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Journal of Mathematical Biology

Peter Clote, Amir H Bayegan
RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny ([Formula: see text]20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm...
August 5, 2017: Journal of Mathematical Biology
Jimin Zhang, Junping Shi, Xiaoyuan Chang
A coupled system of ordinary differential equations and partial differential equations is proposed to describe the interaction of pelagic algae, benthic algae and one essential nutrient in an oligotrophic shallow aquatic ecosystem with ample supply of light. The existence and uniqueness of non-negative steady states are completely determined for all possible parameter range, and these results characterize sharp threshold conditions for the regime shift from extinction to coexistence of pelagic and benthic algae...
August 1, 2017: Journal of Mathematical Biology
Edna Chilenje Manda, Faraimunashe Chirove
Most existing models have considered the immunological processes occurring within the host and the epidemiological processes occurring at population level as decoupled systems. We present a new model using continuous systems of non linear ordinary differential equations by directly linking the within host dynamics capturing the interactions between Langerhans cells, CD4[Formula: see text] T-cells, R5 HIV and X4 HIV and the without host dynamics of a basic compartmental HIV/AIDS model. The model captures the biological theories of the cells that take part in HIV transmission...
July 31, 2017: Journal of Mathematical Biology
Alex Gavryushkin, Chris Whidden, Frederick A Matsen
A time-tree is a rooted phylogenetic tree such that all internal nodes are equipped with absolute divergence dates and all leaf nodes are equipped with sampling dates. Such time-trees have become a central object of study in phylogenetics but little is known about the parameter space of such objects. Here we introduce and study a hierarchy of discrete approximations of the space of time-trees from the graph-theoretic and algorithmic point of view. One of the basic and widely used phylogenetic graphs, the [Formula: see text] graph, is the roughest approximation and bottom level of our hierarchy...
July 29, 2017: Journal of Mathematical Biology
Paul Crewe, Richard Gratwick, Alan Grafen
The recently elucidated definition of fitness employed by Fisher in his fundamental theorem of natural selection is combined with reproductive values as appropriately defined in the context of both random environments and continuing fluctuations in the distribution over classes in a class-structured population. We obtain astonishingly simple results, generalisations of the Price Equation and the fundamental theorem, that show natural selection acting only through the arithmetic expectation of fitness over all uncertainties, in contrast to previous studies with fluctuating demography, in which natural selection looks rather complicated...
July 29, 2017: Journal of Mathematical Biology
Winfried Just, Joan Saldaña, Ying Xin
We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes...
July 28, 2017: Journal of Mathematical Biology
Alejandra Christen, M Angélica Maulén-Yañez, Eduardo González-Olivares, Michel Curé
In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity...
July 27, 2017: Journal of Mathematical Biology
M R Mattei, L Frunzo, B D'Acunto, Y Pechaud, F Pirozzi, G Esposito
The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete...
July 24, 2017: Journal of Mathematical Biology
Lam Si Tung Ho, Jason Xu, Forrest W Crawford, Vladimir N Minin, Marc A Suchard
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation...
July 24, 2017: Journal of Mathematical Biology
David Koslicki, Mark Novak
We consider the goal of predicting how complex networks respond to chronic (press) perturbations when characterizations of their network topology and interaction strengths are associated with uncertainty. Our primary result is the derivation of exact formulas for the expected number and probability of qualitatively incorrect predictions about a system's responses under uncertainties drawn form arbitrary distributions of error. Additional indices provide new tools for identifying which links in a network are most qualitatively and quantitatively sensitive to error, and for determining the volume of errors within which predictions will remain qualitatively determinate (i...
July 22, 2017: Journal of Mathematical Biology
Wendi Bao, Yihong Du, Zhigui Lin, Huaiping Zhu
As vectors, mosquitoes transmit numerous mosquito-borne diseases. Among the many factors affecting the distribution and density of mosquitoes, climate change and warming have been increasingly recognized as major ones. In this paper, we make use of three diffusive logistic models with free boundary in one space dimension to explore the impact of climate warming on the movement of mosquito range. First, a general model incorporating temperature change with location and time is introduced. In order to gain insights of the model, a simplified version of the model with the change of temperature depending only on location is analyzed theoretically, for which the dynamical behavior is completely determined and presented...
July 19, 2017: Journal of Mathematical Biology
P J García-Nieto, E García-Gonzalo, J R Alonso Fernández, C Díaz Muñiz
Eutrophication is a water enrichment in nutrients (mainly phosphorus) that generally leads to symptomatic changes and deterioration of water quality and all its uses in general, when the production of algae and other aquatic vegetations are increased. In this sense, eutrophication has caused a variety of impacts, such as high levels of Chlorophyll a (Chl-a). Consequently, anticipate its presence is a matter of importance to prevent future risks. The aim of this study was to obtain a predictive model able to perform an early detection of the eutrophication in water bodies such as lakes...
July 15, 2017: Journal of Mathematical Biology
Ryan M Evans, David A Edwards
Scientists measure rate constants associated with biochemical reactions in an optical biosensor-an instrument in which ligand molecules are convected through a flow cell over a surface to which receptors are immobilized. We quantify transport effects on such reactions by modeling the associated convection-diffusion equation with a reaction boundary condition. In experimental situations, the full PDE model reduces to a set of unwieldy integrodifferential equations (IDEs). Employing common physical assumptions, we may reduce the system to an ODE model, which is more useful in practice, and which can be easily adapted to the inverse problem of finding rate constants...
July 13, 2017: Journal of Mathematical Biology
Ke Yan, Ho-Lun Cheng, Zhiwei Ji, Xin Zhang, Huijuan Lu
This study proposes a novel approach, namely, skin flow complex algorithm (SFCA), to decompose the molecular skin surface into topological disks. The main contributions of SFCA include providing a simple decomposition and fast calculation of the molecular skin surface. Unlike most existing works which partition the molecular skin surface into sphere and hyperboloid patches, SFCA partitions the molecular skin surface into triangular quadratic patches and rectangular quadratic patches. Each quadratic patch is proven to be a topological disk and rendered by a rational Bézier patch...
July 8, 2017: Journal of Mathematical Biology
Neil Sherborne, Joel C Miller, Konstantin B Blyuss, Istvan Z Kiss
This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes...
July 6, 2017: Journal of Mathematical Biology
Alexandru Hening, Dang H Nguyen, George Yin
This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on [Formula: see text]. We prove that r, the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population...
July 3, 2017: Journal of Mathematical Biology
Pavel Chigansky, Peter Jagers, Fima C Klebaner
Real time, or quantitative, PCR typically starts from a very low concentration of initial DNA strands. During iterations the numbers increase, first essentially by doubling, later predominantly in a linear way. Observation of the number of DNA molecules in the experiment becomes possible only when it is substantially larger than initial numbers, and then possibly affected by the randomness in individual replication. Can the initial copy number still be determined? This is a classical problem and, indeed, a concrete special case of the general problem of determining the number of ancestors, mutants or invaders, of a population observed only later...
June 30, 2017: Journal of Mathematical Biology
Chai Molina, David J D Earn
Two major forces shaping evolution are drift and selection. The standard models of neutral drift-the Wright-Fisher (WF) and Moran processes-can be extended to include selection. However, these standard models are not always applicable in practice, and-even without selection-many other drift models make very different predictions. For example, "generalised Wright-Fisher" models (so-called because their first two conditional moments agree with those of the WF process) can yield wildly different absorption times from WF...
June 29, 2017: Journal of Mathematical Biology
Jude D Kong, Paul Salceanu, Hao Wang
Biodegradation, the disintegration of organic matter by microorganism, is essential for the cycling of environmental organic matter. Understanding and predicting the dynamics of this biodegradation have increasingly gained attention from the industries and government regulators. Since changes in environmental organic matter are strenuous to measure, mathematical models are essential in understanding and predicting the dynamics of organic matters. Empirical evidence suggests that grazers' preying activity on microorganism helps to facilitate biodegradation...
June 29, 2017: Journal of Mathematical Biology
Vincent Renault, Michèle Thieullen, Emmanuel Trélat
We use conductance based neuron models, and the mathematical modeling of optogenetics to define controlled neuron models and we address the minimal time control of these affine systems for the first spike from equilibrium. We apply tools of geometric optimal control theory to study singular extremals, and we implement a direct method to compute optimal controls. When the system is too large to theoretically investigate the existence of singular optimal controls, we observe numerically the optimal bang-bang controls...
June 29, 2017: Journal of Mathematical Biology
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