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Bulletin of Mathematical Biology

Elisabeth O Bangsgaard, Poul G Hjorth, Mette S Olufsen, Jesper Mehlsen, Johnny T Ottesen
During the last decade, there has been an increasing interest in the coupling between the acute inflammatory response and the Hypothalamic-Pituitary-Adrenal (HPA) axis. The inflammatory response is activated acutely by pathogen- or damage-related molecular patterns, whereas the HPA axis maintains a long-term level of the stress hormone cortisol which is also anti-inflammatory. A new integrated model of the interaction between these two subsystems of the inflammatory system is proposed and coined the integrated inflammatory stress (ITIS) model...
June 22, 2017: Bulletin of Mathematical Biology
Elena Fimmel, Christian J Michel, Lutz Strüngmann
Comma-free codes constitute a class of circular codes, which has been widely studied, in particular by Golomb et al. (Biologiske Meddelelser, Kongelige Danske Videnskabernes Selskab 23:1-34, 1958a, Can J Math 10:202-209, 1958b), Michel et al. (Comput Math Appl 55:989-996, 2008a, Theor Comput Sci 401:17-26, 2008b, Inf Comput 212:55-63, 2012), Michel and Pirillo (Int J Comb 2011:659567, 2011), and Fimmel and Strüngmann (J Theor Biol 389:206-213, 2016). Based on a recent approach using graph theory to study circular codes Fimmel et al...
June 22, 2017: Bulletin of Mathematical Biology
Andy Jenkins, Matthew Macauley
The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose...
June 21, 2017: Bulletin of Mathematical Biology
Michael H Cortez, Swati Patel
This paper explores how predator evolution and the magnitude of predator genetic variation alter the population-level dynamics of predator-prey systems. We do this by analyzing a general eco-evolutionary predator-prey model using four methods: Method 1 identifies how eco-evolutionary feedbacks alter system stability in the fast and slow evolution limits; Method 2 identifies how the amount of standing predator genetic variation alters system stability; Method 3 identifies how the phase lags in predator-prey cycles depend on the amount of genetic variation; and Method 4 determines conditions for different cycle shapes in the fast and slow evolution limits using geometric singular perturbation theory...
June 21, 2017: Bulletin of Mathematical Biology
Karen M Hampson, Matthew P Cufflin, Edward A H Mallen
When fixating on a stationary object, the power of the eye's lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i...
June 21, 2017: Bulletin of Mathematical Biology
Zuzanna Szymańska, Maciej Cytowski, Elaine Mitchell, Cicely K Macnamara, Mark A J Chaplain
In this paper, we present two mathematical models related to different aspects and scales of cancer growth. The first model is a stochastic spatiotemporal model of both a synthetic gene regulatory network (the example of a three-gene repressilator is given) and an actual gene regulatory network, the NF-[Formula: see text]B pathway. The second model is a force-based individual-based model of the development of a solid avascular tumour with specific application to tumour cords, i.e. a mass of cancer cells growing around a central blood vessel...
June 20, 2017: Bulletin of Mathematical Biology
M I Betti, L M Wahl, M Zamir
A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number [Formula: see text] of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes...
June 19, 2017: Bulletin of Mathematical Biology
Michael Marcondes de Freitas, Carsten Wiuf, Elisenda Feliu
Known graphical conditions for the generic and global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure to simplify the network, making the graphical conditions considerably easier to check.
June 15, 2017: Bulletin of Mathematical Biology
Christopher Mitchell, Christopher Kribs
When using mathematics to study epidemics, oftentimes the goal is to determine when an infection can invade and persist within a population. The most common way to do so uses threshold quantities called reproductive numbers. An infection's basic reproductive number (BRN), typically denoted [Formula: see text], measures the infection's initial ability to reproduce in a naive population and is tied mathematically to the stability of the disease-free equilibrium. Next-generation methods have long been used to derive [Formula: see text] for autonomous continuous-time systems; however, many diseases exhibit seasonal behavior...
June 15, 2017: Bulletin of Mathematical Biology
Mustafa Erdem, Muntaser Safan, Carlos Castillo-Chavez
The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection...
June 12, 2017: Bulletin of Mathematical Biology
Elena Braverman, Daniel Franco
In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a one-dimensional setting. Here, by introducing target-oriented control for discrete dynamical systems, we prove the possibility to stabilize a chosen state for a wide range of structured population models. The results are illustrated with introducing a control in the celebrated LPA model describing a flour beetle dynamics...
June 12, 2017: Bulletin of Mathematical Biology
Brian Ingalls, Maya Mincheva, Marc R Roussel
A parametric sensitivity analysis for periodic solutions of delay-differential equations is developed. Because phase shifts cause the sensitivity coefficients of a periodic orbit to diverge, we focus on sensitivities of the extrema, from which amplitude sensitivities are computed, and of the period. Delay-differential equations are often used to model gene expression networks. In these models, the parametric sensitivities of a particular genotype define the local geometry of the evolutionary landscape. Thus, sensitivities can be used to investigate directions of gradual evolutionary change...
June 12, 2017: Bulletin of Mathematical Biology
Anna K Miller, Karl Munger, Frederick R Adler
Human papillomaviruses (HPVs) that infect mucosal epithelium can be classified as high risk or low risk based on their propensity to cause lesions that can undergo malignant progression. HPVs produce the E7 protein that binds to cell cycle regulatory proteins including the retinoblastoma tumor suppressor protein (RB) to modulate cell cycle control. Generally, high-risk HPV E7 proteins bind to RB with a higher affinity than low-risk HPV E7s, but both are able to deactivate RB and trigger S phase progression...
June 12, 2017: Bulletin of Mathematical Biology
Roberta Regina Delboni, Hyun Mo Yang
Mathematical modeling is an important tool to assessing quantitative conjectures and to answer specific questions. In the modeling, we assume that a competitor represented by a lactic acid bacterium produces antimicrobial compounds (substances that kill microorganisms or inhibit their growth), such as lactic acid and bacteriocins, with some cost to its own growth. Bacteriocins are protein compounds with antimicrobial effect against related species and bacteria such as Listeria monocytogenes, which is foodborne pathogen that cause listeriosis...
June 8, 2017: Bulletin of Mathematical Biology
Asim Timalsina, Jianjun Paul Tian, Jin Wang
We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity...
June 7, 2017: Bulletin of Mathematical Biology
Kathleen P Wilkie, Philip Hahnfeldt
Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development, cancer dormancy, and immunotherapies. In fact, early immunotherapy failures were partly due to a lack in understanding of the nonlinear growth dynamics these competing immune actions may cause. To study this biological phenomenon theoretically, we construct a minimally parameterized framework that incorporates all aspects of the immune response...
June 5, 2017: Bulletin of Mathematical Biology
Apollos Besse, Geoffrey D Clapp, Samuel Bernard, Franck E Nicolini, Doron Levy, Thomas Lepoutre
We describe here a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in Clapp et al. (Cancer Res 75:4053-4062, 2015). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three-compartment model: two for the leukemic cells (stem cells and mature cells) and one for the immune response...
May 23, 2017: Bulletin of Mathematical Biology
Cicik Alfiniyah, Martin A Bees, A Jamie Wood
Pseudomonas aeruginosa is a Gram-negative bacterium that is responsible for a wide range of infections in humans. Colonies employ quorum sensing (QS) to coordinate gene expression, including for virulence factors, swarming motility and complex social traits. The QS signalling system of P. aeruginosa is known to involve multiple control components, notably the las, rhl and pqs systems. In this paper, we examine the las system and, in particular, the repressive interaction of rsaL, an embedded small regulative protein, employing recent biochemical information to aid model construction...
May 19, 2017: Bulletin of Mathematical Biology
Natalia L Komarova, P van den Driessche
Design principles of biological networks have been studied extensively in the context of protein-protein interaction networks, metabolic networks, and regulatory (transcriptional) networks. Here we consider regulation networks that occur on larger scales, namely the cell-to-cell signaling networks that connect groups of cells in multicellular organisms. These are the feedback loops that orchestrate the complex dynamics of cell fate decisions and are necessary for the maintenance of homeostasis in stem cell lineages...
May 15, 2017: Bulletin of Mathematical Biology
Curtis A Gravenmier, Miriam Siddique, Robert A Gatenby
While most cancers promote ingrowth of host blood vessels, the resulting vascular network usually fails to develop a mature organization, resulting in abnormal vascular dynamics with stochastic variations that include slowing, cessation, and even reversal of flow. Thus, substantial spatial and temporal variations in oxygen concentration are commonly observed in most cancers. Cancer cells, like all living systems, are subject to Darwinian dynamics such that their survival and proliferation are dependent on developing optimal phenotypic adaptations to local environmental conditions...
May 15, 2017: Bulletin of Mathematical Biology
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