http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Mon, 29 Apr 2013 15:12:24 +0000 http://www.hindawi.com/isrn/biomathematics/2013/103708/ Untangling the dynamics between HIV and CD4 cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we propose and show the usefulness of a stochastic approach towards modeling HIV and CD4 cells’ dynamics in vivo by obtaining probability generating function, the moment structures of the healthy CD4 cell and the virus particles at any time t, and the probability of HIV clearance. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Our analysis shows that, when it is assumed that the drug is not completely effective as is the case of HIV in vivo, the probability of HIV clearance depends on two factors: the combination of drug efficacy and length of the intracellular delay and also the education of the infected patients. Comparing simulated data before and after treatment indicates the importance of combined therapeutic intervention and intracellular delay in having low, undetectable viral load in HIV-infected person. Waema R. Mbogo, Livingstone S. Luboobi, and John W. Odhiambo Copyright © 2013 Waema R. Mbogo et al. All rights reserved. Sun, 21 Apr 2013 09:49:29 +0000 http://www.hindawi.com/isrn/biomathematics/2013/845918/ B and T lymphocytes activate the humoral and cellular arms of the adaptive immune system. The adaptive strategy works because receptors of adaptive immune cells can mount an immune response based on their affinity for antigens. Thus, affinity discrimination is central to adaptive immunity and has important biomedical ramifications. Due to its intricate connection to the affinity maturation process, affinity discrimination has a special significance in B-cell-mediated immune response. The role of affinity-matured high-affinity antibodies is increasingly recognized in vaccine development. In this paper, we discuss the recent progress made in mathematical and computational studies to explore the cellular and molecular mechanisms of B-cell affinity discrimination. Formation of B-cell receptor (BCR) oligomers and BCR-lipid rafts, upon antigenic stimulation, emerge to be key factors in B-cell affinity discrimination (at the level of single cells). It also provides a new way of thinking about kinetic proofreading and serial triggering, concepts that have been widely utilized to understand affinity discrimination in adaptive immune cells. Potential future applications of mathematical and computational modeling of affinity discrimination are discussed in the context of autoimmune disorders and vaccine design. Subhadip Raychaudhuri Copyright © 2013 Subhadip Raychaudhuri. All rights reserved. Wed, 27 Mar 2013 15:36:49 +0000 http://www.hindawi.com/isrn/biomathematics/2013/194239/ We report the existence of phase-coupled oscillations in a model neural system. The model consists of a group of excitatory principal cells in interaction with local inhibitory interneurons. The voltages across the membranes of excitatory cells are governed primarily by calcium and potassium ion conductivities. The number of potassium channels open at any given instant changes in accordance with a deterministic law. The time scale of this change is set by a constant which depends on midpoint potentials at which potassium and calcium currents are half-activated. The growth of mean membrane potential of excitatory principal cells is controlled by that of the inhibitory interneurons. Nonlinear oscillatory system associated with these limit cycles starting from two different initial conditions maintain a definite phase relationship. The phase-coupled oscillations in electrical activity of the neuronal cells carry together amplitude, phase, and time information for cellular signaling. This mechanism supports an energy efficient way of information processing in the central nervous system. The information content is encoded as persistent periodic oscillations represented by stable limit cycles in the phase space. Vikas Rai, Sreenivasan Rajamoni Nadar, and Riaz A. Khan Copyright © 2013 Vikas Rai et al. All rights reserved. Wed, 13 Mar 2013 09:44:45 +0000 http://www.hindawi.com/isrn/biomathematics/2013/198185/ The complex dynamics of two types of tritrophic food chain model systems when the species undergo spatial movements, modeling two real situations of marine ecosystem, are investigated in this study analytically and using numerical simulations. The study has been carried out with the objective to explore and compare the competitive effects of fish and molluscs species being the top predators, when phytoplankton and zooplankton species are undergoing spatial movements in the subsurface water. Reaction diffusion systems have been used to represent temporal evolution and spatial interaction among the species. The two model systems differ in an essential way that the top predators are generalist and specialist, respectively, in two models. “Wave of Chaos” mechanism is found to be the responsible factor for the pattern (non-Turing) formation in one dimension seen in the food chain ending with top generalist predator. In the present work we have reported WOC phenomenon, for the first time in the literature, in a three-species spatially extended food chain model system. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions. Constraints on different parameters under which Turing and non-Turing patterns may be observed are obtained analytically. Diffusion-driven analysis is carried out, and the effect of diffusion on the chaotic dynamics of the model systems is studied. The existence of chaotic attractor and long-term chaotic behavior demonstrate the effect of diffusion on the dynamics of the model systems. It is observed from numerical study that food chain model system with top predator as generalist has very rich dynamics and shows very interesting patterns. An ecosystem having top predator as specialist leads to the stability of the system. Nitu Kumari Copyright © 2013 Nitu Kumari. All rights reserved. Thu, 07 Mar 2013 11:33:12 +0000 http://www.hindawi.com/isrn/biomathematics/2013/871472/ This paper provides an overview of different types of models for studying activity of nerve cells and their networks with a special emphasis on neural oscillations. One part describes the neuronal models based on the Hodgkin and Huxley formalism first described in the 1950s. It is discussed how further simplifications of this formalism enable mathematical analysis of the process of neural excitability. The focus of the paper’s second component is on network activity. Understanding network function is one of the important frontiers remaining in neuroscience. At present, experimental techniques can only provide global recordings or samples of the activity of the huge networks that form the nervous system. Models in neuroscience can therefore play a critical role by providing a framework for integration of necessarily incomplete datasets, thereby providing insight into the mechanisms of neural function. Network models can either explicitly contain individual network nodes that model the neurons, or they can be based on representations of compound population activity. The latter approach was pioneered by Wilson and Cowan in the 1970s. Finally I provide an overview and discuss how network models are employed in the study of neuronal network pathology such as epilepsy. Wim van Drongelen Copyright © 2013 Wim van Drongelen. All rights reserved. Sun, 24 Feb 2013 15:14:20 +0000 http://www.hindawi.com/isrn/biomathematics/2013/159170/ We discuss a macroscopical growth model which can be used to simulate growth forms of complex-shaped branching organisms with radiate accretive growth. This type of growth processes can be found in many different marine sessile organisms. We use scleractinian corals and a branching sponge as an example. With the radiate accretive growth model a wide range of morphologies and the influence of the physical environment (light and nutrient distribution by advection-diffusion) can be modelled. We show an (preliminary) example of how the accretive growth model can be coupled with a model of gene regulation and body plan formation in a branching sponge. Jaap A. Kaandorp Copyright © 2013 Jaap A. Kaandorp. All rights reserved. Tue, 12 Feb 2013 08:36:09 +0000 http://www.hindawi.com/isrn/biomathematics/2013/538631/ We begin here a combinatorial study of dinucleotide circular codes. A word written on a circle is called circular. A set of dinucleotides is a circular code if all circular words constructed with this set have a unique decomposition. Propositions based on a letter necklace allow to determine the 24 maximum dinucleotide circular codes (of 6 elements). A partition property is also identified with eight self-complementary maximum dinucleotide circular codes and two classes of eight maximum dinucleotide circular codes in bijective correspondence by the complementarity map. Christian J. Michel and Giuseppe Pirillo Copyright © 2013 Christian J. Michel and Giuseppe Pirillo. All rights reserved. Tue, 29 Jan 2013 12:41:06 +0000 http://www.hindawi.com/isrn/biomathematics/2013/954912/ To incorporate biologically observed epidemics into multistage models of carcinogenesis, in this paper we have developed new stochastic models for human cancers. We have further incorporated genetic segregation of cancer genes into these models to derive generalized mixture models for cancer incidence. Based on these models we have developed a generalized Bayesian approach to estimate the parameters and to predict cancer incidence via Gibbs sampling procedures. We have applied these models to fit and analyze the SEER data of human eye cancers from NCI/NIH. Our results indicate that the models not only provide a logical avenue to incorporate biological information but also fit the data much better than other models. These models would not only provide more insights into human cancers but also would provide useful guidance for its prevention and control and for prediction of future cancer cases. Wai-Yuan Tan and Hong Zhou Copyright © 2013 Wai-Yuan Tan and Hong Zhou. All rights reserved. Wed, 16 Jan 2013 08:16:11 +0000 http://www.hindawi.com/isrn/biomathematics/2013/897658/ Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts. Eberhard O. Voit Copyright © 2013 Eberhard O. Voit. All rights reserved. Wed, 26 Dec 2012 09:20:14 +0000 http://www.hindawi.com/isrn/biomathematics/2012/287394/ While there is a mature literature on biomathematical and biophysical modeling in cancer, many of the existing approaches are not of clinical utility, as they require input data that are extremely difficult to obtain in an intact organism, and/or require a large number of assumptions on the free parameters included in the models. Thus, there has only been very limited application of such models to solve problems of clinical import. More recently, however, there has been increased activity at the interface of quantitative, noninvasive imaging data, and tumor mathematical modeling. In addition to reporting on bulk tumor morphology and volume, emerging imaging techniques can quantitatively report on for example tumor vascularity, glucose metabolism, cell density and proliferation, and hypoxia. In this paper, we first motivate the problem of predicting therapy response by highlighting some (acknowledged) shortcomings in existing methods. We then provide introductions to a number of representative quantitative imaging methods and describe how they are currently (and potentially can be) used to initialize and constrain patient specific mathematical and biophysical models of tumor growth and treatment response, thereby increasing the clinical utility of such approaches. We conclude by highlighting some of the exciting research directions when one integrates quantitative imaging and tumor modeling. Thomas E. Yankeelov Copyright © 2012 Thomas E. Yankeelov. All rights reserved. Mon, 17 Dec 2012 14:54:12 +0000 http://www.hindawi.com/isrn/biomathematics/2012/919502/ Unsafe injecting practices, blood exchange, the use of nonsterile needles, and other cutting instruments for tattooing are common in correctional institutions, resulting in a number of blood transmitted infections. A mathematical model for assessing the dynamics of HCV and HIV coinfection within correctional institutions is proposed and comprehensively analyzed. The HCV-only and HIV-only submodels are first considered. Analytical expressions for the threshold parameter in each submodel and the cointeraction are derived. Global dynamics of this coinfection shows that whenever the threshold parameter for the respective submodels and the coinfection model is less than unity, then the epidemics die out, the reverse condition implies disease persistence within correctional institutions. Numerical simulations using a set of plausible parameter values are provided to support analytical findings. S. Mushayabasa, Claver P. Bhunu, and Alexander G. R. Stewart Copyright © 2012 S. Mushayabasa et al. All rights reserved. Mon, 10 Dec 2012 11:09:23 +0000 http://www.hindawi.com/isrn/biomathematics/2012/256741/ Endo surgiclip instrument is the biomedical instrument that can be applied for endoscopic surgery to assist surgeons in homeostasis and secure mucosal gap surfaces during surgical operations. Since some clinic feedbacks show the surgiclip drop-off incidents which can potentially sever organ and tissue, the improvement of endo surgiclip instrument has been made in these years. Since few research papers were involved in the study of endo surgiclip instrument performance via mathematical modeling and computational simulation, currently some instrumental modifications are mainly based on clinic lab tests which prolong the improvement cycle and increase additional manufacturing cost. This paper introduces a new biomedical surgiclip instrument based on mathematical modeling, computer-aided simulation, and prototype testing. The analytic methodology proposed in this paper can help engineers in biomedical industry develop and improve biomedical instrument. Compared to the current conventional surgiclip instruments, this new surgiclip instrument can properly assist surgeon in surgical procedure with less operational force and no surgiclip drop-off incident. The prototype has also been built and tested. Both computational simulation and prototype testing show close results which validate the feasibility of this newly developed endo surgiclip instrument and the methodologies of mathematical modeling based computational simulation proposed in this paper. Zheng Jeremy Li Copyright © 2012 Zheng Jeremy Li. All rights reserved. Tue, 04 Dec 2012 14:06:12 +0000 http://www.hindawi.com/isrn/biomathematics/2012/127492/ Cholera, an acute intestinal infection caused by the bacterium Vibrio cholerae, remains a major public health problem in many parts of Africa, Asia, and Latin America. A mathematical model is developed, to assess the impact of increasing antimicrobial resistance of Vibrio cholerae on the future trends of the cholera epidemic. Equilibrium states of the model are determined and their stabilities have been examined. The impacts of increasing antimicrobial resistance of Vibrio cholerae on the future trends of cholera epidemic have been investigated through the reproductive number. Numerical results are provided to support analytical findings. Steady Mushayabasa and Claver P. Bhunu Copyright © 2012 Steady Mushayabasa and Claver P. Bhunu. All rights reserved. Thu, 29 Nov 2012 08:40:40 +0000 http://www.hindawi.com/isrn/biomathematics/2012/215124/ We present a delay-differential equation model with optimal control that describes the interactions between human immunodeficiency virus (HIV), CD4+ T cells, and cell-mediated immune response. Both the treatment and the intracellular delay are incorporated into the model in order to improve therapies to cure HIV infection. The optimal controls represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence for the optimal control pair is established, Pontryagin’s maximum principle is used to characterize these optimal controls, and the optimality system is derived. For the numerical simulation, we propose a new algorithm based on the forward and backward difference approximation. Khalid Hattaf and Noura Yousfi Copyright © 2012 Khalid Hattaf and Noura Yousfi. All rights reserved. Sun, 25 Nov 2012 11:55:46 +0000 http://www.hindawi.com/isrn/biomathematics/2012/853056/ The salient hemodynamic flow features in a stenosed artery depend not only on the degree of stenosis, but also on its location in the circulatory system and the physiological condition of the body. The nature of pulsatile flow waveform and local Womersley number vary in different regions of the arterial system and at different physiological state, which affects the local hemodynamic wall parameters, for example, the wall shear stress (WSS) and oscillatory shear index (OSI). Herein, we have numerically investigated the effects of different waveforms and Womersley numbers on the flow pattern and hemodynamic parameters in an axisymmetric stenosed arterial geometry with 50% diametral occlusion. Temporal evolution of the streamlines and hemodynamic parameters are investigated, and the time-averaged hemodynamic wall parameters are compared. Presence of the stenosis is found to increase the OSI of the flow even at the far-downstream side of the artery. At larger Womersley numbers, the instantaneous flow field in the stenosed region is found to have a stronger influence on the flow profiles of the previous time levels. The study delineates how an approximation in the assumption of inlet pulsatility profile may lead to significantly different prediction of hemodynamic wall parameters. Moloy Kumar Banerjee, Ranjan Ganguly, and Amitava Datta Copyright © 2012 Moloy Kumar Banerjee et al. All rights reserved. Tue, 23 Oct 2012 15:47:27 +0000 http://www.hindawi.com/isrn/biomathematics/2012/785791/ This paper presents a review of Bayesian models of brain and behaviour. We first review the basic principles of Bayesian inference. This is followed by descriptions of sampling and variational methods for approximate inference, and forward and backward recursions in time for inference in dynamical models. The review of behavioural models covers work in visual processing, sensory integration, sensorimotor integration, and collective decision making. The review of brain models covers a range of spatial scales from synapses to neurons and population codes, but with an emphasis on models of cortical hierarchies. We describe a simple hierarchical model which provides a mathematical framework relating constructs in Bayesian inference to those in neural computation. We close by reviewing recent theoretical developments in Bayesian inference for planning and control. William Penny Copyright © 2012 William Penny. All rights reserved. Tue, 23 Oct 2012 13:49:29 +0000 http://www.hindawi.com/isrn/biomathematics/2012/132342/ Zoonotic diseases can be transmitted via an arthropod vector, and disease risk maps are often created based on underlying associative factors within the surrounding landscape of known occurrences. A limitation however is the ability to map disease risk at a meaningful geographic scale, and traditional regression modeling approaches may not always be appropriate. Our objective was to determine if nonlinear modeling could improve explanatory power in describing the occurrence of 2 tick-borne diseases (Lyme disease (LD) and Rocky Mountain spotted fever (RMSF)) known to occur in Tennessee. Medically diagnosed cases of LD (ICD-9: 088.81) and RMSF (ICD-9: 082.0) were extracted from a managed care organization data warehouse for the 2000–2009 time period. Four separate modeling techniques were constructed (logistic regression, classification and regression tree (CART), gradient boosted tree (GBT), and neural network (NNET)) and compared for accuracy. Results suggest that areas higher in disease prevalence were not necessarily the same areas having high predicted disease risk. GBT best explained LD occurrence (misclassification rate: 0.232; ROC: 0.789). RMSF prevalence was best explained with an NNET algorithm (misclassification rate: 0.288; ROC: 0.696). Covariates explaining disease risk included forested wetlands, urbanization, and median income. Nonlinear modeling may provide better results than traditional regression-based approaches. Stephen Jones, William Conner, and Bo Song Copyright © 2012 Stephen Jones et al. All rights reserved. Wed, 17 Oct 2012 11:19:33 +0000 http://www.hindawi.com/isrn/biomathematics/2012/930130/ An epidemiological model for the spread of lymphatic filariasis, a mosquito-borne infection, is developed and analysed. The epidemic thresholds known as the reproduction number and equilibria for the model are determined and stabilities analysed. Results from the analysis of the reproduction number suggest that treatment will somehow contribute to a reduction in lymphatic filariasis cases, but what it does not show is the magnitude of the reduction, a part answered by the numerical simulations. Numerical simulations show that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms as well as chemoprophylaxis for the exposed. C. P. Bhunu and S. Mushayabasa Copyright © 2012 C. P. Bhunu and S. Mushayabasa. All rights reserved. Mon, 15 Oct 2012 14:08:25 +0000 http://www.hindawi.com/isrn/biomathematics/2012/192031/ Static representations of protein interactions networks or PIN reflect measurements referred to a variety of conditions, including time. To partially bypass such limitation, gene expression information is usually integrated in the network to measure its “activity level.” In general, the entire PIN modular organization (complexes, pathways) can reveal changes of configuration whose functional significance depends on biological annotation. However, since network dynamics are based on the presence of different conditions leading to comparisons between normal and disease states, or between networks observed sequentially in time, our working hypothesis refers to the analysis of differential networks based on varying modularity and uncertainty. Two popular methods were applied and evaluated, k-core and Q-modularity, over a reference yeast dataset comprising a PIN of literature-curated data obtained from the fusion of heterogeneous measurements sources. While the functional aspect of interest is cell cycle and the corresponding interactions were isolated, the PIN dynamics were externally induced by time-course measured gene expression values, which we consider one of the “modularity drivers.” Notably, due to the nature of such expression values referred to the “just-in-time method,” we could specialize our approach according to three constrained modular configurations then comparatively assessed through local entropy measures. Enrico Capobianco Copyright © 2012 Enrico Capobianco. All rights reserved. Mon, 15 Oct 2012 08:50:36 +0000 http://www.hindawi.com/isrn/biomathematics/2012/516519/ HIV/AIDS remains an important global cause of morbidity and mortality. While medical male circumcision and condom and microbicides use hold great promise for helping to stem the tide of new HIV infections, theoretically providing further evidence of the potential long-term population-level benefit of their combined effects is viable. A deterministic sex-structured model is formulated, the expected lifetime disease reproductive output of an individual (or epidemiological birth) is determined, and the stability of steady states is investigated. To complement HIV treatment with antiretrovirals, which is not yet fully accessible to all those in need, microbicides and nontherapeutic measures such as male circumcision and condoms provide additional potential impact on curtailing the spread of HIV/AIDS. Felix Elias and Jean M. Tchuenche Copyright © 2012 Felix Elias and Jean M. Tchuenche. All rights reserved. Thu, 20 Sep 2012 10:33:06 +0000 http://www.hindawi.com/isrn/biomathematics/2012/802450/ Chronic wasting disease (CWD) is a prion infectious disease that affects members of the deer family in North America. Concerns about the economic consequences of the presence of CWD have led management agencies to seek effective strategies to control CWD distribution and prevalence. Current mathematical models are either based on complex simulations or overly simplified compartmental models. We develop a mathematical model that includes gender structure to describe CWD in a logistically growing population. The model includes harvesting as a management strategy for the disease. We determine the stability conditions of the disease-free equilibrium for the model and calculate the basic reproduction number. We find an optimum interval of harvesting: with too little harvesting, the disease persists, whereas too much harvesting results in extinction of the population. A sensitivity analysis shows that the disease threshold is more sensitive to female than male harvesting and that harvesting has the greatest effect on the basic reproduction number. However, while harvesting may be a way to control CWD, the range of admissible harvesting rates may be very narrow, depending on other parameters. Mo'tassem Al-Arydah, Robert J. Smith?, and Frithjof Lutscher Copyright © 2012 Mo'tassem Al-Arydah et al. All rights reserved. Thu, 23 Aug 2012 15:20:39 +0000 http://www.hindawi.com/isrn/biomathematics/2012/170594/ The kidney plays an indispensable role in the regulation of whole-organism water balance, electrolyte balance, and acid-base balance, and in the excretion of metabolic wastes and toxins. In this paper, we review representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, and regulation of renal oxygen transport. We discuss how such modeling efforts have significantly expanded our understanding of renal function in both health and disease. Anita T. Layton Copyright © 2012 Anita T. Layton. All rights reserved. Thu, 16 Aug 2012 11:06:51 +0000 http://www.hindawi.com/isrn/biomathematics/2012/459829/ Tuberculosis, an airborne disease affecting almost a third of the world’s population remains one of the major public health burdens globally, and the resurgence of multidrug-resistant tuberculosis in some parts of sub-Saharan Africa calls for concern. To gain insight into its qualitative dynamics at the population level, mathematical modeling which require as inputs key demographic and epidemiological information can fill in gaps where field and lab data are not readily available. A deterministic model for the transmission dynamics of multi-drug resistant tuberculosis to assess the impact of diagnosis, treatment, and health education is formulated. The model assumes that exposed individuals develop active tuberculosis due to endogenous activation and exogenous re-infection. Treatment is offered to all infected individuals except those latently infected with multi-drug resistant tuberculosis. Qualitative analysis using the theory of dynamical systems shows that, in addition to the disease-free equilibrium, there exists a unique dominant locally asymptotically stable equilibrium corresponding to each strain. Numerical simulations suggest that, at the current level of control strategies (with Malawi as a case study), the drug-sensitive tuberculosis can be completely eliminated from the population, thereby reducing multi-drug resistant tuberculosis. M. Maliyoni, P. M. M. Mwamtobe, S. D. Hove-Musekwa, and J. M. Tchuenche Copyright © 2012 M. Maliyoni et al. All rights reserved. Sun, 01 Jul 2012 14:29:04 +0000 http://www.hindawi.com/isrn/biomathematics/2012/546315/ The dynamical complexity of a system of ordinary differential equations (ODEs) modeling the dynamics of a neuron that interacts with other neurons through on-off excitatory and inhibitory synapses in a neural system was investigated in detail. The model used Morris-Lecar (ML) equations with an additional autonomous variable representing the input from interaction of excitatory neuronal cells with local interneurons. Numerical simulations yielded a rich repertoire of dynamical behavior associated with this three-dimensional system, which included periodic, chaotic oscillation and rare bursts of episodic periodicity called the transient periodicity. Sreenivasan Rajamoni Nadar and Vikas Rai Copyright © 2012 Sreenivasan Rajamoni Nadar and Vikas Rai. All rights reserved. Tue, 12 Jun 2012 11:56:50 +0000 http://www.hindawi.com/isrn/biomathematics/2012/613174/ Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of possible models fitting the available data is huge, and identifying a biologically relevant model is of great interest. Nested canalyzing functions, where variables in a given order dominate the function, have recently been proposed as a framework for modeling gene regulatory networks. Previously, we described this class of functions as an algebraic toric variety. In this paper, we present an algorithm that identifies all nested canalyzing models that fit the given data. We demonstrate our methods using a well-known Boolean model of the cell cycle in budding yeast. Franziska Hinkelmann and Abdul Salam Jarrah Copyright © 2012 Franziska Hinkelmann and Abdul Salam Jarrah. All rights reserved. Thu, 24 May 2012 12:17:09 +0000 http://www.hindawi.com/isrn/biomathematics/2012/796783/ We have proposed a nutrient-consumer-predator model with additional food to predator, at variable nutrient enrichment levels. The boundedness property and the conditions for local stability of boundary and interior equilibrium points of the system are derived. Bifurcation analysis is done with respect to quality and quantity of additional food and consumer’s death rate for the model. The system has stable as well as unstable dynamics depending on supply of additional food to predator. This model shows that supply of additional food plays an important role in the biological controllability of the system. Banshidhar Sahoo Copyright © 2012 Banshidhar Sahoo. All rights reserved. Wed, 23 May 2012 10:54:48 +0000 http://www.hindawi.com/isrn/biomathematics/2012/726429/ This paper presents an algorithm called DPClusO for partitioning simple graphs into overlapping modules, that is, clusters constrained by density and periphery tracking. The major advantages of DPClusO over the related and previously published algorithm DPClus are shorter running time and ensuring coverage, that is, each node goes to at least one module. DPClusO is a general-purpose clustering algorithm and useful for finding overlapping cohesive groups in a simple graph for any type of application. This work shows that the modules generated by DPClusO from several PPI networks of yeast with high-density constraint match with more known complexes compared to some other recently published complex generating algorithms. Furthermore, the biological significance of the high density modules has been demonstrated by comparing their P values in the context of Gene Ontology (GO) terms with those of the randomly generated modules having the same size, distribution, and zero density. As a consequence, it was also learnt that a PPI network is a combination of mainly high-density and star-like modules. Md. Altaf-Ul-Amin, Masayoshi Wada, and Shigehiko Kanaya Copyright © 2012 Md. Altaf-Ul-Amin et al. All rights reserved. Wed, 09 May 2012 09:26:48 +0000 http://www.hindawi.com/isrn/biomathematics/2012/872956/ This review article provides an introduction to statistical issues that arise when some statistical model parameters are constrained. This often happens in applications, in particular in testing for variance components (e.g., genomics) and construction of one-sided confidence intervals (e.g., environmental risk analysis). Heuristic explanations are provided, and a number of general and recent statistical results that appeared in statistical literature are summarized for use in applications. Simulation results are shown for illustration of consequences of ignoring parameters on the boundary. Special attention is paid to likelihood ratio tests, but other approaches to confidence interval construction, such as Wald, bootstrap, and Bayesian are also briefly discussed. This paper presents examples from the risk assessment field and genomics, but all conclusions apply to whenever one-sided testing is conducted. Recommendations are provided for dealing with parameters on the boundary for a range of situations. Leonid Kopylev Copyright © 2012 Leonid Kopylev. All rights reserved. Tue, 08 May 2012 08:31:00 +0000 http://www.hindawi.com/isrn/biomathematics/2012/621939/ Cholera still remains as a severe global threat and is currently spreading in Africa and other parts of the world. The role of lytic bacteriophage as an intervention of cholera outbreaks is investigated using a mathematical model. Dynamics of cholera is discussed on basis of the basic reproduction number 𝑅0. Conditions of Hopf bifurcation are also derived for a positive net growth rate of Vibrio cholerae. Stability analysis and numerical simulations suggest that bacteriophage may contribute to lessening the severity of cholera epidemics by reducing the number of Vibrio cholerae in the environment. Hence with the presence of phage virus, cholera is self-limiting in nature. By using phage as a biological control agent in endemic areas, one may also influence the temporal dynamics of cholera epidemics while reducing the excessive use of chemicals. We also performed stochastic analysis which suggests that the model system is globally asymptotically stable in probability when the strengths of white noise are less than some specific quantities. Prasenjit Das and Debasis Mukherjee Copyright © 2012 Prasenjit Das and Debasis Mukherjee. All rights reserved. Wed, 14 Mar 2012 11:47:52 +0000 http://www.hindawi.com/isrn/biomathematics/2012/384275/ Recombination within a DNA segment during the neutral fixation process is studied to determine the number of individuals in previous generations which carry genetic material ancestral to that region in the present generation. If 𝑁𝑟≪1, where 𝑁 is the population size and 𝑟 is the probability of a recombination event within that region per individual in a generation, the ancestors of all the base pairs in that segment were probably in the same individual in an arbitrary generation in the asymptotic past (prior to the most recent common ancestor) and all the base pairs in that segment share a common coalescent. If 𝑁𝑟≫1, the ancestors of the base pairs in a segment are probably spread among several individuals in asymptotic generations; hence, there is not an ancestral individual, but an ancestral pool, and the coalescents of base pairs do not coincide. The overlap of the ancestral pools of unlinked genetic segments is less than 2𝑝𝑞 where 𝑝 and 𝑞 are the relative frequencies of the two ancestral pools, which provides that the size of the ancestral pool for the human genome is close to the .80 upper bound which ensues from the Poisson progeny distribution. R. B. Campbell Copyright © 2012 R. B. Campbell. All rights reserved.