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Bulletin of Mathematical Biology

Alexander R A Anderson, Philip K Maini
No abstract text is available yet for this article.
April 20, 2018: Bulletin of Mathematical Biology
Chiu-Ju Lin, Lin Wang, Gail S K Wolkowicz
We study an alternative single species logistic distributed delay differential equation (DDE) with decay-consistent delay in growth. Population oscillation is rarely observed in nature, in contrast to the outcomes of the classical logistic DDE. In the alternative discrete delay model proposed by Arino et al. (J Theor Biol 241(1):109-119, 2006), oscillatory behavior is excluded. This study adapts their idea of the decay-consistent delay and generalizes their model. We establish a threshold for survival and extinction: In the former case, it is confirmed using Lyapunov functionals that the population approaches the delay modified carrying capacity; in the later case the extinction is proved by the fluctuation lemma...
April 19, 2018: Bulletin of Mathematical Biology
David F Anderson, Chaojie Yuan
A number of coupling strategies are presented for stochastically modeled biochemical processes with time-dependent parameters. In particular, the stacked coupling is introduced and is shown via a number of examples to provide an exceptionally low variance between the generated paths. This coupling will be useful in the numerical computation of parametric sensitivities and the fast estimation of expectations via multilevel Monte Carlo methods. We provide the requisite estimators in both cases.
April 18, 2018: Bulletin of Mathematical Biology
P van den Driessche, Abdul-Aziz Yakubu
We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease...
April 12, 2018: Bulletin of Mathematical Biology
Rachael M Milwid, Federico Frascoli, Marc Steben, Jane M Heffernan
Human papillomavirus (HPV), a sexually transmitted infection, is the necessary cause of cervical cancer, the third most common cancer affecting women worldwide. Prevention and control strategies include vaccination, screening, and treatment. While HPV prevention and control efforts are important worldwide, they are especially important in low-income areas with a high infection rate or high rate of cervical cancer. This study uses mathematical modeling to explore various vaccination and treatment strategies to control for HPV and cervical cancer while using Nepal as a case study...
April 12, 2018: Bulletin of Mathematical Biology
Per Lötstedt
An algorithm for computing the linear noise approximation (LNA) of the reaction-diffusion master equation (RDME) is developed and tested. The RDME is often used as a model for biochemical reaction networks. The LNA is derived for a general discretization of the spatial domain of the problem. If M is the number of chemical species in the network and N is the number of nodes in the discretization in space, then the computational work to determine approximations of the mean and the covariances of the probability distributions is proportional to [Formula: see text] in a straightforward implementation...
April 11, 2018: Bulletin of Mathematical Biology
Muruhan Rathinam, Yuriy Sverchkov
We study the dynamics of flagellar growth in eukaryotes where intraflagellar transporters (IFT) play a crucial role. First we investigate a stochastic version of the original balance point model where a constant number of IFT particles move up and down the flagellum. The detailed model is a discrete event vector-valued Markov process occurring in continuous time. First the detailed stochastic model is compared and contrasted with a simple scalar ordinary differential equation (ODE) model of flagellar growth...
April 11, 2018: Bulletin of Mathematical Biology
Adrianne L Jenner, Chae-Ok Yun, Peter S Kim, Adelle C F Coster
Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity Kim et al. (Biomaterials 32(9):2314-2326, 2011) modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. Whilst PEG modification appeared to improve plasma retention and initial infectivity, it also increased the virus particle arrival time...
April 11, 2018: Bulletin of Mathematical Biology
Joseba Dalmau
We study Eigen's quasispecies model in the asymptotic regime where the length of the genotypes goes to [Formula: see text] and the mutation probability goes to 0. A limiting infinite system of differential equations is obtained. We prove convergence of trajectories, as well as convergence of the equilibrium solutions. We give analogous results for a discrete-time version of Eigen's model, which coincides with a model proposed by Moran.
April 2, 2018: Bulletin of Mathematical Biology
Irina Bashkirtseva, Lev Ryashko
A susceptibility of population systems to the random noise is studied on the base of the conceptual Ricker-type model taking into account the delay and Allee effect. This two-dimensional discrete model exhibits the persistence in the form of equilibria, discrete cycles, closed invariant curves, and chaotic attractors. It is shown how the Allee effect constrains the persistence zones with borders defined by crisis bifurcations. We study the role of random noise on the contraction and destruction of these zones...
April 2, 2018: Bulletin of Mathematical Biology
John Lagergren, Amanda Reeder, Franz Hamilton, Ralph C Smith, Kevin B Flores
In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set...
April 2, 2018: Bulletin of Mathematical Biology
Arturo Araujo, Leah M Cook, Conor C Lynch, David Basanta
Prostate cancer (PCa) impacts over 180,000 men every year in the USA alone, with 26,000 patients expected to succumb to the disease ( ). The primary cause of death is metastasis, with secondary lesions most commonly occurring in the skeleton. Prostate cancer to bone metastasis is an important, yet poorly understood, process that is difficult to explore with experimental techniques alone. To this end we have utilized a hybrid (discrete-continuum) cellular automaton model of normal bone matrix homeostasis that allowed us to investigate how metastatic PCa can disrupt the bone microenvironment...
March 29, 2018: Bulletin of Mathematical Biology
Jeffrey Saltzman, Claus Bendtsen
An important part the absorption, distribution, metabolism and excretion of an oral therapeutic is the flux rate of drug compound crossing the mucus lining of the gut. To understand this part of the absorption process, we develop a mathematical model of advection, diffusion and binding of drug compounds within the mucus layer of the intestines. Analysis of this model yields simple, measurable criteria for the successful mucin layer traversal of drug compound.
March 28, 2018: Bulletin of Mathematical Biology
Ryan Suderman, Eshan D Mitra, Yen Ting Lin, Keesha E Erickson, Song Feng, William S Hlavacek
Gillespie's direct method for stochastic simulation of chemical kinetics is a staple of computational systems biology research. However, the algorithm requires explicit enumeration of all reactions and all chemical species that may arise in the system. In many cases, this is not feasible due to the combinatorial explosion of reactions and species in biological networks. Rule-based modeling frameworks provide a way to exactly represent networks containing such combinatorial complexity, and generalizations of Gillespie's direct method have been developed as simulation engines for rule-based modeling languages...
March 28, 2018: Bulletin of Mathematical Biology
Katharina T Huber, Vincent Moulton, Mike Steel
Given a collection [Formula: see text] of subsets of a finite set X, we say that [Formula: see text] is phylogenetically flexible if, for any collection R of rooted phylogenetic trees whose leaf sets comprise the collection [Formula: see text], R is compatible (i.e. there is a rooted phylogenetic X-tree that displays each tree in R). We show that [Formula: see text] is phylogenetically flexible if and only if it satisfies a Hall-type inequality condition of being 'slim'. Using submodularity arguments, we show that there is a polynomial-time algorithm for determining whether or not [Formula: see text] is slim...
March 27, 2018: Bulletin of Mathematical Biology
Stefan Hoehme, Francois Bertaux, William Weens, Bettina Grasl-Kraupp, Jan G Hengstler, Dirk Drasdo
Recently, hepatocyte-sinusoid alignment (HSA) has been identified as a mechanism that supports the coordination of hepatocytes during liver regeneration to reestablish a functional micro-architecture (Hoehme et al. in Proc Natl Acad Sci 107(23):10371-10376, 2010). HSA means that hepatocytes preferentially align along the closest micro-vessels. Here, we studied whether this mechanism is still active in early hepatocellular tumors. The same agent-based spatiotemporal model that previously correctly predicted HSA in liver regeneration was further developed to simulate scenarios in early tumor development, when individual initiated hepatocytes gain increased proliferation capacity...
March 22, 2018: Bulletin of Mathematical Biology
Ivan Tyukin, Alexander N Gorban, Carlos Calvo, Julia Makarova, Valeri A Makarov
Codifying memories is one of the fundamental problems of modern Neuroscience. The functional mechanisms behind this phenomenon remain largely unknown. Experimental evidence suggests that some of the memory functions are performed by stratified brain structures such as the hippocampus. In this particular case, single neurons in the CA1 region receive a highly multidimensional input from the CA3 area, which is a hub for information processing. We thus assess the implication of the abundance of neuronal signalling routes converging onto single cells on the information processing...
March 19, 2018: Bulletin of Mathematical Biology
Garrett Otto, Sharon Bewick, Bingtuan Li, William F Fagan
In this paper, we develop a phenologically explicit reaction-diffusion model to analyze the spatial spread of a univoltine insect species. Our model assumes four explicit life stages: adult, two larval, and pupa, with a fourth, implicit, egg stage modeled as a time delay between oviposition and emergence as a larva. As such, our model is broadly applicable to holometabolous insects. To account for phenology (seasonal biological timing), we introduce four time-dependent phenological functions describing adult emergence, oviposition and larval conversion, respectively...
March 16, 2018: Bulletin of Mathematical Biology
Tanvi V Joshi, Daniele Avitabile, Markus R Owen
Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network)...
March 16, 2018: Bulletin of Mathematical Biology
Thomas J X Li, Christian M Reidys
In this paper, we analyze the length spectrum of rainbows in RNA secondary structures. A rainbow in a secondary structure is a maximal arc with respect to the partial order induced by nesting. We show that there is a significant gap in this length spectrum. We shall prove that there asymptotically almost surely exists a unique longest rainbow of length at least [Formula: see text] and that with high probability any other rainbow has finite length. We show that the distribution of the length of the longest rainbow converges to a discrete limit law and that, for finite k, the distribution of rainbows of length k becomes for large n a negative binomial distribution...
March 14, 2018: Bulletin of Mathematical Biology
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