Public perceptions and sentiments play a crucial role in the success of vaccine uptake in the community. While vaccines have proven to be the best preventive method to combat the flu, the attitude and knowledge about vaccines are a major hindrance to higher uptake in most of the countries. The yearly coverage, especially in the vulnerable groups in the population, often remains below the herd immunity

Chronic dermal-wound patients frequently suffer from diabetes type 2 and obesity; without treatment or early intervention, these patients are at risk of amputation. In this paper, we identified four factors that impair wound healing in these populations: excessive production of glycation, excessive production of leukotrient, decreased production of stromal derived factor (SDF-1), and insulin resistance

Ecosystems engineers are species that can substantially alter their abiotic environment and thereby enhance their population growth. The net growth rate of obligate engineers is even negative unless they modify the environment. We derive and analyze a model for the spread and invasion of such species. Prior to engineering, the landscape consists of unsuitable habitat; after engineering, the habitat

Reaction–diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models. We derive conditions for diffusion-driven instability of

In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the ageing eye that lead to disease and those changes that are considered part of a healthy, ageing eye. Various studies investigating the multitude of mechanisms involved in the aetiology of AMD exist within the field of ophthalmology and related medical fields

Computational modeling of skeletal tissue seeks to predict the structural adaptation of bone in response to mechanical loading. The theory of continuum damage–repair, a mathematical description of structural adaptation based on principles of damage mechanics, continues to be developed and utilized for the prediction of long-term peri-implant outcomes. Despite its technical soundness, CDR does not account

A growing number of rna sequences are now known to exist in some distribution with two or more different stable structures. Recent algorithms attempt to reconstruct such mixtures using the list of nucleotides in a sequence in conjunction with auxiliary experimental footprinting data. In this paper, we demonstrate some challenges which remain in addressing this problem; in particular we consider the

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could

We study the dynamics of two competing species in three-patch models and illustrate how the topology of directed river network modules may affect the evolution of dispersal. Each model assumes that patch 1 is at the upstream end, patch 3 is at the downstream end, but patch 2 could be upstream, or middle stream, or downstream, depending on the specific topology of the modules. We posit that individuals

Mechanical cell competition is important during tissue development, cancer invasion, and tissue ageing. Heterogeneity plays a key role in practical applications since cancer cells can have different cell stiffness and different proliferation rates than normal cells. To study this phenomenon, we propose a one-dimensional mechanical model of heterogeneous epithelial tissue dynamics that includes cell-length-dependent

We model and study the patterns created through the interaction of collectively moving self-propelled particles (SPPs) and elastically tethered obstacles. Simulations of an individual-based model reveal at least three distinct large-scale patterns: travelling bands, trails and moving clusters. This motivates the derivation of a macroscopic partial differential equations model for the interactions between

We have developed a computational model to study electrical propagation of vasodilatory signals and arteriolar regulation of blood flow depending on the oxygen tension and agonist distribution in the capillary network. The involving key parameters of endothelial cell-to-cell electrical conductivity and plasma membrane area per unit volume were calibrated with the experimental data on an isolated endothelial

We live in a data-rich world with rapidly growing databases with zettabytes of data. Innovation, computation, and technological advances have now tremendously accelerated the pace of discovery, providing driverless cars, robotic devices, expert healthcare systems, precision medicine, and automated discovery to mention a few. Even though the definition of the term data science continues to evolve, the

In many biological systems, the movement of individual agents is characterized having multiple qualitatively distinct behaviors that arise from a variety of biophysical states. For example, in cells the movement of vesicles, organelles, and other intracellular cargo is affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical

The question of why males invest more into competition than offspring care is an age-old problem in evolutionary biology. On the one hand, paternal care could increase the fraction of offspring surviving to maturity. On the other hand, competition could increase the likelihood of more paternities and thus the relative number of offspring produced. While drivers of these behaviours are often intertwined

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

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

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 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

Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this

Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology

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

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)

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

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 \(R_0\), 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

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

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

We study the basic reproduction numbers for a class of reaction-diffusion epidemic models that are developed from autonomous ODE systems. 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

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

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

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

In a grassland ecosystem, the dynamics and coexistence mechanisms of two herbivores competing for one herbaceous plant have been widely studied, while the chemical heterogeneity of herbaceous plant’s aboveground and belowground parts is usually ignored in dynamic modeling. Based on the traditional two herbivore-one herbaceous plant competition model, a new stoichiometric competition model, which incorporates

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

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 \((n,\ell )\), an integer k such that every k-circular \(\ell \)-letter code over an alphabet of cardinality n is circular

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

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

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

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

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

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

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

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

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

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 \({\text {Ca}}^{2+}\) and \(\text {K}^+\) fluxes in the cell membrane of a smooth muscle cell. First we reduce a pacemaker

Most of the plant viral diseases spread through vectors. In case of the persistently transmitted disease, there is a latent time of infection inside the vector after acquisition of the virus from the infected plant. Again, the plant after getting infectious agent shows an incubation time after the interaction with an infected vector before it becomes diseased. The goal of this work is to study the

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

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.

Modern cancer research, and the wealth of data across multiple spatial and temporal scales, has created the need for researchers that are well versed in the life sciences (cancer biology, developmental biology, immunology), medical sciences (oncology) and natural sciences (mathematics, physics, engineering, computer sciences). College undergraduate education traditionally occurs in disciplinary silos

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

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

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

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

Social media plays an important role in alerting and educating the public during disease outbreaks. By increasing awareness of the disease and its prevention, it can lead to a modification of behaviour which then affects contact/incidence rates. Social media data may also be used when formulating, developing and parameterising models. As mobile technology continues to evolve and proliferate, social

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

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 regions with high non-physiological shear stresses (NPSS) are inevitable in blood-contacting medical devices (BCMDs) used for mechanically assisted circulatory support. NPSS can cause platelet activation and receptor shedding potentially resulting in the alteration of hemostatic function. In this study, we developed a dissipative particle dynamics model to characterize clot formation (platelet–collagen

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

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

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