Mathematical Biology Research Papers

walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets... more

We formulate a susceptible-vaccinated-infected-recovered (SVIR) model by incorporating the vaccination of newborns, vaccineage, and mortality induced by the disease into the SIR epidemic model. It is assumed that the period of immunity... more

In epidemiological models of infectious diseases the basic reproduction number ${\mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian... more

The telomere length can either be shortened or elongated by an enzyme called telomerase after each cell division. Interestingly, the shortest telomere is involved in controlling the ability of a cell to divide. Yet, its dynamics remains... more

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- by Khanh Dao Duc
- •
- 7
  Stochastic Process, Mathematical Biology, Senescence, Telomeres

In this study, delay differential equations are investigated using the variational iteration method. Delay differential equations (DDEs) have a wide range of application in science and engineering. They arise when the rate of change of a... more

The reports published by WHO on a daily basis suggest that tuberculosis (TB) remains the top infectious killer as in 2016 in SouthEast Asia, and hence considered a " burden " in these countries. Very few studies on the burden of TB in... more

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- by Kalyan Das and +1
  Anisha Das
- •
- Mathematical Biology

This is one of the first books to study neural development using computational and mathematical modeling. Modeling provides precise and exact ways of expression, which allow us to go beyond the insights that intuitive or commonsense... more

Diabetes mellitus is a disease characterized by a range of metabolic complications involving an individual&amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;s blood glucose levels, and its main regulator, insulin. These... more

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During a primary immune response generally two classes of antibody are produced, immunogtobulin M (IgM) and immunoglobulin G (IgG). It is currently thought that some lymphocytes which initially produce IgM switch to the production of IgG... more

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- by Byron Goldstein and +1
  Alan Perelson
- •
- 9
  Immune response, Mathematical Biology, Kinetics, Biological Sciences

A mathematical analysis of the process of gas exchange in the lung is presented taking into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. Since the rate at... more

A mathematical analysis of the process of gas exchange in the lung is presented taking into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. Since the rate at which blood gets oxygenated in the pulmonary capillaries is very fast, it is difficult to set up an experimental study to determine the effects of various parameters on equilibration rate. The proposed study is aimed at determining the effects of various physiological parameters on equilibration rate in pathological conditions. Among the significant results are that 1. dissolved oxygen takes longer to achieve equilibration across the pulmonary membrane and carbon dioxide attains equilibration faster, 2. the equilibration length increases with increase in blood velocity, haemoglobin concentration, calibre of pulmonary capillaries and fall in alveolar PO2, 3. the alveolar PCO 2 and forward and backward reaction rates of haemoglobin with CO2 do not materially affect the equilibration rate or length. 4. At complete equilibration, by the end of the pulmonary capillary 92% of the total haemoglobin has combined with oxygen and 8% free pigment is left which is present as carbamino haemoglobin, met haemoglobin, carboxy haemoglobin etc. These results are of some importance for anaemic conditions, muscular exercise, meditation, altitude physiology, hypo-ventilation, hyperventilation, etc. Symbols: H+: hydrogen ion; 02: oxygen; C02: carbondioxide; Hb02: oxyhaemoglobin; HbC02: carbaminohaemoglobin ; P02 : partial pressure of 02 ; PC02 : partial pressure of CO2 ; PaO2 : 02 tension in arterial blood; PaC02:CO2 tension in arterial blood; k~: forward rate constant for Eq. (1); k2: backward rate constant for Eq. (1); m~ : forward rate constant for Eq. (2); m2: backward rate constant for Eq. (2); k: equilibration rate; a: radius of the capillary; Q: velocity of blood; L: length of the capillary; Do: diffusion coefficient of O2 ; Dc: diffusion coefficient of CO2 ; Du : diffusion coefficient of Hb ; H: total haemoglobin concentration; A : matrix ; c~ : concentration of dissolved 02 in blood ; c2 : concentration of HbO2 in blood ; c3 : concentration of dissolved CO2 in blood ; c4 : concentration of HbCO2 in blood; cs: concentration of haemoglobin; Cl a~v: concentration of O2 in the alveolar region; c3 a~v : concentration of CO2 in the alveolar region ; C~ven : concentration of the ith species in venous blood; CZ,rt: concentrations of the ith species in arterial blood; F'~s: concentrations of the species in dimensionless form; J0, Io : Bessel's functions; Pa~v02 : tension of 02 in alveolar region; P.~vC02 : tension of CO2 in alveolar region.

Many bird species, especially song birds but also for instance some hummingbirds and parrots, have noted dialects. By this we mean that locally a particular song is sung by the majority of the birds, but that neighbouring patches may... more

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- by Nick Britton
- •
- 9
  Acoustics, Mathematical Biology, Animal communication, Learning

If the ureter becomes blocked, the resultant increased pressure may be relieved by inserting a double-J stent (a polymer tube, usually punctuated with holes). A major clinical problem associated with stent use is reflux (retrograde flow... more

Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored... more

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- by Peter R Greene
- •
- 3
  Bioengineering, Mathematical Biology, Myopia

The author \mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1- \alpha }}{\Gamma({\alpha})} \int^x_a... more

The biological control of the McDaniel spider mite, which is a pest on apple tree foliage, by a predacious mite species, which feeds upon it, is represented by a continuous-discrete time hybrid model incorporating temperature effects... more

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical... more

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- by Dirk Drasdo
- •
- 18
  Mathematical Biology, Agent Based, Cell Migration, Cell Adhesion

This article takes on a perhaps impossible task: not only to reconstruct the core argument of Arthur Peacocke's program in science and religion but also to evaluate it in two major areas where it would seem to be vulnerable, namely, more... more

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- by Philip Clayton
- •
- 7
  Sociology, Philosophy, Philosophy of Mind, Mathematical Biology

BACKGROUND: In spite of its indusrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including... more

BACKGROUND:
In spite of its indusrial usefulness and varied daily uses, lead (Pb) pollution is a widespread ecological problem that faces the humans in the 21th century. Pb was found to produces a wide range of toxic effects including neurotoxicity especially to the developing and young offspring. Recently, the utilization of herbal plants has received a significant attention where there has been rising awareness in their therapeutic use; among these is the garlic.
AIM OF THE WORK:
In light of the above, the current study is designed experimentally in female pregnant rats in order to investigate the beneficial role of garlic extract in the protection from the maternal and fetal cerebellar damage that produced by administration of different doses of Pb during pregnancy.
MATERIALS AND METHODS:
Positively pregnant female rats were divided into five groups; one control group, two Pb-treated groups (exposed to 160 and 320 mg/kg b.wt. of Pb, respectively) and two groups treated with both Pb and garlic (exposed to Pb as previous groups together with 250 mg/ kg b.wt. /day of garlic extract). Treatments started from day 1 till day 20 of pregnancy, where the mother rats of different experimental groups were sacrified to obtain the fetuses. Pb level in the maternal nd fetal blood and cerebellum was estimated by spectrophotometry. Specimens of the cerebellum of different mother and fetal groups were processed to histological and immunohistochemical staining for microscopic examination.
RESULTS:
The results showed that administration of Pb to pregnant rats resulted in a dose-dependent toxicity for both mothers and fetuses in the form of decrease of maternal weight gain, placental and fetal weights, brain weight and diminished fetal growth parameters, which were prominent in rat's group treated with larger dose of Pb. In Pb-treated rats, Pb level in blood and cerebellum was high when compared to the control. The histopathological examination of the cerebellum of treated dams and fetuses showed marked alterations mainly in the form of Purkinje cell degeneration and lack of deveopmet of fetal cerebellum. Co-treatment of garlic extract along with Pb resulted in a significant decrease in Pb levels as compared with those treated with Pb alone with improvement of the histopathological changes.
CONCLUSIONS:
This study was useful in evaluating the hazardous effects of uncontrolled use of Pb in general and in assessing the developmental and neurotoxicity of fetuses due to exposure during pregnancy in particular. Co-administration of garlic has beneficial effects in amelioration of Pb-induced neurotoxicity and reversing the histopathological changes of the cerebellum of mother rats and fetuses.
KEYWORDS:
garlic; glial fibrillary acidic protein; lead; purkinje cells

Sickle cell disorder (SCD) is a chronic illness that in England disproportionately affects marginalized ethnic groups, but has yet to feature extensively within educational or disability research. This review of existing literature makes... more

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- by Karl Atkin
- •
- 12
  Sociology, Social Work, Mathematical Biology, Health Education

Biological cells are considered as the building units of life. It was Robert Hooke who coined the word cell in histological description of cork and other specimens using coarse optical lenses, as published in his Micrographia in 1665... more

Biological cells are considered as the building units of life. It was Robert Hooke who coined the word cell in histological description of cork and other specimens using coarse optical lenses, as published in his Micrographia in 1665 [10]. A few years later, Anthonie van Leeuwenhoek used a self-built microscope to observe living microorganisms which he called animalcules ('little animals') which are known today as protozoa, bacteria, and other forms of life [6]. Since these early years of observation, researchers have come a long way to decipher many features of life, ranging from the structural and functional organization of single-and multi-cell organisms to entire populations, communities, and ecosystems. Researchers recognized that the mathematical language is also a powerful tool for explaining biological phenomena. More specifically, the dynamics of biological systems can be described, simulated, and often predicted in the form of mathematical formulas, algorithms, and computer models. In recent years, computational biology (which includes a quantitative data analysis approach, theoretical methods, mathematical modelling, and computational simulation techniques) has become essential in biological research. This is because modern experimental methods (e.g. advanced imaging techniques, biochemical, genetic, immunological, and molecular analyses) are generating massive data sets at an unprecedented rate, detail, and complexity. The book by Chauvière, Preziosi, and Verdier focuses on an area of research known as cell mechanics. Here, investigators attempt to illuminate how cells sense and identify, interact with each other, and respond to the physical properties of the environment in which they live. Cell mechanics, which draws investigators from various disciplines such as biology, physics, mathematics, computer science, and engineering, has proven to be indispensable for elucidating mechanisms involved in many aspects of cell dynamics, including cell structure, movement, and adhesion [2-4] embryogenesis and embryonics [7], wound healing and tissue engineering [1,11], viable cell growth arrest and apoptosis [5,8], as well as the development of diseases such as asthma, glaucoma, and cancer [9]. The editors point out in the preface that the book is the result of many years of collaboration among researchers of the European Research and Training Network on a topic entitled 'Modeling, Mathematical Methods and Computer Simulation of Tumour Growth and Therapy'. The book contains reviews that describe experimental and applied mathematical approaches to illuminate how cells behave at various scales. The editors emphasize that it became clear while researching these biological phenomena from different points of view that 'multiscale problems are ubiquitous and fundamental in cell mechanics'.

"""Lyapunov functions for some mathematical models of ecological commensalism between two species are introduced. Global stability of the unique positive equilibrium is thereby established. Keyword: Models of ecological commensalism;... more

Richard "Dick" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who had researched diversity in human... more

Richard "Dick" Levins (June 1, 1930 – January 19, 2016) was an ex-tropical farmer turned ecologist, a population geneticist, biomathematician, mathematical ecologist, and philosopher of science who had researched diversity in human populations. Until his death, Levins was a university professor at the Harvard T.H. Chan School of Public Health and a long-time political activist. He was best known for his work on evolution and complexity in changing environments and on metapopulations.

Levins' writing and speaking is extremely condensed. This, combined with his Marxism, has made his analyses less well-known than those of some other ecologists and evolutionists who were adept at popularization. One story of his Chicago years is that, in order to understand his lectures, his graduate students each needed to attend Levins' courses three times: the first time to acclimate themselves to the speed of his delivery and the difficulty of his mathematics; the second to get the basic ideas down; and the third to pick up his subtleties and profundities.

Levins also had written on philosophical issues in biology and modelling. One of his influential articles is "The Strategy of Model Building in Population Biology". He has influenced a number of contemporary philosophers of biology.[citation needed] Levins often boasted publicly that he was a 'fourth generation Marxist' and often had said that the methodology in his Evolution in Changing Environments was based upon the introduction to Marx's Grundrisse, the rough draft of Das Kapital. With the evolutionary geneticist Richard Lewontin (1929–), Levins had written a number of articles on methodology, philosophy, and social implications of biology. Many of these are collected in The Dialectical Biologist. In 2007, the duo published a second thematic collection of essays titled Biology Under the Influence: Dialectical Essays on Ecology, Agriculture, and Health.

Also with Lewontin, Levins had co-authored a number of satirical articles criticizing sociobiology, systems modeling in ecology, and other topics under the pseudonym Isadore Nabi. Levins and Lewontin managed to place a ridiculous biography of Nabi and his achievements in American Men of Science, thereby showing how little editorial care and fact-checking work went on in that respected reference work.

A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and... more

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- by ADAMU ISHAKU and +2
  Shuaibu Abdullahi
  Nafiu Hussaini
- •
- 3
  Mathematical Biology, Biological Sciences, Mathematical Sciences

The astonishing diversity of life has evolved over many millions of years of natural selection. Yet natural selection, as often taught in introductory courses and textbooks on population genetics, seems to explain why diversity should not... more

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- by Géza Meszéna
- •
- 8
  Mathematical Biology, Ecology, Biological Sciences, Adaptive Dynamics

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- by Paolo Di Pasquale
- •
- 123
  Engineering, Chemical Engineering, Cognitive Science, Mathematics

Non protein-coding RNAs (ncRNAs) are a research hotspot in bioinformatics. Recent discoveries have revealed new ncRNA families performing a variety of roles, from gene expression regulation to catalytic activities. It is also believed... more

"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and... more

"Networks are mathematically directed (in practical applications also undirected) graphs and a graph is a one-dimensional abstract complex, i.e., a topological space. Network theory focuses on various topological structures and properties, dynamic properties, and functionality-topology relationship, etc. There are some common mathematical foundations, theories and methodology for network analysis, in which graph theory, statistics, and operational research, etc., are the fundamental sciences of network analysis. Various emerging biological networks, at both micro- and macro- levels, will provide numerous sources for the development of general network theory and methodology and also facilitate the development of theory and methodology of biological networks.

Biological network analysis is a fast moving science. Many core scientific issues, for example, ecological structure, co-evolution, co-extinction and biodiversity conservation in ecology, and cancer development and metabolic regulation in health science, etc., are expected to be addressed by network approaches and network analysis. Network analysis is becoming the core methodology to treat complex biological systems. As the fast development of this area, more and more papers on biological networks are published.

At present explosive numbers of quality papers on biological networks are being published each year. The initiation of the journal, Network Biology, will provide a public and unified platform for the publication of these studies. From this integrated and unique journal, researchers, university teachers and students will thoroughly have an in-depth and complete insight on knowledge, methodology and recent advances of biological networks.

In the view of system dynamics, biological networks are always self-organized systems with emergent, autonomous and adaptive properties. Their dynamics can be represented by agent-based modeling, individual-based modeling and some other methodologies like neural network modeling. Therefore, agent-based modeling, individual-based modeling, self-organization of biological systems, and neural network modeling, etc., fall into the aims and scope of the journal, Network Biology.

The NETWORK BIOLOGY (ISSN 2220-8879) is an open access, peer-reviewed online journal that considers scientific articles in all different areas of network biology. It is the transactions of the International Society of Network Biology.It dedicates to the latest advances in network biology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Network Biology include, but are not limited to:

•Theories, algorithms and programs of network analysis
•Innovations and applications of biological networks
•Dynamics, optimization and control of biological networks
•Ecological networks, food webs and natural equilibrium
•Co-evolution, co-extinction, biodiversity conservation
•Metabolic networks, protein-protein interaction networks, biochemical reaction networks, gene networks, transcriptional regulatory networks, cell cycle networks, phylogenetic networks, network motifs
•Physiological networks
•Network regulation of metabolic processes, human diseases and ecological systems
•Social networks, epidemiological networks
•System complexity, self-organized systems, emergence of biological systems, agent-based modeling, individual-based modeling, neural network modeling, and other network-based modeling, etc.
We are also interested in short communications that clearly address a specific issue or completely present a new ecological network, food web, or metabolic or gene network, etc.

Authors can submit their works to the email box of this journal, networkbiology@iaees.org. All manuscripts submitted to this journal must be previously unpublished and may not be considered for publication elsewhere at any time during review period of this journal. Authors are asked to read Author Guidelines before submitting manuscripts.

In addition to free submissions from authors around the world, special issues are also accepted. The organizer of a special issue can collect submissions (yielded from a research project, a research group, etc.) on a specific research topic, or submissions of a scientific conference for publication of special issue.

Network Biology
ISSN 2220-8879
URL: http://www.iaees.org/publications/journals/nb/online-version.asp
RSS feed: http://www.iaees.org/publications/journals/nb/rss.xml
E-mail: networkbiology@iaees.org
Editor-in-Chief: WenJun Zhang"

This paper addresses the global stability of a two-species Lotka-Volterra cooperative system with four discrete delays via the method of Lyapunov functionals. We apply our Lyapunov functional techniques to prove stability of... more

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up... more

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- by Bertrand Wong
- •
- 48
  Mathematics, Applied Mathematics, Mathematical Statistics, Statistics

Not original research

In this paper we propose and study a three dimensional continuous time dynamical system modelling a three team consists of two preys and one predator with the assumption that during predation the members of both teams of preys help each... more

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- by Syed Abbas
- •
- 7
  Applied Mathematics, Mathematical Biology, Competition, Persistence

A mathematical model of contracting skeletal muscle is studied. The model is composed by an elastic element (SE) in series with a contractile dement (CE) that describes the cross bridge kinetics with a formulation derived by that proposed... more

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- by Eihab Bashier
- •
- 2
  Mathematical Biology, Singular Perturbations

The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a... more

The aim of this book is to give a contemporary review of tree growth modelling and represent our own results in this field. We demonstrate that the growth inhibition can be a result of a systemic level effect, which can be seen in a whole-tree physiological model which includes submodels for the processes of photosynthesis, mineral nutrition, respiration, phloem and xylem transport, and growth of roots, stems, and leaves.

The parts 1, 2 and 3 represent the review and analysis of existing models, beginning with simple growth formulas and then concentrating in contemporary dynamic (ecophysiological) models which contain many state variables and tens of parameters. The analysis of these models is given by the main components of growth process.

Part 4 deals with the most important problem of causal tree growth analysis – the reason of growth cessation (self-inhibition) of too big tree. The arguments are given, showing the inadequacy of explanations which are based on Pütter-Bertalanffy equation. In the fig. 4.5 the numerical scheme of carbon balance for whole tree is represented, based on the experimental results of Estonian researchers.

In part 5 the description of our model PUU-1 is given. It contains 9 state variables (see List of symbols), 6 driving variables (table 6.1) and 43 parameters (table 6.3). The model enables to analyze both seasonal and ontogenetic dynamics of evergreen tree growth. The summary of all equations of the model is represented in ch. 5.9.

Part 6 deals with identification of the model: getting initial values of state variables and values of parameters and driving variables. More than half of them are based on the measurements made by Estonian researchers in Picea abies, others are taken from literature.

Part 7 gives the results of numerical experiments with our model – analysis of sensitivity of model variables and parameters, examples of growth dynamics, including numerical experiments with fertilization. The model fits satisfactorily with measured data. The comparison of calculated tree ring dynamics with dendrochronological data shows great perspectives in applying dynamical growth models of whole tree in dendrochronology, as well as in growth analysis and prediction, including situations
and problems which arise in agroforestry.

The most important theoretical result of our modelling is connected with self-inhibition of growth in tree ontogeny. It is shown, that self-inhibition of growth is taking place even without any aging factor, only because of size effects, which are mostly connected with changes in tree water exchange and trans port of assimilates (supplying of roots with assimilates becoming worse according to monotonous growth of cambium area). In the last chapter (7.6) the perspectives of tree growth modelling are discussed.

Plant growth modeling, especially that of crops such as the legumes used in this project are useful in crop management, pest and disease management, and yield forecasting. Using a new method for modeling, the user will benefit from the... more

We try to study the general properties of the Van der Pol oscillator like the occurrence of Hopf bifurcation and limit cycles. Thereafter we try to see the behavior of the oscillator near the limit cycle under periodic forcing and and... more

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- by Sunirmal Roy
- •
- Mathematical Biology

Every even integer > 2 is the sum of two prime numbers
& equivalent
Each odd integer > 5 is the sum of three prime numbers
USING THE SIEVE OF ERATOSTHENES

This article surveys and synthesizes dynamic systems models of development from biology, neuroscience, and psychology in order to propose an integrated account of growth, learning, and behavior. Key to this account is the concept of... more

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- by Noah Moss Brender
- •
- 58
  Genetics, Neuroscience, Psychology, Cognitive Science

Includes a description of history of theoretical biology and the author's contributions to the Estonian Spring Schools in Theoretical Biology (1975–2019) – altogether over 50 essays. University of Tartu Press, 495 pp.

We present 1) a novel unified conception of science, cognition and phenomenology in terms of the Klein Bottle logophysics, 2) as a supradual creative agency based on self and hetero-reference and multistate logic associated to the... more

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- by Diego Lucio Rapoport (Campodonico) and +1
  Jean-claude Perez
- •
- 17
  Semiotics, Bioinformatics, Evolutionary Biology, Neuroscience

Mathematical Biology

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