A comparison of three different stochastic population models with regard to persistence time

Results are summarized from the literature on three commonly used stochastic population models with regard to persistence time. In addition, several new results are introduced to clearly illustrate similarities between the models. Specifically, the relations between the mean persistence time and higher-order moments for discrete-time Markov chain models, continuous-time Markov chain models, and stochastic differential equation models are compared for populations experiencing demographic variability. Similarities between the models are demonstrated analytically, and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models are consistently formulated. As an example, the three stochastic models are applied to a population satisfying logistic growth. Logistic growth is interesting as different birth and death rates can yield the same logistic differential equation. However, the persistence behavior of the population is strongly dependent on the explicit forms for the birth and death rates. Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth.     

Epidemic growth rate and household reproduction number in communities of households,schools and workplaces

In this paper we present a novel and coherent modelling framework for the characterisation of the real-time growth rate in SIR models of epidemic spread in populations with social structures of increasing complexity. Known results about homogeneous mixing and multitype models are included in the framework, which is then extended to models with households and models with households and schools/workplaces. Efficient methods for the exact computation of the real-time growth rate are presented for the standard SIR model with constant infection and recovery rates (Markovian case). Approximate methods are described for a large class of models with time-varying infection rates (non-Markovian case). The quality of the approximation is assessed via comparison with results from individual-based stochastic simulations. The methodology is then applied to the case of influenza in models with households and schools/workplaces, to provide an estimate of a household-to-household reproduction number and thus asses the effort required to prevent an outbreak by targeting control policies at the level of households. The results highlight the risk of underestimating such effort when the additional presence of schools/workplaces is neglected. Our framework increases the applicability of models of epidemic spread in socially structured population by linking earlier theoretical results, mainly focused on time-independent key epidemiological parameters (e.g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics.     

Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia

Two multiscale (hybrid) stochastic reaction–diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction–diffusion models. The first hybrid model is based on the models previously developed in the literature. The second hybrid model is based on the application of a recently developed two-regime method (TRM) to a fully molecular-based model, which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model.     

Parameter redundancy in mark‐recovery models

We provide a definitive guide to parameter redundancy in mark‐recovery models, indicating, for a wide range of models, in which all the parameters are estimable, and in which models they are not. For these parameter‐redundant models, we identify the parameter combinations that can be estimated. Simple, general results are obtained, which hold irrespective of the duration of the studies. We also examine the effect real data have on whether or not models are parameter redundant, and show that results can be robust even with very sparse data. Covariates, as well as time‐ or age‐varying trends, can be added to models to overcome redundancy problems. We show how to determine, without further calculation, whether or not parameter‐redundant models are still parameter redundant after the addition of covariates or trends.     

Evaluations of Interventions Using Mathematical Models with Exponential and Non-exponential Distributions for Disease Stages: The Case of Ebola

Many mathematical models for the disease transmission dynamics of Ebola have been developed and studied, particularly during and after the 2014 outbreak in West Africa. Most of these models are systems of ordinary differential equations (ODEs). One of the common assumptions made in these ODE models is that the duration of disease stages, such as latent and infectious periods, follows an exponential distribution. Gamma distributions have also been used in some of these models. It has been demonstrated that, when the models are used to evaluate disease control strategies such as quarantine or isolation, the models with exponential and Gamma distribution assumptions may generate contradictory results (Feng et al. in Bull Math Biol 69(5):1511–1536, 2007). Several Ebola models are considered in this paper with various stage distributions, including exponential, Gamma and arbitrary distributions. These models are used to evaluate control strategies such as isolation (or hospitalization) and timely burial and to identify potential discrepancies between the results from models with exponential and Gamma distributions.     

Comparing functional responses in predator-infected eco-epidemics models

The current paper deals with the mathematical models of predator–prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator–prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.     

Exploring the structure of opioid receptors with homology modeling based on single and multiple templates and subsequent docking: A comparative study

Opioid receptors are the principal targets for opioids, which have been used as analgesics for centuries. Opioid receptors belong to the rhodopsin family of G-protein coupled receptors (GPCRs). In the absence of crystal structures of opioid receptors, 3D homology models have been reported with bovine rhodopsin as a template, though the sequence homology is low. Recently, it has been reported that use of multiple templates results in a better model for a target having low sequence identity with a single template. With the objective of carrying out a comparative study on the structural quality of the 3D models based on single and multiple templates, the homology models for opioid receptors (mu, delta and kappa) were generated using bovine rhodopsin as single template and the recently deposited crystal structures of squid rhodopsin, turkey β-1 and human β-2 adrenoreceptors along with bovine rhodopsin as multiple templates. In this paper we report the results of comparison between the refined 3D models based on multiple sequence alignment (MSA) and models built with bovine rhodopsin as template, using validation programs PROCHECK, PROSA, Verify 3D, Molprobity and docking studies. The results indicate that homology models of mu and kappa with multiple templates are better than those built with only bovine rhodopsin as template, whereas, in many aspects, the homology model of delta opioid receptor with single template is better with respect to the model based on multiple templates. Three nonselective ligands were docked to both the models of mu, delta and kappa opioid receptors using GOLD 3.1. The results of docking complied well with the pharamacophore, reported for nonspecific opioid ligands. The comparison of docking results for models with multiple templates and those with single template have been discussed in detail. Three selective ligands for each receptor were also docked. As the crystallographic structures are not yet known, this comparison will help in choosing better homology models of opioid receptors for studying ligand receptor interactions to design new potent opioid antagonists.     

Conformations of C-DNA in Agreement with Fiber X-ray and Infrared Dichroísm

Abstract

Different left handed double helices are proposed as models for DNA fibers in the C form. These conformations have geometrical parameters which agree well with fiber X-ray data and the orientations of their phosphate groups are in good agreement with infrared dichroísm results. A complete set of atomic coordinates and dihedral angles are given together with curves of calculated diffracted intensities. The present results are compared with experimental values and with the other C-DNA models.     

A Comparative Survey of Automated Parameter-Search Methods for Compartmental Neural Models

One of the most difficult and time-consuming aspects of building compartmental models of single neurons is assigning values to free parameters to make models match experimental data. Automated parameter-search methods potentially represent a more rapid and less labor-intensive alternative to choosing parameters manually. Here we compare the performance of four different parameter-search methods on several single-neuron models. The methods compared are conjugate-gradient descent, genetic algorithms, simulated annealing, and stochastic search. Each method has been tested on five different neuronal models ranging from simple models with between 3 and 15 parameters to a realistic pyramidal cell model with 23 parameters. The results demonstrate that genetic algorithms and simulated annealing are generally the most effective methods. Simulated annealing was overwhelmingly the most effective method for simple models with small numbers of parameters, but the genetic algorithm method was equally effective for more complex models with larger numbers of parameters. The discussion considers possible explanations for these results and makes several specific recommendations for the use of parameter searches on neuronal models.     

Homogenized constrained mixture models for anisotropic volumetric growth and remodeling

Constrained mixture models for soft tissue growth and remodeling have attracted increasing attention over the last decade. They can capture the effects of the simultaneous presence of multiple constituents that are continuously deposited and degraded at in general different rates, which is important to understand essential features of living soft tissues that cannot be captured by simple kinematic growth models. Recently the novel concept of homogenized constrained mixture models was introduced. It was shown that these models produce results which are very similar (and in certain limit cases even identical) to the ones of constrained mixture models based on multi-network theory. At the same time, the computational cost and complexity of homogenized constrained mixture models are much lower. This paper discusses the theory and implementation of homogenized constrained mixture models for anisotropic volumetric growth and remodeling in three dimensions. Previous constrained mixture models of volumetric growth in three dimensions were limited to the special case of isotropic growth. By numerical examples, comparison with experimental data and a theoretical discussion, we demonstrate that there is some evidence raising doubts whether isotropic growth models are appropriate to represent growth and remodeling of soft tissue in the vasculature. Anisotropic constrained mixture models, as introduced in this paper for the first time, may be required to avoid unphysiological results in simulations of vascular growth and remodeling.     

Two Models of Population Growth

Two simple models of the ecology of population growth are described: "exponential" growth with "r -selection," and "logistic" growth, with "K- selection." Various methods for estimating the parameters of these models are presented in detail, along with statistical methods of evaluation and comparison. Also briefly discussed are more complex models of population growth sometimes used by demographers and ecologists. The two simpler models of population growth are then applied, by way of illustration, to two episodes of population growth in protohistoric southwest Iran, dating from 4000–2350 B. C. Interpretation of the results and the implications for future research are then discussed . [population growth, statistical models, exponential growth, logistic growth, early Iran]     

Stochastic models for toxicant-stressed populations

We obtain conditions for the existence of an invariant distribution on (0, ∞) for stochastic growth models of Ito type. We interpret the results in the case where the intrinsic growth rate is adjusted to account for the impact of a toxicant on the population. Comparisons with related results for ODE models by Hallamet al. are given, and consequences of taking the Stratonovich interpretation for the stochastic models are mentioned.     

A Bayesian Approach to Joint Mixed‐Effects Models with a Skew‐Normal Distribution and Measurement Errors in Covariates

Summary In recent years, nonlinear mixed‐effects (NLME) models have been proposed for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain intersubject variations. However, one often assumes that both model random error and random effects are normally distributed, which may not always give reliable results if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. In this article, we address these issues simultaneously by jointly modeling the response and covariate processes using a Bayesian approach to NLME models with covariate measurement errors and a skew‐normal distribution. A real data example is offered to illustrate the methodologies by comparing various potential models with different distribution specifications. It is showed that the models with skew‐normality assumption may provide more reasonable results if the data exhibit skewness and the results may be important for HIV/AIDS studies in providing quantitative guidance to better understand the virologic responses to antiretroviral treatment.     

Data quality

A methodology is presented that enables incorporating expert judgment regarding the variability of input data for environmental life cycle assessment (LCA) modeling. The quality of input data in the life-cycle inventory (LCI) phase is evaluated by LCA practitioners using data quality indicators developed for this application. These indicators are incorporated into the traditional LCA inventory models that produce non-varying point estimate results (i.e., deterministic models) to develop LCA inventory models that produce results in the form of random variables that can be characterized by probability distributions (i.e., stochastic models). The outputs of these probabilistic LCA models are analyzed using classical statistical methods for better decision and policy making information. This methodology is applied to real-world beverage delivery system LCA inventory models. The inventory study results for five beverage delivery system alternatives are compared using statistical methods that account for the variance in the model output values for each alternative. Sensitivity analyses are also performed that indicate model output value variance increases as input data uncertainty increases (i.e., input data quality degrades). Concluding remarks point out the strengths of this approach as an alternative to providing the traditional qualitative assessment of LCA inventory study input data with no efficient means of examining the combined effects on the model results. Data quality assessments can now be captured quantitatively within the LCA inventory model structure. The approach produces inventory study results that are variables reflecting the uncertainty associated with the input data. These results can be analyzed using statistical methods that make efficient quantitative comparisons of inventory study alternatives possible. Recommendations for future research are also provided that include the screening of LCA inventory model inputs for significance and the application of selection and ranking techniques to the model outputs.     

马铃薯干物质分配与器官建成的动态模拟研究

根据多年不同保护地栽培田间试验的结果,利用Origin软件结合马铃薯生长发育的基本特点,提出了以发育生理日为驱动变量的光合产物在不同器官间分布的数值模型,方法简便,机理明确,模拟精度高.研究还给出了不同发育时期马铃薯不同器官的干物率变化模型,并依此推导出器官的鲜重模型,进行了马铃薯块茎产量的模拟,结果表明模拟值与实测值具有良好的一致性。     

Conditions for periodic solutions of volterra differential systems

As a contribution to the discussion of oscillatory models for interacting species it is shown that two-species Volterra models can never have limit cycles, and a complete enumeration is given of conditions which the parameters of these models must satisfy in order that a part of the phase space be filled with a family of closed curves; sketches of phase portraits are also given. These results complement and correct older results by Bautin and by Coppel on quadratic differential systems. The paper opens with a brief discussion of some more practical aspects of the ecological application of oscillatory models.     

Dynamics of a feline retrovirus (FeLV) in host populations with variable spatial structure.

The predictions of epidemic models are remarkably affected by the underlying assumptions concerning host population dynamics and the relation between host density and disease transmission. Furthermore, hypotheses underlying distinct models are rarely tested. Domestic cats (Felis catus) can be used to compare models and test their predictions, because cat populations show variable spatial structure that probably results in variability in the relation between density and disease transmission. Cat populations also exhibit various dynamics. We compare four epidemiological models of Feline Leukaemia Virus (FeLV). We use two different incidence terms, i.e. proportionate mixing and pseudo-mass action. Population dynamics are modelled as logistic or exponential growth. Compared with proportionate mixing, mass action incidence with logistic growth results in a threshold population size under which the virus cannot persist in the population. Exponential growth of host populations results in systems where FeLV persistence at a steady prevalence and depression of host population growth are biologically unlikely to occur. Predictions of our models account for presently available data on FeLV dynamics in various populations of cats. Thus, host population dynamics and spatial structure can be determinant parameters in parasite transmission, host population depression, and disease control.     

The conformations and energetics of photodamaged DNA

Energy minimization techniques are used in conjunction with the results of small molecule crystallographic studies on relevant compounds to propose structural models for photodamaged DNAs. Specifically, we present models both for a DNA molecule containing a psoralen photo-crosslink and for a DNA molecule containing a thymine photodimer. In both models, significant distortions of the nucleic acid helix are observed, including kinking and unwinding at the damage site and numerous changes in the backbone torsion angles relative to their standard conformations. Both the torsion angle geometries and the energetics of the models are presented in detail.     

乙型肝炎流行病学数学模型

本文根据乙型肝炎的自然传播过程,建立由偏微分方程表达的数学模型．模型中所有参数都由实际资料估计所得,而且考虑了乙型肝炎感染与转归随年龄变化的特点．免疫接种前、后模型模拟的结果与实际观察值相符,这说明模型能够反映乙型肝炎在人群中的传播过程．