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Response of Tumor Spheroids to Radiation: Modeling and Parameter Estimation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We propose a spatially distributed continuous model for the spheroid response to radiation, in which the oxygen distribution is represented by means of a diffusion-consumption equation and the radiosensitivity parameters depend on the oxygen concentration. The induction of lethally damaged cells by a pulse of radiation, their death, and the degradation of dead cells are included. The compartments of lethally damaged cells and of dead cells are subdivided into different subcompartments to simulate the delays that occur in cell death and cell degradation, with a gain in model flexibility. It is shown that, for a single i...
Source: Bulletin of Mathematical Biology - November 14, 2009 Category: Bioinformatics Authors: Bertuzzi A, Bruni C, Fasano A, Gandolfi A, Papa F, Sinisgalli C Tags: Bull Math Biol Source Type: journals

Hyperbolic Saturation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Several hyperbolically saturating empirical models, such as the Michaelis-Menten rate equation, Monod's relative population growth rate, competitive inhibition, and Langmuir's adsorption, are rederived from a simple queuing relation. The resulting derivations reveal and potentially explain the underlying structure and meaning of such empirical models. This view is proposed as a unifying heuristic. PMID: 19915923 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)
Source: Bulletin of Mathematical Biology - November 14, 2009 Category: Bioinformatics Authors: Jackson JH, Maccluer CR Tags: Bull Math Biol Source Type: journals

Efficient or Inaccurate? Analytical and Numerical Modelling of Random Search Strategies.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A large number of observational and theoretical studies have investigated animal movement strategies for finding randomly located food items. Many of these studies have claimed that a particular strategy is advantageous over other strategies or that the spatial distribution of the food items affects the search efficiency. Here, we study a deliberately idealised problem, in which a blind forager searches for re-visitable food items. We show analytically that the forager's efficiency is completely independent of both its movement strategy and the spatial pattern of the food items and depends only on the density of food i...
Source: Bulletin of Mathematical Biology - November 14, 2009 Category: Bioinformatics Authors: James A, Pitchford JW, Plank MJ Tags: Bull Math Biol Source Type: journals

On the Modelling of Biological Patterns with Mechanochemical Models: Insights from Analysis and Computation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The diversity of biological form is generated by a relatively small number of underlying mechanisms. Consequently, mathematical and computational modelling can, and does, provide insight into how cellular level interactions ultimately give rise to higher level structure. Given cells respond to mechanical stimuli, it is therefore important to consider the effects of these responses within biological self-organisation models. Here, we consider the self-organisation properties of a mechanochemical model previously developed by three of the authors in Acta Biomater. 4, 613-621 (2008), which is capable of reproducing the be...
Source: Bulletin of Mathematical Biology - November 14, 2009 Category: Bioinformatics Authors: Moreo P, Gaffney EA, García-Aznar JM, Doblaré M Tags: Bull Math Biol Source Type: journals

Maximum Urine Concentrating Capability in a Mathematical Model of the Inner Medulla of the Rat Kidney.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In a mathematical model of the urine concentrating mechanism of the inner medulla of the rat kidney, a nonlinear optimization technique was used to estimate parameter sets that maximize the urine-to-plasma osmolality ratio (U/P) while maintaining the urine flow rate within a plausible physiologic range. The model, which used a central core formulation, represented loops of Henle turning at all levels of the inner medulla and a composite collecting duct (CD). The parameters varied were: water flow and urea concentration in tubular fluid entering the descending thin limbs and the composite CD at the outer-inner medullary...
Source: Bulletin of Mathematical Biology - November 14, 2009 Category: Bioinformatics Authors: Marcano M, Layton AT, Layton HE Tags: Bull Math Biol Source Type: journals

Interaction of Tumor with Its Micro-environment: A Mathematical Model.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor micro-environment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-beta) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-beta induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable ...
Source: Bulletin of Mathematical Biology - November 12, 2009 Category: Bioinformatics Authors: Kim Y, Friedman A Tags: Bull Math Biol Source Type: journals

Mathematical Model for Optimal Use of Sulfadoxine-Pyrimethamine as a Temporary Malaria Vaccine.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper, we introduce a deterministic malaria model for determining the drug administration protocol that leads to the smallest first malaria episodes during the wet season. To explore the effects of administering the malaria drug on different days during the wet season while minimizing the potential harmful effects of drug overdose, we define 40 drug administration protocols. Our results fit well with the clinical studies of Coulibaly et al. at a site in Mali. In addition, we provide protocols that lead to smaller number of first malaria episodes during the wet season than the protocol of Coulibaly et al. PM...
Source: Bulletin of Mathematical Biology - November 12, 2009 Category: Bioinformatics Authors: Dembele B, Friedman A, Yakubu AA Tags: Bull Math Biol Source Type: journals

Stability and Bifurcations in an Epidemic Model with Varying Immunity Period.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and endemic. It is proved that the disease-free equilibrium is locally and globally asymptotically stable. When an endemic equilibrium exists, it is possible to analytically prove its local and global stability using Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and traceDDE to investigate different dynamical regimes in the model using numerical continuation for...
Source: Bulletin of Mathematical Biology - November 7, 2009 Category: Bioinformatics Authors: Blyuss KB, Kyrychko YN Tags: Bull Math Biol Source Type: journals

Irreducibility in RNA Structures.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper, we study irreducibility in RNA structures. By RNA structure, we mean RNA secondary as well as RNA pseudoknot structures as abstract contact structures. We give an analysis contrasting random and minimum free energy (mfe) configurations and secondary versus pseudoknots structures. In the process, we compute various distributions: the numbers of irreducible substructures and their locations and sizes, parameterized in terms of the maximal number of mutually crossing arcs, k-1, and the minimal size of stacks sigma. In particular, we analyze the size of the largest irreducible substructure for random and mfe...
Source: Bulletin of Mathematical Biology - November 5, 2009 Category: Bioinformatics Authors: Jin EY, Reidys CM Tags: Bull Math Biol Source Type: journals

Mathematical Model of the Formation of Morphogen Gradients Through Membrane-Associated Non-receptors.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The importance of morphogens is a central concept in developmental biology. Multiple-fate patterning and the robustness of the morphogen gradient are essential for embryo development. The ways by which morphogens diffuse from a local source to form long distance gradients can differ from one morphogen to the other, and for the same morphogen in different organs. This paper will study the mechanism by which morphogens diffuse through the aid of membrane-associated non-receptors and will investigate how the membrane-associated non-receptors help the morphogen to form long distance gradients and to achieve good robustness...
Source: Bulletin of Mathematical Biology - October 31, 2009 Category: Bioinformatics Authors: Lei J, Song Y Tags: Bull Math Biol Source Type: journals

From Microscopic to Macroscopic Descriptions of Cell Migration on Growing Domains.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is an almost ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environm...
Source: Bulletin of Mathematical Biology - October 28, 2009 Category: Bioinformatics Authors: Baker RE, Yates CA, Erban R Tags: Bull Math Biol Source Type: journals

A Structured Threshold Model for Mountain Pine Beetle Outbreak.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A vigor-structured model for mountain pine beetle outbreak dynamics within a forest stand is proposed and analyzed. This model explicitly tracks the changing vigor structure in the stand. All model parameters, other than beetle vigor preference, were determined by fitting model components to empirical data. An abrupt threshold for tree mortality to beetle densities allows for model simplification. Based on initial beetle density, model outcomes vary from decimation of the entire stand in a single year, to inability of the beetles to infect any trees. An intermediate outcome involves an initial infestation which subsequ...
Source: Bulletin of Mathematical Biology - October 24, 2009 Category: Bioinformatics Authors: Lewis MA, Nelson W, Xu C Tags: Bull Math Biol Source Type: journals

General Model of Inflammation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Dysfunctions in the immune system, due to genetics, disease or environmental factors, can cause bacterial colonization and chronic inflammation. In cystic fibrosis and chronic obstructive pulmonary disease, respiratory infections can initiate inflammation of the airway. We propose a system of nonlinear ordinary differential equations to describe interactions between macrophages, both inflammatory and anti-inflammatory cytokines, and bacteria. Small changes in parameters governing inflammatory cytokine production and macrophage sensitivity to cytokines result in dramatically different model behaviors. When the immune sy...
Source: Bulletin of Mathematical Biology - October 23, 2009 Category: Bioinformatics Authors: Herald MC Tags: Bull Math Biol Source Type: journals

Oscillations in an Intra-host Model of Plasmodium Falciparum Malaria Due to Cross-reactive Immune Response.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We consider an intra-host model of malaria that allows for antigenic variation within a single species. More specifically, the host's immune response is compartmentalized into reactions to major and minor epitopes. We investigate the conditions that lead to transient oscillations, which correspond to recurrent clinical episodes of the diseases, and how a small delay in the activation of the immune response can lead to persistent oscillations. We find that the efficacies of the immune responses to the major and minor epitopes, defined in terms of rate constants, play a crucial role in determining when there will be tran...
Source: Bulletin of Mathematical Biology - October 19, 2009 Category: Bioinformatics Authors: Mitchell JL, Carr TW Tags: Bull Math Biol Source Type: journals

Hantavirus Transmission in Sylvan and Peridomestic Environments.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We developed a compartmental model for hantavirus infection in deer mice (Peromyscus maniculatus) with the goal of comparing relative importance of direct and indirect transmission in sylvan and peridomestic environments. A direct transmission occurs when the infection is mediated by the contact of an infected and an uninfected mouse, while an indirect transmission occurs when the infection is mediated by the contact of an uninfected mouse with, for instance, infected soil. Based on population dynamics data and estimates of hantavirus decay in the two types of environments, our model predicts that direct transmission d...
Source: Bulletin of Mathematical Biology - October 9, 2009 Category: Bioinformatics Authors: Gedeon T, Bodelón C, Kuenzi A Tags: Bull Math Biol Source Type: journals

Leading Students to Investigate Diffusion as a Model of Brine Shrimp Movement.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We present our teaching philosophy, lecture notes, instructional and lab procedures, and the results of our class-tested experiments so that others can implement this exercise in their classes. Our own experience has led us to appreciate the pedagogical value of allowing students and faculty to grapple with open-ended questions, imperfect data, and the various issues of modeling biological phenomena. PMID: 19816745 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)
Source: Bulletin of Mathematical Biology - October 8, 2009 Category: Bioinformatics Authors: Kohler BR, Swank RJ, Haefner JW, Powell JA Tags: Bull Math Biol Source Type: journals

Properties of Normal Phylogenetic Networks.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A phylogenetic network is a rooted acyclic digraph with vertices corresponding to taxa. Let X denote a set of vertices containing the root, the leaves, and all vertices of outdegree 1. Regard X as the set of vertices on which measurements such as DNA can be made. A vertex is called normal if it has one parent, and hybrid if it has more than one parent. The network is called normal if it has no redundant arcs and also from every vertex there is a directed path to a member of X such that all vertices after the first are normal. This paper studies properties of normal networks.Under a simple model of inheritance that allo...
Source: Bulletin of Mathematical Biology - September 29, 2009 Category: Bioinformatics Authors: Willson SJ Tags: Bull Math Biol Source Type: journals

Modeling Spatial Spread of Infectious Diseases with a Fixed Latent Period in a Spatially Continuous Domain.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may diffuse, we formulate an SIR model with a simple demographic structure for the population living in a spatially continuous environment. The model is given by a system of reaction-diffusion equations with a discrete delay accounting for the latency and a spatially non-local term caused by the mobility of the individuals during the latent period. We address the existence, uniqueness, and positivity of solution to the initial-value problem for this type of system. Moreov...
Source: Bulletin of Mathematical Biology - September 28, 2009 Category: Bioinformatics Authors: Li J, Zou X Tags: Bull Math Biol Source Type: journals

Optimization of Virotherapy for Cancer.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Several viruses preferentially infect and replicate in cancer cells by usurping pathways that are defective in the tumor cell population. Such viruses have a potential as oncolytic agents. The aim of tumor virotherapy is that after injection of the replicating virus, it propagates in the tumor cell population with amplification. As a result, the oncolytic virus spreads to eradicate the tumor. The outcome of tumor virotherapy is determined by population dynamics and different from standard cancer therapy. Several models have been developed that provided considerable insights on the potential therapeutic scenarios. Howev...
Source: Bulletin of Mathematical Biology - September 28, 2009 Category: Bioinformatics Authors: Biesecker M, Kimn JH, Lu H, Dingli D, Bajzer Z Tags: Bull Math Biol Source Type: journals

Modelling Disease Introduction as Biological Control of Invasive Predators to Preserve Endangered Prey.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Invasive species are a significant cause of bio-diversity loss particularly in island ecosystems. It has been suggested to release pathogenic parasites as an efficient control measure of these mostly immune-naïve populations. In order to explore the potential impacts of such bio-control approach, we construct and investigate mathematical models describing disease dynamics in a host population that acts as a predator embedded in a simple food chain. The consequences of Feline Immunodeficiency Virus (FIV) introduction into a closed ecosystem are addressed using a bi-trophic system, comprising an indigenous prey (bir...
Source: Bulletin of Mathematical Biology - September 28, 2009 Category: Bioinformatics Authors: Oliveira NM, Hilker FM Tags: Bull Math Biol Source Type: journals

Revisiting an Equivalence Between Maximum Parsimony and Maximum Likelihood Methods in Phylogenetics.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Tuffley and Steel (Bull. Math. Biol. 59:581-607, 1997) proved that maximum likelihood and maximum parsimony methods in phylogenetics are equivalent for sequences of characters under a simple symmetric model of substitution with no common mechanism. This result has been widely cited ever since. We show that small changes to the model assumptions suffice to make the two methods inequivalent. In particular, we analyze the case of bounded substitution probabilities as well as the molecular clock assumption. We show that in these cases, even under no common mechanism, maximum parsimony and maximum likelihood might make conf...
Source: Bulletin of Mathematical Biology - September 28, 2009 Category: Bioinformatics Authors: Fischer M, Thatte B Tags: Bull Math Biol Source Type: journals

Theoretical Considerations of Fisher's Theorem in Small At-Risk Populations.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Small populations at risk of extinction due to threshold or competitive exclusion have a vested interest in rapid growth. Taking chance of survival into account for diploid populations, Fisher's theorem predicts a sex ratio favoring females under certain circumstances. Theoretical consideration of competitive exclusion shows such circumstances are reasonable under accepted modeling assumptions. PMID: 19771480 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)
Source: Bulletin of Mathematical Biology - September 21, 2009 Category: Bioinformatics Authors: Johnson SD Tags: Bull Math Biol Source Type: journals

A Mathematical Exploration of the Mystery of Loudness Adaptation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Loudness adaptation, or the decrease in perceived loudness of a steady, prolonged tone is rather a mysterious phenomenon. When measured by one technique (utilizing both ears), loudness of an extended tone will decrease by as much as 35 decibels; when measured by another technique (using only a single ear), loudness does not adapt at all regardless of how long the tone persists. The mystery is even more intriguing. When loudness adaptation does occur, the fractional reduction in the loudness of a tone (adaptation dB/sound level of extended tone dB SL) provides a good measure of the Stevens exponent, n, for loudness, an ...
Source: Bulletin of Mathematical Biology - September 1, 2009 Category: Bioinformatics Authors: Norwich KH Tags: Bull Math Biol Source Type: journals

Impacts of Foraging Facilitation Among Predators on Predator-prey Dynamics.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Whereas impacts of predator interference on predator-prey dynamics have received considerable attention, the "inverse" process-foraging facilitation among predators-have not been explored yet. Here we show, via mathematical models, that impacts of foraging facilitation on predator-prey dynamics depend on the way this process is modeled. In particular, foraging facilitation destabilizes predator-prey dynamics when it affects the encounter rate between predators and prey. By contrast, it might have a stabilizing effect if the predator handling time of prey is affected. Foraging facilitation is an Allee effect mechanism a...
Source: Bulletin of Mathematical Biology - August 20, 2009 Category: Bioinformatics Authors: Berec L Tags: Bull Math Biol Source Type: journals

Tubuloglomerular Feedback Signal Transduction in a Short Loop of Henle.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model does not represent other segments of the nephron, the water, and NaCl transport along which may impact fluid flow rate and NaCl transport along the TAL. To investigate the extent to which those transport processes affect TGF mediation, we have developed a mathematical model for TGF signal transduction in a short loop nephron. The model combines a simple representation of the renal cortex with a highly-detailed representation of the outer medulla (OM). ...
Source: Bulletin of Mathematical Biology - August 5, 2009 Category: Bioinformatics Authors: Layton AT, Edwards A Tags: Bull Math Biol Source Type: journals

Time Series Analysis of Particle Tracking Data for Molecular Motion on the Cell Membrane.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Biophysicists use single particle tracking (SPT) methods to probe the dynamic behavior of individual proteins and lipids in cell membranes. The mean squared displacement (MSD) has proven to be a powerful tool for analyzing the data and drawing conclusions about membrane organization, including features like lipid rafts, protein islands, and confinement zones defined by cytoskeletal barriers. Here, we implement time series analysis as a new analytic tool to analyze further the motion of membrane proteins. The experimental data track the motion of 40 nm gold particles bound to Class I major histocompatibility complex (MH...
Source: Bulletin of Mathematical Biology - August 5, 2009 Category: Bioinformatics Authors: Ying W, Huerta G, Steinberg S, Zúñiga M Tags: Bull Math Biol Source Type: journals

Numerical Equilibrium Analysis for Structured Consumer Resource Models.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of indivi...
Source: Bulletin of Mathematical Biology - July 30, 2009 Category: Bioinformatics Authors: de Roos AM, Diekmann O, Getto P, Kirkilionis MA Tags: Bull Math Biol Source Type: journals

A Model of Hydrodynamic Interaction Between Swimming Bacteria.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We study the dynamics and interaction of two swimming bacteria, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by "pushing" or "pulling" both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics of the pair, which complemented by numerical experiments, indicate that the tendency of bacteria to swim in or swim off depends strongly on the position of the propulsion force. In particular, we observe that positioning of the effective propulsion force inside the du...
Source: Bulletin of Mathematical Biology - July 30, 2009 Category: Bioinformatics Authors: Gyrya V, Aranson IS, Berlyand LV, Karpeev D Tags: Bull Math Biol Source Type: journals

The Allee Effect in Mechanistic Models Based on Inter-individual Interaction Processes.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Recently, Eskola and Geritz (Bull. Math. Biol. 69:329-346, 2007) showed that several discrete-time population models can be derived mechanistically within a single ecological framework by varying the within-season patterns of reproduction and inter-individual aggression. However, these models do not have the Allee effect. In this paper, we modify the original modelling framework by adding different mate finding processes, and thus derive mechanistically several population models with the Allee effect. PMID: 19639368 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)
Source: Bulletin of Mathematical Biology - July 28, 2009 Category: Bioinformatics Authors: Eskola HT, Parvinen K Tags: Bull Math Biol Source Type: journals

Candidate Genes Associated with Susceptibility for SARS-Coronavirus.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Assuming that no human had any previously acquired immunoprotection against severe acute respiratory syndrome coronavirus (SARS-CoV) during the 2003 SARS outbreak, the biological bases for possible difference in individual susceptibility are intriguing. However, this issue has never been fully elucidated. Based on the premise that SARS patients belonging to a given genotype group having a significantly higher SARS infection rate than others would imply that genotype group being more susceptible, we make use of a compartmental model describing disease transmission dynamics and clinical and gene data of 100 laboratory co...
Source: Bulletin of Mathematical Biology - July 9, 2009 Category: Bioinformatics Authors: Hsieh YH, Chen CW, Schmitz SF, King CC, Chen WJ, Wu YC, Ho MS Tags: Bull Math Biol Source Type: journals

Neurochemical Oscillations in the Basal Ganglia.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This work represents an attempt to elucidate the neurochemical processes in the basal ganglia by mathematical modelling. The correlation between neurochemistry and electrophysiology has been used to construct a dynamical system based on the basal ganglia's network structure. Mathematical models were constructed for different physical scales to reformulate the neurochemical and electrophysiological behaviour from synapses up to multi-compartment systems. Transformation functions have been developed to transit between the different scales. We show through numerical simulations that this network produces oscillations in t...
Source: Bulletin of Mathematical Biology - July 8, 2009 Category: Bioinformatics Authors: Noori HR, Jäger W Tags: Bull Math Biol Source Type: journals

Mathematical Study of the Role of Gametocytes and an Imperfect Vaccine on Malaria Transmission Dynamics.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite) in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features. It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by [Symbol: see text](0)), is less than unity. Further, it has a unique endemic equilibrium if [Symbol: see text](0)>1. The model is extended to...
Source: Bulletin of Mathematical Biology - June 30, 2009 Category: Bioinformatics Authors: Teboh-Ewungkem MI, Podder CN, Gumel AB Tags: Bull Math Biol Source Type: journals

Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The research presented in this paper addresses the problem of fitting a mathematical model to epidemic data. We propose an implementation of the Landweber iteration to solve locally the arising parameter estimation problem. The epidemic models considered consist of suitable systems of ordinary differential equations. The results presented suggest that the inverse problem approach is a reliable method to solve the fitting problem. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters against real data sets for the case of recurrent epidemics caused by th...
Source: Bulletin of Mathematical Biology - June 30, 2009 Category: Bioinformatics Authors: Capistrán MA, Moreles MA, Lara B Tags: Bull Math Biol Source Type: journals

Transmission Dynamics of an Influenza Model with Vaccination and Antiviral Treatment.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However, the benefit of antiviral use can be compromised if drug-resistant strains arise. In this paper, we develop a mathematical model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes both drug-sensitive and resistant strains. Analytical results of the model show that the quantities [Symbol: see text]( SC ) and [Symbol: see text]( RC ), which represent the control reproduction numbers of the sensitive and resistant strains, respect...
Source: Bulletin of Mathematical Biology - June 29, 2009 Category: Bioinformatics Authors: Qiu Z, Feng Z Tags: Bull Math Biol Source Type: journals

Effects of Predator and Prey Dispersal on Success or Failure of Biological Control.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Biological control, defined as the reduction of pest populations by natural enemies, is often a component of integrated pest management strategies. Augmentation of natural enemy numbers by planned releases is a common biological control method, the successes and failures of which have been extensively reviewed. The effectiveness of biological control is influenced by how populations of predators and prey (or hosts and parasitoids) disperse in patchy environments. Here, we address the question of whether such dispersal leads to beneficial or detrimental pest control outcomes by developing a simple predator-prey model wi...
Source: Bulletin of Mathematical Biology - June 26, 2009 Category: Bioinformatics Authors: Tang S, Cheke RA, Xiao Y Tags: Bull Math Biol Source Type: journals

A Geometric Buildup Algorithm for the Solution of the Distance Geometry Problem Using Least-Squares Approximation.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We describe the least-squares formulations and their solution methods, and present the test results from applying the new algorithm for the determination of a set of protein structures with varying degrees of availability and accuracy of the distances. We show that the new development of the algorithm increases the modeling ability, and improves stability and robustness of the geometric buildup approach significantly from both theoretical and practical points of view. PMID: 19533250 [PubMed - as supplied by publisher] (Source: Bulletin of Mathematical Biology)
Source: Bulletin of Mathematical Biology - June 16, 2009 Category: Bioinformatics Authors: Sit A, Wu Z, Yuan Y Tags: Bull Math Biol Source Type: journals

The Role of Spatial Refuges in Coupled Map Lattice Model for Host-Parasitoid Systems.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
A Coupled Map Lattice (CML) model, for host-parasitoid Nicholson-Bailey interactions, with an explicit spatial distribution of partial refuge areas, is presented by considering the parasitoid attack rate as a patch dependent parameter. The effect of habitat heterogeneity on the dynamics of both populations, that is, on their spatial distribution and temporal behavior is analyzed. Our results show that depending on many features such as position, size, and fragmentation of a refuge, as well as the dispersal parameters of hosts and parasitoids, together with the parasitoid attack rate, the inclusion of refuges may as wel...
Source: Bulletin of Mathematical Biology - June 4, 2009 Category: Bioinformatics Authors: Mistro DC, Rodrigues LA, Varriale MC Tags: Bull Math Biol Source Type: journals

A Theoretical Analysis of Temporal Difference Learning in the Iterated Prisoner's Dilemma Game.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
Direct reciprocity is a chief mechanism of mutual cooperation in social dilemma. Agents cooperate if future interactions with the same opponents are highly likely. Direct reciprocity has been explored mostly by evolutionary game theory based on natural selection. Our daily experience tells, however, that real social agents including humans learn to cooperate based on experience. In this paper, we analyze a reinforcement learning model called temporal difference learning and study its performance in the iterated Prisoner's Dilemma game. Temporal difference learning is unique among a variety of learning models in that it...
Source: Bulletin of Mathematical Biology - May 29, 2009 Category: Bioinformatics Authors: Masuda N, Ohtsuki H Tags: Bull Math Biol Source Type: journals

On the Final Size of Epidemics with Seasonality.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number [Symbol: see text](0) or of the initial fraction of infected people. Moreover, large epidemics can happen even if [Symbol: see text](0)<1. But like in a constant environment, the final epidemic size tends to 0 when [Symbol: see text](0)<1 and the initial fraction of infected people tends to 0. When [Symbol: see text](0)>1, the final epidemic size is bigger t...
Source: Bulletin of Mathematical Biology - May 28, 2009 Category: Bioinformatics Authors: Bacaër N, Gomes MG Tags: Bull Math Biol Source Type: journals

The Effect of Time Distribution Shape on a Complex Epidemic Model.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
In elaborating a model of the progress of an epidemic, it is necessary to make assumptions about the distributions of latency times and infectious times. In many models, the often implicit assumption is that these times are independent and exponentially distributed. We explore the effects of altering the distribution of latency and infectious times in a complex epidemic model with regional divisions connected by a travel intensity matrix. We show a delay in spread with more realistic latency times. More realistic infectiousness times lead to faster epidemics. The effects are similar but accentuated when compared to a p...
Source: Bulletin of Mathematical Biology - May 28, 2009 Category: Bioinformatics Authors: Camitz M, Svensson A Tags: Bull Math Biol Source Type: journals

The Evolution of Conditional Dispersal Strategies in Spatially Heterogeneous Habitats.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
To understand the evolution of dispersal, we study a Lotka-Volterra reaction-diffusion-advection model for two competing species in a heterogeneous environment. The two species are assumed to be identical except for their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but with slightly different random dispersal or advection rates. Two new phenomena are found for one-dimensional habitats and monotone intrinsic growth rates: (i) If both species disperse only by random diffusion, i.e., no advection, it was well known that the slower diffuser always wins. We sh...
Source: Bulletin of Mathematical Biology - May 28, 2009 Category: Bioinformatics Authors: Hambrock R, Lou Y Tags: Bull Math Biol Source Type: journals

Modeling HIV/AIDS and Tuberculosis Coinfection.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An HIV/AIDS and TB coinfection model which considers antiretroviral therapy for the AIDS cases and treatment of all forms of TB, i.e., latent and active forms of TB, is presented. We begin by presenting an HIV/AIDS-TB coinfection model and analyze the TB and HIV/AIDS submodels separately without any intervention strategy. The TB-only model is shown to exhibit backward bifurcation when its corresponding reproduction number is less than unity. On the other hand, the HIV/AIDS-only model has a globally asymptotically stable disease-free equilibrium when its corresponding reproduction number is less than unity. We proceed t...
Source: Bulletin of Mathematical Biology - May 28, 2009 Category: Bioinformatics Authors: Bhunu CP, Garira W, Mukandavire Z Tags: Bull Math Biol Source Type: journals

Reduced Models of Algae Growth.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The simulation of biological systems is often plagued by a high level of noise in the data, as well as by models containing a large number of correlated parameters. As a result, the parameters are poorly identified by the data, and the reliability of the model predictions may be questionable. Bayesian sampling methods provide an avenue for proper statistical analysis in such situations. Nevertheless, simulations should employ models that, on the one hand, are reduced as much as possible, and, on the other hand, are still able to capture the essential features of the phenomena studied. Here, in the case of algae growth ...
Source: Bulletin of Mathematical Biology - May 23, 2009 Category: Bioinformatics Authors: Haario H, Kalachev L, Laine M Tags: Bull Math Biol Source Type: journals

The Mutation Process in Colored Coalescent Theory.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The mutation process is introduced into the colored coalescent theory. The mutation process can be viewed as an independent Poisson process running on the colored genealogical random tree generated by the colored coalescent process, with the edge lengths of the random tree serving as the time scale for the mutation process. Moving backward along the colored genealogical tree, the color of vertices may change in two ways, when two vertices coalesce, or when a mutation happens. The rule that governs the coalescent change of color involves a parameter x; the rule that governs the mutation involves a parameter mu. Explicit...
Source: Bulletin of Mathematical Biology - May 22, 2009 Category: Bioinformatics Authors: Tian JP, Lin XS Tags: Bull Math Biol Source Type: journals

Stochastic Kinetic Modeling of Vesicular Stomatitis Virus Intracellular Growth.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
By building kinetic models of biological networks one may advance the development of new modeling approaches while gaining insights into the biology. We focus here on building a stochastic kinetic model for the intracellular growth of vesicular stomatitis virus (VSV), a well-studied virus that encodes five genes. The essential network of VSV reactions creates challenges to stochastic simulation owing to (i) delayed reactions associated with transcription and genome replication, (ii) production of large numbers of intermediate proteins by translation, and (iii) the presence of highly reactive intermediates that rapidly ...
Source: Bulletin of Mathematical Biology - May 21, 2009 Category: Bioinformatics Authors: Hensel SC, Rawlings JB, Yin J Tags: Bull Math Biol Source Type: journals

A Computational Analysis of Localized Ca(2+)-Dynamics Generated by Heterogeneous Release Sites.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We investigate the role of heterogeneous expression of IP(3)R and RyR in generating diverse elementary Ca(2+) signals. It has been shown empirically (Wojcikiewicz and Luo in Mol. Pharmacol. 53(4):656-662, 1998; Newton et al. in J. Biol. Chem. 269(46):28613-28619, 1994; Smedt et al. in Biochem. J. 322(Pt. 2):575-583, 1997) that tissues express various proportions of IP(3) and RyR isoforms and this expression is dynamically regulated (Parrington et al. in Dev. Biol. 203(2):451-461, 1998; Fissore et al. in Biol. Reprod. 60(1):49-57, 1999; Tovey et al. in J. Cell Sci. 114(Pt. 22):3979-3989, 2001). Although many previous th...
Source: Bulletin of Mathematical Biology - May 14, 2009 Category: Bioinformatics Authors: Cooper Z, Greenwood M, Mazzag B Tags: Bull Math Biol Source Type: journals

Sequential Activation of Metabolic Pathways: a Dynamic Optimization Approach.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
The regulation of cellular metabolism facilitates robust cellular operation in the face of changing external conditions. The cellular response to this varying environment may include the activation or inactivation of appropriate metabolic pathways. Experimental and numerical observations of sequential timing in pathway activation have been reported in the literature. It has been argued that such patterns can be rationalized by means of an underlying optimal metabolic design. In this paper we pose a dynamic optimization problem that accounts for time-resource minimization in pathway activation under constrained total en...
Source: Bulletin of Mathematical Biology - May 2, 2009 Category: Bioinformatics Authors: Oyarzún DA, Ingalls BP, Middleton RH, Kalamatianos D Tags: Bull Math Biol Source Type: journals

Periodic Matrix Population Models: Growth Rate, Basic Reproduction Number, and Entropy.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
This article considers three different aspects of periodic matrix population models. First, a formula for the sensitivity analysis of the growth rate lambda is obtained that is simpler than the one obtained by Caswell and Trevisan. Secondly, the formula for the basic reproduction number [Symbol: see text](0) in a constant environment is generalized to the case of a periodic environment. Some inequalities between lambda and [Symbol: see text](0) proved by Cushing and Zhou are also generalized to the periodic case. Finally, we add some remarks on Demetrius' notion of evolutionary entropy H and its relationship to the growth ...
Source: Bulletin of Mathematical Biology - May 2, 2009 Category: Bioinformatics Authors: Bacaër N Tags: Bull Math Biol Source Type: journals

A Model for Plant Invasions: the Role of Distributed Generation Times.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
An analytical model consisting of adult plants and two types of seeds (unripe and mature) is considered and successfully tested using experimental data available for some invasive weeds (Echium plantagineum, Cytisus scoparius, Carduus nutans andCarduus acanthoides) from their native and exotic ranges. The model accounts for probability distribution functions (pdfs) for times of germination, growth, death and dispersal on two dimensions, so the general life-cycle of individuals is considered with high level of description. Our work provides for the first time, for a model containing all that life-cycle information, expl...
Source: Bulletin of Mathematical Biology - May 2, 2009 Category: Bioinformatics Authors: Méndez V, Campos D, Sheppard AW Tags: Bull Math Biol Source Type: journals

Deriving Macroscopic Myocardial Conductivities by Homogenization of Microscopic Models.Email this article to a colleague. Save this article to My Clippings. Discuss or comment on this article.
We derive the values for the intracellular and extracellular conductivities needed for bidomain simulations of cardiac electrophysiology using homogenization of partial differential equations. In our model, cardiac myocytes are rectangular prisms and gap junctions appear in a distributed manner as flux boundary conditions for Laplace's equation. Using directly measurable microproperties such as cellular dimensions and end-to-end and side-to-side gap junction coupling strengths, we inexpensively obtain effective conductivities close to those given by simulations with a detailed cyto-architecture (Stinstra et al. in Ann....
Source: Bulletin of Mathematical Biology - May 2, 2009 Category: Bioinformatics Authors: Hand PE, Griffith BE, Peskin CS Tags: Bull Math Biol Source Type: journals