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Bulletin of Mathematical Biology

Stefan Engblom
We take up the challenge of designing realistic computational models of large interacting cell populations. The goal is essentially to bring Gillespie's celebrated stochastic methodology to the level of an interacting population of cells. Specifically, we are interested in how the gold standard of single-cell computational modeling, here taken to be spatial stochastic reaction-diffusion models, may be efficiently coupled with a similar approach at the cell population level. Concretely, we target a recently proposed set of pathways for pattern formation involving Notch-Delta signaling mechanisms...
June 20, 2018: Bulletin of Mathematical Biology
Colby Long, Laura Kubatko
Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees, and consequently, a site pattern probability distribution. It has been shown that the unrooted topology of the species tree parameter of the multispecies coalescent is generically identifiable, and a reconstruction method called SVDQuartets has been developed to infer this topology. In this paper, we describe a modified multispecies coalescent model that allows for varying effective population size and violations of the molecular clock...
June 20, 2018: Bulletin of Mathematical Biology
Jaehee Kim, Filippo Disanto, Naama M Kopelman, Noah A Rosenberg
The neighbor-joining algorithm for phylogenetic inference (NJ) has been seen to have three specific properties when applied to distance matrices that contain an admixed taxon: (1) antecedence of clustering, in which the admixed taxon agglomerates with one of its source taxa before the two source taxa agglomerate with each other; (2) intermediacy of distances, in which the distance on an inferred NJ tree between an admixed taxon and either of its source taxa is smaller than the distance between the two source taxa; and (3) intermediacy of path lengths, in which the number of edges separating the admixed taxon and either of its source taxa is less than or equal to the number of edges between the source taxa...
June 6, 2018: Bulletin of Mathematical Biology
J Darby Smith, Scott A McKinley
The bidirectional movement of intracellular cargo is usually described as a tug-of-war among opposite-directed families of molecular motors. While tug-of-war models have enjoyed some success, recent evidence suggests underlying motor interactions are more complex than previously understood. For example, these tug-of-war models fail to predict the counterintuitive phenomenon that inhibiting one family of motors can decrease the functionality of opposite-directed transport. In this paper, we use a stochastic differential equations modeling framework to explore one proposed physical mechanism, called microtubule tethering, that could play a role in this "co-dependence" among antagonistic motors...
June 4, 2018: Bulletin of Mathematical Biology
Bin Huang, Ning Zhong, Lili Xia, Guiping Yu, Hongbao Cao
Precision medicine and personalized treatment have attracted attention in recent years. However, most genetic medicines mainly target one genetic site, while complex diseases like esophageal squamous cell carcinoma (ESCC) usually present heterogeneity that involves variations of many genetic markers. Here, we seek an approach to leverage genetic data and ESCC knowledge data to forward personalized diagnosis and treatment for ESCC. First, 851 ESCC-related gene markers and their druggability were studied through a comprehensive literature analysis...
June 4, 2018: Bulletin of Mathematical Biology
Katharina T Huber, Vincent Moulton, Charles Semple, Taoyang Wu
An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set X of species from a collection of trees, each having leaf-set some subset of X. In the 1980s, Colonius and Schulze gave certain inference rules for deciding when a collection of 4-leaved trees, one for each 4-element subset of X, can be simultaneously displayed by a single supertree with leaf-set X...
June 4, 2018: Bulletin of Mathematical Biology
Casper H L Beentjes, Ruth E Baker
Quasi-Monte Carlo methods have proven to be effective extensions of traditional Monte Carlo methods in, amongst others, problems of quadrature and the sample path simulation of stochastic differential equations. By replacing the random number input stream in a simulation procedure by a low-discrepancy number input stream, variance reductions of several orders have been observed in financial applications. Analysis of stochastic effects in well-mixed chemical reaction networks often relies on sample path simulation using Monte Carlo methods, even though these methods suffer from typical slow [Formula: see text] convergence rates as a function of the number of sample paths N...
May 25, 2018: Bulletin of Mathematical Biology
Woldegebriel A Woldegerima, Miranda I Teboh-Ewungkem, Gideon A Ngwa
A model is developed and used to study within-human malaria parasite dynamics. The model integrates actors involved in the development-progression of parasitemia, gametocytogenesis and mechanisms for immune response activation. Model analyses under immune suppression reveal different dynamical behaviours for different healthy red blood cell (HRBC) generation functions. Existence of a threshold parameter determines conditions for HRBCs depletion. Oscillatory dynamics reminiscent of malaria parasitemia are obtained...
May 24, 2018: Bulletin of Mathematical Biology
Stephen Smith, Ramon Grima
Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing models is vast, but two stand out by virtue of their popularity: the reaction-diffusion master equation and Brownian dynamics. In this review, we critically address a number of open questions surrounding these models: How can they be justified physically? How do they relate to each other? How do they fit into the wider landscape of chemical models, ranging from the rate equations to molecular dynamics? This review assumes no prior knowledge of modelling chemical kinetics and should be accessible to a wide range of readers...
May 21, 2018: Bulletin of Mathematical Biology
Alex P Farrell, James P Collins, Amy L Greer, Horst R Thieme
For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. However, if the incidence function is also lower density-dependent, very infectious diseases can lead to a drastic decline of the host population. Further, the final population size after an epidemic outbreak can possibly be substantially affected by the infection-age distribution of the initial infectives if the life expectations of infected individuals are an unbounded function of infection age (time since infection)...
May 21, 2018: Bulletin of Mathematical Biology
Xiunan Wang, Xingfu Zou
Mosquito-borne diseases remain a significant threat to public health and economics. Since mosquitoes are quite sensitive to temperature, global warming may not only worsen the disease transmission case in current endemic areas but also facilitate mosquito population together with pathogens to establish in new regions. Therefore, understanding mosquito population dynamics under the impact of temperature is considerably important for making disease control policies. In this paper, we develop a stage-structured mosquito population model in the environment of a temperature-controlled experiment...
May 21, 2018: Bulletin of Mathematical Biology
N Rodríguez, G Malanson
Motivated by the importance of understanding the dynamics of the growth and dispersal of plants in various environments, we introduce and analyze a discrete agent-based model based on a birth-jump process, which exhibit wave-like solutions. To rigorously analyze these traveling wave phenomena, we derive the diffusion limit of the discrete model and prove the existence of traveling wave solutions (sharp and continuously differentiable) assuming a logarithmic-type growth. Furthermore, we provide a variational speed for the minimum speed of the waves and perform numerical experiments that confirm our results...
May 10, 2018: Bulletin of Mathematical Biology
Nara Yoon, Robert Vander Velde, Andriy Marusyk, Jacob G Scott
Despite major strides in the treatment of cancer, the development of drug resistance remains a major hurdle. One strategy which has been proposed to address this is the sequential application of drug therapies where resistance to one drug induces sensitivity to another drug, a concept called collateral sensitivity. The optimal timing of drug switching in these situations, however, remains unknown. To study this, we developed a dynamical model of sequential therapy on heterogeneous tumors comprised of resistant and sensitive cells...
May 7, 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
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
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