionts. Maintaining such a pulsing behavior comes at a high energetic cost, and it has been proposed that coordinating the pulse of individual polyps within a colony might enhance the efficiency of fluid transport. In this paper, we test whether patterns of collective pulsing emerge in coral colonies and investigate possible interactions ...

**Source: **Bulletin of Mathematical Biology - July 7, 2020 **Category: **Bioinformatics **Authors: **Samson JE, Ray DD, Porfiri M, Miller LA, Garnier S **Tags: **Bull Math Biol **Source Type: **research

**Introductory College Mathematics for the Life Sciences: Has Anything Changed?**

Abstract
This paper focuses on issues concerning the introductory college mathematics sequence with an emphasis on students interested in the life sciences, and concentration on the time after the publication of BIO2010 (BIO2010 in Transforming Undergraduate Education for Future Research Biologists, National Academies of Science, Medicine and Engineering, Washington, 2003). It also explores the potential uses of books targeted at introductory mathematics courses for life science majors today. As relevant background, we look at the evolution of the way that calculus has been taught over the past 50 years, incl...

**Source: **Bulletin of Mathematical Biology - July 7, 2020 **Category: **Bioinformatics **Authors: **Cozzens M, Roberts FS **Tags: **Bull Math Biol **Source Type: **research

**Trending on Social Media: Integrating Social Media into Infectious Disease Dynamics.**

This article presents a review of existing models incorporating media in general and highlights opportunities for social media to enhance traditional compartmental models so as to make the best use of this resource in controlling the spread of disease.
PMID: 32617673 [PubMed - in process] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - July 2, 2020 **Category: **Bioinformatics **Authors: **Sooknanan J, Comissiong DMG **Tags: **Bull Math Biol **Source Type: **research

**The Impact of Pre-exposure Prophylaxis for Human Immunodeficiency Virus on Gonorrhea Prevalence.**

Abstract
Pre-exposure prophylaxis (PrEP) has been shown to be highly effective in reducing the risk of HIV infection in gay and bisexual men who have sex with men (GbMSM). However, PrEP does not protect against other sexually transmitted infections (STIs). In some populations, PrEP has also led to riskier behavior such as reduced condom usage, with the result that the prevalence of bacterial STIs like gonorrhea has increased. Here, we develop a compartmental model of the transmission of HIV and gonorrhea and the impacts of PrEP, condom usage, STI testing frequency and potential changes in sexual risk behavior stem...

**Source: **Bulletin of Mathematical Biology - July 1, 2020 **Category: **Bioinformatics **Authors: **Pharaon J, Bauch CT **Tags: **Bull Math Biol **Source Type: **research

**A Mathematical Model for Inheritance of DNA Methylation Patterns in Somatic Cells.**

Abstract
DNA methylation is an essential epigenetic mechanism used by cells to regulate gene expression. Interestingly, DNA replication, a function necessary for cell division, disrupts the methylation pattern. Since perturbed methylation patterns are associated with aberrant gene expression and many diseases, including cancer, restoration of the correct pattern following DNA replication is crucial. However, the exact mechanisms of this restoration remain under investigation. DNA methyltransferases (Dnmts) perform methylation by adding a methyl group to cytosines at CpG sites in the DNA. These CpG sites are found ...

**Source: **Bulletin of Mathematical Biology - July 1, 2020 **Category: **Bioinformatics **Authors: **Utsey K, Keener JP **Tags: **Bull Math Biol **Source Type: **research

**Modeling Clot Formation of Shear-Injured Platelets in Flow by a Dissipative Particle Dynamics Method.**

In this study, we developed a dissipative particle dynamics model to characterize clot formation (platelet-collagen and inter-platelet adhesion) of NPSS-traumatized blood at a vascular injury site. A rectangular tube of 50 × 50 × 200 µm with an 8 × 8 µm collagen-coated area was modeled as a small blood vessel and perfusion with blood. Clot formation dynamics during perfusion was simulated. NPSS-traumatized blood was modeled to have more activated platelet and fewer adhesion receptors with weakened inter-platelet binding. Computational results...

**Source: **Bulletin of Mathematical Biology - June 22, 2020 **Category: **Bioinformatics **Authors: **Wang L, Chen Z, Zhang J, Zhang X, Wu ZJ **Tags: **Bull Math Biol **Source Type: **research

**A Mathematical Dissection of the Adaptation of Cell Populations to Fluctuating Oxygen Levels.**

nzi T
Abstract
The disordered network of blood vessels that arises from tumour angiogenesis results in variations in the delivery of oxygen into the tumour tissue. This brings about regions of chronic hypoxia (i.e. sustained low oxygen levels) and regions with alternating periods of low and relatively higher oxygen levels, and makes it necessary for cancer cells to adapt to fluctuating environmental conditions. We use a phenotype-structured model to dissect the evolutionary dynamics of cell populations exposed to fluctuating oxygen levels. In this model, the phenotypic state of every cell is described by a continu...

**Source: **Bulletin of Mathematical Biology - June 16, 2020 **Category: **Bioinformatics **Authors: **Ardaševa A, Gatenby RA, Anderson ARA, Byrne HM, Maini PK, Lorenzi T **Tags: **Bull Math Biol **Source Type: **research

**Multiple Attractors and Long Transients in Spatially Structured Populations with an Allee Effect.**

We present a discrete-time model of a spatially structured population and explore the effects of coupling when the local dynamics contain a strong Allee effect and overcompensation. While an isolated population can exhibit only bistability and essential extinction, a spatially structured population can exhibit numerous coexisting attractors. We identify mechanisms and parameter ranges that can protect the spatially structured population from essential extinction, whereas it is inevitable in the local system. In the case of weak coupling, a state where one subpopulation density lies above and the other one below the Allee t...

**Source: **Bulletin of Mathematical Biology - June 16, 2020 **Category: **Bioinformatics **Authors: **Vortkamp I, Schreiber SJ, Hastings A, Hilker FM **Tags: **Bull Math Biol **Source Type: **research

**Game-Theoretical Model of Retroactive Hepatitis B Vaccination in China.**

lor D
Abstract
Hepatitis B (HepB) is one of the most common infectious diseases affecting over two billion people worldwide. About one third of all HepB cases are in China. In recent years, China made significant efforts to implement a nationwide HepB vaccination program and reduced the number of unvaccinated infants from 30 to 10%. However, many individuals still remain unprotected, particularly those born before 2003. Consequently, a catch-up retroactive vaccination is an important and potentially cost-effective way to reduce HepB prevalence. In this paper, we analyze a game theoretical model of HepB dynamics th...

**Source: **Bulletin of Mathematical Biology - June 15, 2020 **Category: **Bioinformatics **Authors: **Chouhan A, Maiwand S, Ngo M, Putalapattu V, Rychtář J, Taylor D **Tags: **Bull Math Biol **Source Type: **research

**Thermodynamic Inhibition in Chemostat Models : With an Application to Bioreduction of Uranium.**

Abstract
We formulate a mathematical model of bacterial populations in a chemostat setting that also accounts for thermodynamic growth inhibition as a consequence of chemical reactions. Using only elementary mathematical and chemical arguments, we carry this out for two systems: a simple toy model with a single species, a single substrate, and a single reaction product, and a more involved model that describes bioreduction of uranium[VI] into uranium[IV]. We find that in contrast to most traditional chemostat models, as a consequence of thermodynamic inhibition the equilibria concentrations of nutrient substrates ...

**Source: **Bulletin of Mathematical Biology - June 13, 2020 **Category: **Bioinformatics **Authors: **Gaebler HJ, Eberl HJ **Tags: **Bull Math Biol **Source Type: **research

**A Framework for Network-Based Epidemiological Modeling of Tuberculosis Dynamics Using Synthetic Datasets.**

We present a framework for discrete network-based modeling of TB epidemiology in US counties using publicly available synthetic datasets. We explore the dynamics of this modeling framework by simulating the hypothetical spread of disease over 2 years resulting from a single active infection in Washtenaw County, MI. We find that for sufficiently large transmission rates that active transmission outweighs reactivation, disease prevalence is sensitive to the contact weight assigned to transmissions between casual contacts (that is, contacts that do not share a household, workplace, school, or group quarter). Workplace an...

**Source: **Bulletin of Mathematical Biology - June 13, 2020 **Category: **Bioinformatics **Authors: **Renardy M, Kirschner DE **Tags: **Bull Math Biol **Source Type: **research

**Correction to: Modulation of the cAMP Response by G[Formula: see text] and G[Formula: see text]: A Computational Study of G Protein Signaling in Immune Cells.**

Abstract
The original version of this article unfortunately contained mistakes.
PMID: 32535846 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)

**Source: **Bulletin of Mathematical Biology - June 13, 2020 **Category: **Bioinformatics **Authors: **Leander R, Friedman A **Tags: **Bull Math Biol **Source Type: **research

**Nonreflecting Boundary Conditions for a CSF Model of Fourth Ventricle: Spinal SAS Dynamics.**

Abstract
In this paper, we introduce a one-dimensional model for analyzing the cerebrospinal fluid dynamics within the fourth ventricle and the spinal subarachnoid space (SSAS). The model has been derived starting from an original model of Linninger et al. and from the detailed mathematical analysis of two different reformulations. We show the steps of the modelization and the rigorous analysis of the first-order nonlinear hyperbolic system of equations which rules the new CSF model, whose conservative-law form and characteristic form are required for the boundary conditions treatment. By assuming sub-critical flo...

**Source: **Bulletin of Mathematical Biology - June 13, 2020 **Category: **Bioinformatics **Authors: **Donatelli D, Romagnoli L **Tags: **Bull Math Biol **Source Type: **research

**Optimizing the Timing and Composition of Therapeutic Phage Cocktails: A Control-Theoretic Approach.**

In this study, we evaluate principles underlying why careful application of multiple phage (i.e., a 'cocktail') might lead to therapeutic success in contrast to the failure of single-strain phage therapy to control an infection. First, we use a nonlinear dynamics model of within-host interactions to show that a combination of fast intra-host phage decay, evolution of phage resistance amongst bacteria, and/or compromised immune response might limit the effectiveness of single-strain phage therapy. To resolve these problems, we combine dynamical modeling of phage, bacteria, and host immune cell populations with control-theor...

**Source: **Bulletin of Mathematical Biology - June 12, 2020 **Category: **Bioinformatics **Authors: **Li G, Leung CY, Wardi Y, Debarbieux L, Weitz JS **Tags: **Bull Math Biol **Source Type: **research