**Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions.**

Abstract
Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle an...

**Source: **Mathematical Biosciences - August 8, 2019 **Category: **Statistics **Authors: **Piretto E, Delitala M, Kim PS, Frascoli F **Tags: **Math Biosci **Source Type: **research

**Fundamental constraints of vessels network architecture properties revealed by reconstruction of a rat brain vasculature.**

Abstract
The studies of mammalian vasculature are an essential part of biomedical research, enabling the development of physiological understanding and forming the background of medical techniques and therapy. Despite the fact that the basic principles of vessel network description were established in the first quarter of the twentieth century, a digital model describing the vasculature in full accordance with experimental data has not yet been created. In the present study, we combine the determined structure design of basic arterial vessels with the stochastic creation of small vessel networks. By the example of...

**Source: **Mathematical Biosciences - August 1, 2019 **Category: **Statistics **Authors: **Kopylova VS, Boronovskiy SE, Nartsissov YR **Tags: **Math Biosci **Source Type: **research

**How trait distributions evolve in populations with parametric heterogeneity.**

Abstract
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which heterogeneity is described by an individual specific parameter that differs in general from individual to individual, but does not change with time for the whole lifespan of this individual. Such a restriction allows obtaining a number of simple and yet important analytical results. In particular we show that initial assumptions on time-dependent behavior of various characteris...

**Source: **Mathematical Biosciences - July 24, 2019 **Category: **Statistics **Authors: **P Karev G, S Novozhilov A **Tags: **Math Biosci **Source Type: **research

**A Physiologically-Structured Fish Population Model with Size-Dependent Foraging.**

Abstract
A previous physiologically-structured model for a fish population based on individual-level characteristics is studied. The foraging rate is generalized to include a size-dependent functional response and the energy distribution of adults is generalized to permit both reproduction and growth. Equilibria are determined and their stability studied along with a discussion of harvesting strategies. The model with these generalizations is shown to give different predictions than the original model regarding age distribution of fish and harvesting strategies.
PMID: 31344381 [PubMed - as supplied by publish...

**Source: **Mathematical Biosciences - July 22, 2019 **Category: **Statistics **Authors: **Gwhila M, Willms AR **Tags: **Math Biosci **Source Type: **research

**Optimal control of epidemic size and duration with limited resources.**

Abstract
The total number of infections (epidemic size) and the time needed for the infection to go extinct (epidemic duration) represent two of the main indicators for the severity of infectious disease epidemics in human and livestock. However, few attempts have been made to address the problem of minimizing at the same time the epidemic size and duration from a theoretical point of view by using optimal control theory. Here, we investigate the multi-objective optimal control problem aiming to minimize, through either vaccination or isolation, a suitable combination of epidemic size and duration when both maximu...

**Source: **Mathematical Biosciences - July 19, 2019 **Category: **Statistics **Authors: **Bolzoni L, Bonacini E, Marca RD, Groppi M **Tags: **Math Biosci **Source Type: **research

**Intrinsic kinetic model of photoautotrophic microalgae based on chlorophyll fluorescence analysis.**

Abstract
As photoautotrophic microorganisms, microalgae feature complex mechanisms of photosynthesis and light energy transfer and as such studying their intrinsic growth kinetics is fairly difficult. In this article, the quantum yield of photochemical reaction was introduced in a study of microalgal kinetics to establish an intrinsic kinetic model of photoautotrophic microalgal growth. The blue-green algae Synechococcus sp. PCC7942 was used to verify the kinetic model developed using chlorophyll fluorescence analysis and growth kinetics determination. Results indicate that the kinetic model can realistically refl...

**Source: **Mathematical Biosciences - July 19, 2019 **Category: **Statistics **Authors: **Xiong J, Yu L, Zhang Z, Wang Y, Wang W, Yang H, Yan R, Zhu D **Tags: **Math Biosci **Source Type: **research

**Identification of potential biomarkers on microarray data using distributed gene selection approach.**

Abstract
In recent times, several feature selection (FS) methods have introduced to identify the biomarkers from gene expression datasets. It has gained extensive attention to solve cancer classification problem, but they have some limitations. First, the majority of FS approaches increases the computational cost due to the centralized data structure. Second, an irrelevant ranked gene that could perform well regarding classification accuracy with suitable subset of genes will be left out of the selection. To resolve these problems, we introduce a novel two-stage FS approach by combining Spearman's Correlation (SC)...

**Source: **Mathematical Biosciences - July 18, 2019 **Category: **Statistics **Authors: **Shukla AK, Tripathi D **Tags: **Math Biosci **Source Type: **research

**Mixed circular codes.**

n L
Abstract
By an extensive statistical analysis in genes of bacteria, archaea, eukaryotes, plasmids and viruses, a maximal C3-self-complementary trinucleotide circular code has been found to have the highest average occurrence in the reading frame of the ribosome during translation. Circular codes may play an important role in maintaining the correct reading frame. On the other hand, as several evolutionary theories propose primeval codes based on dinucleotides, trinucleotides and tetranucleotides, mixed circular codes were investigated. By using a graph-theoretical approach of circular codes recently developed,...

**Source: **Mathematical Biosciences - July 17, 2019 **Category: **Statistics **Authors: **Fimmel E, Michel CJ, Pirot F, Sereni JS, Strüngmann L **Tags: **Math Biosci **Source Type: **research

**Role of infarct scar dimensions, border zone repolarization properties and anisotropy in the origin and maintenance of cardiac reentry.**

Abstract
Cardiac ventricular tachycardia (VT) is a life-threatening arrhythmia consisting of a well organized structure of reentrant electrical excitation pathways. Understanding the generation and maintenance of the reentrant mechanisms, which lead to the onset of VT induced by premature beats in presence of infarct scar, is one of the most important issues in current electrocardiology. We investigate, by means of numerical simulations, the role of infarct scar dimension, repolarization properties and anisotropic fiber structure of scar tissue border zone (BZ) in the genesis of VT. The simulations are based on th...

**Source: **Mathematical Biosciences - July 17, 2019 **Category: **Statistics **Authors: **Colli Franzone P, Gionti V, Pavarino LF, Scacchi S, Storti C **Tags: **Math Biosci **Source Type: **research

**Predicting lncRNA-disease associations using network topological similarity based on deep mining heterogeneous networks.**

Abstract
A kind of noncoding RNA with length more than 200 nucleotides named long noncoding RNA (lncRNA) has gained considerable attention in recent decades. Many studies have confirmed that human genome contains many thousands of lncRNAs. LncRNAs play significant roles in many important biological processes, including complex disease diagnosis, prognosis, prevention and treatment. For some important diseases such as cancer, lncRNAs have been novel candidate biomarkers. However, the role of lncRNAs in human diseases is still in its infancy, and only a small part of lncRNA-disease associations have been experimenta...

**Source: **Mathematical Biosciences - July 16, 2019 **Category: **Statistics **Authors: **Zhang H, Liang Y, Peng C, Han S, Du W, Li Y **Tags: **Math Biosci **Source Type: **research

**Optimizing treatment combination for lymphoma using an optimization heuristic.**

CONCLUSIONS: In in-silico experiments, optimal protocols achieve significant gains over standard protocols when considering overall survival probabilities. Our optimization algorithm enables us to efficiently tackle this numerical problem with a large dimensionality. The in-vivo implications of our in-silico results remain to be explored.
PMID: 31302209 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - July 11, 2019 **Category: **Statistics **Authors: **Houy N, Le Grand F **Tags: **Math Biosci **Source Type: **research

**State and Parameter Estimation for a Class of Schistosomiasis Models.**

Abstract
We develop a general framework to estimate the proportion of infected snails and snail-human transmission parameter of a class of models that describes the evolution of schistosomiasis. To do so, we consider simultaneously the dynamics of schistosomiasis, captured by the homogeneous version of the classical MacDonald's model, and the measurable output: the number of female schistosomes per single host. The proposed method consists of designing an auxiliary dynamical system, called observer, whose solutions converge exponentially to those of the system capturing the schistosomiasis model. Moreover, we deri...

**Source: **Mathematical Biosciences - July 6, 2019 **Category: **Statistics **Authors: **Bichara DM, Guiro A, Iggidr A, Ngom D **Tags: **Math Biosci **Source Type: **research

**R0 and Sensitivity Analysis of a Predator-Prey Model with Seasonality and Maturation Delay.**

Abstract
Coexistence and seasonal fluctuations of predator and prey populations are common and well documented in ecology. Under what conditions can predators coexist with prey in a seasonally changing environment? What factors drive long-term population cycles of some predator and prey species? To answer these questions, we investigate an improved predator-prey model based on the Rosenzweig-MacArthur [1] model. Our model incorporates seasonality and a predator maturation delay, leading to a system of periodic differential equations with a time delay. We define the basic reproduction ratio R0 and show that it is a...

**Source: **Mathematical Biosciences - July 5, 2019 **Category: **Statistics **Authors: **Wang X, Wang H, Li MY **Tags: **Math Biosci **Source Type: **research

**The basic reproduction number, R0, in structured populations.**

Abstract
In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, R0, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both SIR and SIS epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that ou...

**Source: **Mathematical Biosciences - July 2, 2019 **Category: **Statistics **Authors: **Neal P, Theparod T **Tags: **Math Biosci **Source Type: **research

**Modeling the Effects of Muscle Contraction on the Mechanical Response and Circumferential Stability of Coronary Arteries.**

Abstract
Smooth muscle contraction regulates the size of the blood vessel lumen which directly affects the mechanical response of the vessel. Folding in arteries has been observed in arteries during excessive contraction, known as a coronary artery spasm. The interplay of muscle contraction, geometry, and material responses and their effects on stability can be understood through mathematical models. Here, we consider a three-layer cross-sectional model of a coronary artery with anisotropic properties and intimal thickening, and perform a linear stability analysis to investigate the circumferential folding pattern...

**Source: **Mathematical Biosciences - July 2, 2019 **Category: **Statistics **Authors: **Sanft R, Power A, Nicholson C **Tags: **Math Biosci **Source Type: **research

**Biomathematical Model for Simulating Abnormal Orifice Patterns in Colonic Crypts.**

Abstract
Colonic polyps, which are abnormal growths in the colon, are a major concern in colon cancer diagnosis and prevention. Medical studies evidence that there is a correlation between histopathology and the shapes of the orifices in colonic crypts. We propose a biomathematical model for simulating the appearance of anomalous shapes for the orifices of colonic crypts, associated to an abnormal cell proliferation. It couples a mechanical model that is a mixed elastic/viscoelastic quasi-static model describing the deformation of the crypt orifice, with a convection-diffusion model that simulates the crypt cell d...

**Source: **Mathematical Biosciences - July 1, 2019 **Category: **Statistics **Authors: **Figueiredo IN, Leal C, Romanazzi G, Engquist B **Tags: **Math Biosci **Source Type: **research

**Is the addition of higher-order interactions in ecological models increasing the understanding of ecological dynamics?**

Abstract
Recent work has shown that higher-order terms in population dynamics models can increase the stability, promote the diversity, and better explain the dynamics of ecological systems. While it is known that these perceived benefits come from an increasing number of alternative solutions given by the nature of multivariate polynomials, this mathematical advantage has not been formally quantified. Here, we develop a general method to quantify the mathematical advantage of adding higher-order interactions in ecological models based on the number of free-equilibrium points that can emerge in a system (i.e., equ...

**Source: **Mathematical Biosciences - June 28, 2019 **Category: **Statistics **Authors: **AlAdwani M, Saavedra S **Tags: **Math Biosci **Source Type: **research

**A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails.**

Abstract
The Michaelis-Menten reaction scheme is among the most influential models in the field of biochemistry, since it led to a very popular expression for the rate of an enzyme-catalysed reaction. After the realisation that this expression is valid in a limited region of the parameter space, two additional expressions were later introduced. The range of validity of these three expressions has been studied thoroughly, since the significance of a reliable rate is not based only on the accuracy of its predictive abilities but also on the physical insight that is acquired in the process of its constructi...

**Source: **Mathematical Biosciences - June 27, 2019 **Category: **Statistics **Authors: **Patsatzis DG, Goussis DA **Tags: **Math Biosci **Source Type: **research

**Optimal control of a Multi-patch Dengue Model under the Influence of Wolbachia Bacterium.**

Abstract
In this work, a multi-patch model for dengue transmission dynamics including the bacterium Wolbachia is studied and by that the control efforts to minimize the disease spread by host and vector control are investigated. The multi-patch system models the host movement within the patches which coupled via a residence-time budgeting matrix P. Numerical results confirm that the control mechanism embedded in incidence rates of the disease transmission, effectively reduce the spread of the disease.
PMID: 31229468 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - June 20, 2019 **Category: **Statistics **Authors: **Bock W, Jayathunga Y **Tags: **Math Biosci **Source Type: **research

**Drug delivery from microcapsules: how can we estimate the release time?**

Abstract
Predicting the release performance of a drug delivery device is an important challenge in pharmaceutics and biomedical science. In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exa...

**Source: **Mathematical Biosciences - June 18, 2019 **Category: **Statistics **Authors: **Carr EJ, Pontrelli G **Tags: **Math Biosci **Source Type: **research

**Termite population size estimation based on termite tunnel patterns using a convolutional neural network.**

In this study, we explored how the termite population size can be estimated using partial information on tunnel patterns. To achieve this, we used an agent-based model to create tunnel patterns that were characterized by three variables: the number of simulated termites (N), passing probability of two termites encountering one another (P), and distance that termites move soil particles (D). To explore whether the N value could be estimated using a partial termite tunnel pattern, we generated four tunnel pattern groups by partially obscuring different areas in an image of a complete tunnel pattern, where: (1) the outer area...

**Source: **Mathematical Biosciences - June 18, 2019 **Category: **Statistics **Authors: **Seo JK, Baik S, Lee SH **Tags: **Math Biosci **Source Type: **research

**Conservation Region Finding for Influenza A Viruses by Machine Learning methods of N-linked Glycosylation Sites and B-cell Epitopes.**

This study focused on three genetic features of viral surface proteins: ribonucleic acid (RNA) sequence conservation, linear B-cell epitopes, and N-linked glycosylation. On the basis of these three properties, we analyzed 12,832 HA and 9487 NA protein sequences, which we retrieved from the influenza virus database. We classified the viral surface protein sequences into the 18 HA and 11 NA subtypes that have been identified thus far. Using available analytic tools, we searched for the representative strain of each virus subtype. Furthermore, using machine learning methods, we looked for conservation regions with sequences s...

**Source: **Mathematical Biosciences - June 17, 2019 **Category: **Statistics **Authors: **Liu JH, Chang CC, Chen CW, Wong LT, Chu YW **Tags: **Math Biosci **Source Type: **research

**On the Z-type control of backward bifurcations in epidemic models.**

Abstract
We investigate how the Z-type dynamic approach can be applied to control backward bifurcation phenomena in epidemic models. Because of its rich phenomenology, that includes stationary or oscillatory subcritical persistence of the disease, we consider the SIR model introduced by Zhou & Fan in [Nonlinear Analysis: Real World Applications, 13(1), 312-324, 2012] and apply the Z-control approach in the specific case of indirect control of the infective population. We derive the associated Z-controlled model both when the desired Z-controlled equilibrium is an endemic equilibrium with a very low number of i...

**Source: **Mathematical Biosciences - June 13, 2019 **Category: **Statistics **Authors: **Lacitignola D, Diele F **Tags: **Math Biosci **Source Type: **research

**Generalized concentration addition for ligands that bind to homodimers.**

Abstract
Concentration addition/dose addition (CA) has proved to be a powerful tool for estimating the combined effect of mixtures that act by similar mechanisms. We earlier proposed generalized concentration addition (GCA) to deal with the inability of CA to estimate effects of mixtures above the level of the least efficacious component. GCA requires specifying mathematical concentration response functions for each mixture component that must be invertible, yielding real numbers. We construct concentration response functions using pharmacodynamic models of ligand-receptor interaction, an important molecular initi...

**Source: **Mathematical Biosciences - June 12, 2019 **Category: **Statistics **Authors: **Webster TF, Schlezinger JJ **Tags: **Math Biosci **Source Type: **research

**Numerical optimal control of a size-structured PDE model for metastatic cancer treatment.**

Abstract
In this paper, we propose a unified size-structured PDE model for the growth of metastatic tumors, which extends a well-known coupled ODE-PDE dynamical model developed and studied in the literature. A treatment model based on the proposed unified PDE model is investigated via optimal control theory, where its first-order necessary optimality system characterizing the optimal control is derived. We prove that the uniqueness of the optimal control depends on the chosen objective functional, and the optimal control is of bang-bang type when it is unique. For obtaining its efficient numerical solutions, a pro...

**Source: **Mathematical Biosciences - June 6, 2019 **Category: **Statistics **Authors: **Liu J, Wang XS **Tags: **Math Biosci **Source Type: **research

**Implementation of Control Strategies for Sterile Insect Techniques.**

Abstract
In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-...

**Source: **Mathematical Biosciences - June 6, 2019 **Category: **Statistics **Authors: **Bliman PA, Cardona-Salgado D, Dumont Y, Vasilieva O **Tags: **Math Biosci **Source Type: **research

**Where to Look and How to Look: Combining Global Sensitivity Analysis with Fast/Slow Analysis to Study Multi-Timescale Oscillations.**

In this study, we combine the two techniques in the analysis of bursting behavior in a model of insulin-secreting pancreatic β-cells, with the goal of determining the key parameters setting the period of the bursting oscillations, and understanding why they are so influential. This can be viewed as a case study for combining mathematical techniques to build on the strengths of each and thereby achieve a better understanding of what most influences the range of model behaviors and how this influence is brought about.
PMID: 31128125 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - May 22, 2019 **Category: **Statistics **Authors: **Aggarwal M, Cogan N, Bertram R **Tags: **Math Biosci **Source Type: **research

**Parameter estimation in a minimal model of cardio-pulmonary interactions.**

Abstract
Mechanical ventilation is a widely used breathing support for patients in intensive care. Its effects on the respiratory and cardiovascular systems are complex and difficult to predict. This work first presents a minimal mathematical model representing the mechanics of both systems and their interaction, in terms of flows, pressures and volumes. The aim of this model is to get insight on the two systems' status when mechanical ventilation settings, such as positive end-expiratory pressure, are changing. The parameters of the model represent cardiac elastances and vessel compliances and resistances. As a s...

**Source: **Mathematical Biosciences - May 22, 2019 **Category: **Statistics **Authors: **de Bournonville S, Pironet A, Pretty C, Chase JG, Desaive T **Tags: **Math Biosci **Source Type: **research

**Problems with the WHO TB Model.**

Abstract
WHO tuberculosis researchers recently published a mathematical model to predict TB incidence decline with fulfillment of Sustainable Development Goal (SDG) subtargets [1]. This model omitted the subtargets of land rights and basic services and of reduction in deaths from climatic disaster, likely highly influential factors, and retained only social insurance and reduction of extreme poverty as independent variables. The model predicted that fulfillment of these two subtargets will result in very large declines in TB incidence. This paper critiques the WHO model, reviews historic documents in TB social epi...

**Source: **Mathematical Biosciences - May 16, 2019 **Category: **Statistics **Authors: **Wallace D, Wallace R **Tags: **Math Biosci **Source Type: **research

**Anterior-Posterior patterning of Drosophila wing disc I: A baseline mathematical model.**

Abstract
Wing imaginal disc of Drosophila is one of the commonly used model systems for the studies of patterning, growth, and scaling. Development of the wing disc involves many interacting components as well as a variety of compound processes whose underlying mechanisms are still under investigation. For instance, it remains unclear about how to form compound experimentally-measured patterns of Decapentaplegic (Dpp) type-I receptor Thickveins (Tkv), as well as phosphorylated Mothers Against Dpp (pMad) which is the indicator of Dpp signaling activities. In this work, we proposed a baseline mathematical model that...

**Source: **Mathematical Biosciences - May 11, 2019 **Category: **Statistics **Authors: **Chen Z, Zou Y **Tags: **Math Biosci **Source Type: **research

**A Class of Phylogenetic Networks Reconstructable from Ancestral Profiles.**

Abstract
Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set X of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate processes (for example, hybrid evolution, endosymbiosis, and lateral gene transfer). A major goal in systematic biology is to infer evolutionary relationships, and while phylogenetic trees can be uniquely determined from various simple combinatorial data on X, for networks the reconstruction question is much more subtle. Here we ask when can a network be uniquely reconstructed...

**Source: **Mathematical Biosciences - May 8, 2019 **Category: **Statistics **Authors: **L Erdős P, Semple C, Steel M **Tags: **Math Biosci **Source Type: **research

**A Bayesian hierarchical point process model for epidermal nerve fiber patterns.**

auml; A
Abstract
We introduce the Thomas process in a Bayesian hierarchical setting as a model for point pattern data with a nested structure. This model is applied to a nerve fiber data set which consists of several point patterns of nerve entry points from 47 subjects divided into 3 groups, where the grouping is based on the diagnosed severity of a certain nerve disorder. The modeling assumption is that each point pattern is a realization of a Thomas process, with parameter values specific to the subject. These parameter values are in turn assumed to come from distributions that depend on which group the subject...

**Source: **Mathematical Biosciences - April 30, 2019 **Category: **Statistics **Authors: **Andersson C, Rajala T, Särkkä A **Tags: **Math Biosci **Source Type: **research

**Enhanced Disinfection of Bacterial Populations By Nutrient and Antibiotic Challenge Timing.**

In this study, we investigate how manipulating the application of antibiotics and addition of nutrients enhances the disinfection of a bacterial population in batch culture. Eliminating persister bacteria is considered as a challenge for the food industry or wastewater treatment, since the failure may result in food contamination and disease transmission. Previous studies focused on the antimicrobial agent as a control variable to eliminate the bacterial population. In addition to antibiotic, we consider the significance of the nutrient in eradicating the susceptible and persister cells since the disinfection of susceptibl...

**Source: **Mathematical Biosciences - April 29, 2019 **Category: **Statistics **Authors: **Acar N, Cogan NG **Tags: **Math Biosci **Source Type: **research

**Spatial Models of Vector-Host Epidemics with Directed Movement of Vectors Over Long Distances.**

Abstract
We investigate a time-dependent spatial vector-host epidemic model with non-coincident domains for the vector and host populations. The host population resides in small non-overlapping sub-regions, while the vector population resides throughout a much larger region. The dynamics of the populations are modeled by a reaction-diffusion-advection compartmental system of partial differential equations. The disease is transmitted through vector and host populations in criss-cross fashion. We establish global well-posedness and uniform a prior bounds as well as the long-term behavior. The model is applied to sim...

**Source: **Mathematical Biosciences - April 27, 2019 **Category: **Statistics **Authors: **Fitzgibbon WE, Morgan JJ, Webb GF, Wu Y **Tags: **Math Biosci **Source Type: **research

**Predicting miRNA-lncRNA interactions and recognizing their regulatory roles in stress response of plants.**

In this study, we investigated miRNA and long non-coding RNA (lncRNA) interactions using support vector regression (SVR) for prediction of new target genes in Arabidopsis thaliana and identify some regulatory roles in stress response. The networks of miRNA-mRNA, miRNA-lncRNA and miRNA-mRNA-lncRNA were constructed. They were further analyzed and interpreted in R. We showed that miRNA with low sequence number, targeted lncRNA with high sequence number and miRNA with high sequence number targeted lncRNA with low sequence number. The experimental results showed that there is a regulatory relationship between miRNA-lncRNA. New ...

**Source: **Mathematical Biosciences - April 26, 2019 **Category: **Statistics **Authors: **Bouba I, Kang Q, Luan YS, Meng J **Tags: **Math Biosci **Source Type: **research

**Stochastic Population Model of Zea mays L.**

Abstract
We propose a minimalist stochastic population model of maize, focused on the description of the maize vegetative stages (seedlings with different number of leaves) involved in the propagation of vector-borne diseases. This model was parameterized from laboratory and field experiments and from observational field studies for multiple hybrids and different weather and soil conditions, taking into account only temperature as input variable. We propose three different submodels to estimate the distribution of the Final Leaf Number NFLN in the plants and to estimate the tassel initiation probability. The first...

**Source: **Mathematical Biosciences - April 25, 2019 **Category: **Statistics **Authors: **Barriga Rubio RH, Solari HG, Otero M **Tags: **Math Biosci **Source Type: **research

**Growth of a Long Bone Cross Section - A 2D Phase-Field Model.**

le P
Abstract
An approach to model the effect of exercise on the growth of mammal long bones is described. A Ginzburg-Landau partial differential equation system is utilised to study the change of size and shape of a cross-section caused by mechanically enhanced bone growth. The concept is based on a phase variable that keeps track of the material properties during the evolution of the bone. The relevant free energies are assumed to be elastic strain energy, concentration gradient energy and a double well chemical potential. The equation governing the evolution of the phase is derived from the total free energy an...

**Source: **Mathematical Biosciences - April 25, 2019 **Category: **Statistics **Authors: **Lindberg G, Ståhle P **Tags: **Math Biosci **Source Type: **research

**A novel CTAC coding method for predicting protein-protein interaction based on amino acid sequence.**

PMID: 31029609 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - April 25, 2019 **Category: **Statistics **Authors: **Wang X, Wang R, Wei Y, Gui Y **Tags: **Math Biosci **Source Type: **research

**Improved Model Prediction of Glioma Growth Utilizing Tissue-Specific Boundary Effects.**

CONCLUSION: Anatomical boundaries to tumor growth measurably deflect progression and affect estimates of kinetic parameters. The presented method reliably updates kinetic parameters to fit anatomic computational models to clinically derived subject data when those data are in a linear regime.
PMID: 31009624 [PubMed - as supplied by publisher] (Source: Mathematical Biosciences)

**Source: **Mathematical Biosciences - April 19, 2019 **Category: **Statistics **Authors: **Jacobs J, Rockne RC, Hawkins-Daarud AJ, Jackson PR, Johnston SK, Kinahan P, Swanson KR **Tags: **Math Biosci **Source Type: **research

**A Hybrid Method for Micro-Mesoscopic Stochastic Simulation of Reaction-Diffusion Systems.**

Abstract
The present paper introduces a new micro-meso hybrid algorithm based on the Ghost Cell Method (GCM) concept in which the microscopic subdomain is governed by the Reactive Multi-Particle Collision (RMPC) dynamics. The mesoscopic subdomain is modelled using the Reaction-Diffusion Master Equation (RDME). The RDME is solved by means of the Inhomogeneous Stochastic Simulation Algorithm (ISSA). No hybrid algorithm has hitherto used the RMPC dynamics for modeling reactions and the trajectories of each individual particle. The RMPC is faster than other molecular based methods and has the advantage of conserving m...

**Source: **Mathematical Biosciences - April 15, 2019 **Category: **Statistics **Authors: **Sayyidmousavi A, Rohlf K, Ilie S **Tags: **Math Biosci **Source Type: **research

**Bifurcation manifolds in predator-prey models computed by Gr öbner basis method.**

Bifurcation manifolds in predator-prey models computed by Gröbner basis method.
Math Biosci. 2019 Apr 01;:
Authors: Hajnová V, Přibylová L
Abstract
Many natural processes studied in population biology, systems biology, biochemistry, chemistry or physics are modeled by dynamical systems with polynomial or rational right-hand sides in state and parameter variables. The problem of finding bifurcation manifolds of such discrete or continuous dynamical systems leads to a problem of finding solutions to a system of non-linear algebraic equations. This approach often fails since it is not...

**Source: **Mathematical Biosciences - April 1, 2019 **Category: **Statistics **Authors: **Hajnová V, Přibylová L **Tags: **Math Biosci **Source Type: **research

**General Mathematical Formula for Near Equilibrium Relaxation Kinetics of Basic Enzyme Reactions and its Applications to Find Conformational Selection Steps.**

Abstract
A general mathematical formula of basic enzyme reactions was derived with nearly no dependence on conditions nor assumptions on relaxation kinetic processes near equilibrium in a simple single-substrate-single-product enzyme reaction. The new formula gives precise relationships between the rate constants of the elementary reaction steps and the apparent relaxation rate constant, rather than the initial velocity that is generally used to determine enzymatic parameters according to the Michaelis-Menten theory. The present formula is shown to be complementary to the Michaelis-Menten formulae in a sense that ...

**Source: **Mathematical Biosciences - March 29, 2019 **Category: **Statistics **Authors: **Egawa T, Callender R **Tags: **Math Biosci **Source Type: **research

**A Structure Preserving Model Order Reduction Method for Calcium Homeostatic System.**

Abstract
Calcium Homeostasis is a complex physiological process. Its mathematical model results in high order differential equation. In this paper, a model order reduction technique, based on time scale separation is proposed for a 27th order Calcium Homeostasis and Bone Remodeling(CHBR) system. The original state-space model after linearization has been decoupled into three reduced order subsystems: "Very-Slow", "Slow" and "Fast", at the same time preserving the structure of the system. The time and frequency response of individual reduced order model has been compared with the respo...

**Source: **Mathematical Biosciences - March 28, 2019 **Category: **Statistics **Authors: **Biswal B, Sen S, Maka S **Tags: **Math Biosci **Source Type: **research

**An investigation of the combined effect of an annual mass gathering event and seasonal infectiousness on disease outbreak.**

Abstract
In this paper, we investigate the effects of recurring mass gathering event on the spread of an epidemic. Mass gatherings take place when a large number of people from different locations visit a particular region during a short time period. Such activity plays a crucial role in the epidemic spread as traveling facilitates the spread of an epidemic between disparate locations and crowded conditions can accelerate the disease transmission. An additional component that affects disease spread is the seasonality in transmission. In this paper, we study the interplay between the periodic natures of seasonal tr...

**Source: **Mathematical Biosciences - March 21, 2019 **Category: **Statistics **Authors: **Xu F, Connell McCluskey C **Tags: **Math Biosci **Source Type: **research

**Prediction of aptamer-protein interacting pairs based on sparse autoencoder feature extraction and an ensemble classifier.**

In this study, a novel ensemble method is presented to predict aptamer-protein interacting pairs by integrating sequence characteristics derived from aptamers and the target proteins. The features extracted for aptamers were the compositions of amino acids and pseudo K-tuple nucleotides. In addition, a sparse autoencoder was used to characterize features for the target protein sequences. To remove redundant features, gradient boosting decision tree (GBDT) and incremental feature selection (IFS) methods were used to obtain the optimum combination of sequence characters. Based on 616 selected features, an ensemble of three s...

**Source: **Mathematical Biosciences - March 14, 2019 **Category: **Statistics **Authors: **Yang Q, Jia C, Li T **Tags: **Math Biosci **Source Type: **research

**Numerical discovery and continuation of points of infinitesimal homeostasis.**

Abstract
Homeostasis is the biological notion of certain outputs being stable with respect to input perturbations, at least over a relatively broad range. In general this is a result of coordination of regulatory mechanisms, and is thought to occur throughout biology. Recently the mathematical concept of infinitesimal homeostasis has been introduced, with the key idea being that the emergence of homeostasis is governed by certain geometric structures; these have previously been found in several mathematical models of biological processes. The theory of infinitesimal homeostasis has been applied to several specific...

**Source: **Mathematical Biosciences - March 13, 2019 **Category: **Statistics **Authors: **Donovan GM **Tags: **Math Biosci **Source Type: **research

**Modeling the impact of sterile males on an Aedes aegypti population with optimal control.**

Abstract
We use partial differential equations to describe the dynamics of an Aedes aegypti mosquito population on an island, and the effects of a sterile male release. The model includes mosquito movement and an Allee effect to capture extinction events. We apply optimal control theory to identify the release strategy that eliminates the mosquitoes most rapidly, conditional on a limited availability of sterile males. The optimal solution for a single location is to initially release a substantial number of mosquitoes and to subsequently release fewer sterile males proportionally to the decreasing female populatio...

**Source: **Mathematical Biosciences - March 8, 2019 **Category: **Statistics **Authors: **Multerer L, Smith T, Chitnis N **Tags: **Math Biosci **Source Type: **research

**Robust model selection between population growth and multiple merger coalescents.**

Abstract
We study the effect of biological confounders on the model selection problem between Kingman coalescents with population growth, and Ξ-coalescents involving simultaneous multiple mergers. We use a low dimensional, computationally tractable summary statistic, dubbed the singleton-tail statistic, to carry out approximate likelihood ratio tests between these model classes. The singleton-tail statistic has been shown to distinguish between them with high power in the simple setting of neutrally evolving, panmictic populations without recombination. We extend this work by showing that cryptic recombination ...

**Source: **Mathematical Biosciences - March 6, 2019 **Category: **Statistics **Authors: **Koskela J, Berenguer MW **Tags: **Math Biosci **Source Type: **research

**Optimal Control of Environmental Cleaning and Antibiotic Prescription in an Epidemiological Model of Methicillin-resistant Staphylococcus aureus Infections in Hospitals.**

Abstract
We consider a deterministic model of Methicillin-resistant Staphylococcus aureus infections in hospitals with seasonal oscillations of the antibiotic prescription rate. The model compartments consist of uncolonized patients with or without antibiotic exposure, colonized patients with or without antibiotic exposure, uncontaminated or contaminated healthcare workers, and free-living bacteria in the environment. We apply optimal control theory to this seven-compartment periodic system of ordinary differential equations to minimize the number of colonized patients and density of bacteria in the environment wh...

**Source: **Mathematical Biosciences - March 5, 2019 **Category: **Statistics **Authors: **Huang Q, Huo X, Ruan S **Tags: **Math Biosci **Source Type: **research

**Parasitic plasmid-host dynamics and host competition in flowing habitats.**

Abstract
Competition and coexistence were examined for two bacterial species, each potentially carrying a fitness-reducing, parasitic plasmid that was vertically transmitted with possible loss through segregation. Here, the fitness reduction of hosts was due to a toxin produced by plasmid-bearing cells and inhibiting plasmid-free cells. These populations were placed in a flow reactor habitat representing an idealized mammal gut. It was numerically shown that parasitic plasmids can mediate coexistence of competing host species, in conditions where plasmid-free hosts could not coexist. Numerical construction of a co...

**Source: **Mathematical Biosciences - March 5, 2019 **Category: **Statistics **Authors: **Grover JP, Wang FB **Tags: **Math Biosci **Source Type: **research