Coexistence of multiple pathogen strains in stochastic epidemic models with density-dependent mortality

Stochastic differential equations that model an SIS epidemic with multiple pathogen strains are derived from a system of ordinary differential equations. The stochastic model assumes there is demographic variability. The dynamics of the deterministic model are summarized. Then the dynamics of the stochastic model are compared to the deterministic model. In the deterministic model, there can be either disease extinction, competitive exclusion, where only one strain persists, or coexistence, where more than one strain persists. In the stochastic model, all strains are eventually eliminated because the disease-free state is an absorbing state. However, if the population size and the initial number of infected individuals are sufficiently large, it may take a long time until all strains are eliminated. Numerical simulations of the stochastic model show that coexistence cases predicted by the deterministic model are an unlikely occurrence in the stochastic model even for short time periods. In the stochastic model, either disease extinction or competitive exclusion occur. The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model.     

Analysis of several biomechanical models for the simulation of lamb liver behaviour using similarity coefficients from medical image

In this study, six biomechanical models for simulating lamb liver behaviour are presented. They are validated using similarity coefficients from Medical Image on reconstructed volumes from computerised tomography images. In particular, the Jaccard and Hausdorff coefficients are used. Loads of 20 and 40 g are applied to the livers and their deformation is simulated by means of the finite element method. The models used are a linear elastic model, a neo-Hookean model, a Mooney–Rivlin model, an Ogden model, a linear viscoelastic model and a viscohyperelastic model. The model that provided a behaviour that is closest to reality was the viscohyperelastic model, where the hyperelastic part was modelled with an Ogden model.     

Segregating Sites in a Gene Conversion Model with Mutation

Formulae for the expectation and variance of the number of segregating and homogeneous sites in a sample of two chromosomes are found. The model includes gene conversion and infinitely-many-alleles mutation in a coalescent framework. The corresponding infinitely-many-sites model limits are also found. The formulae for the expectation are extended to any sample size. Comparisons are drawn between the pure mutation model and the model where gene conversion has been added.     

A Population-Based Morphologically Structured Model for Hyphal Growth and Product Formation in Streptomycin Fermentation

Summary A population model discriminating the hyphae according to the hyphal length and a morphologically structured model considering the specific function of different morphological forms of a hypha are combined together to describe mycelial growth, substrate consumption and secondary metabolite formation in streptomycin fermentation. In the population model, the growth modes of hyphae with different age or length are considered, while in the morphologically structured model, the morphological forms of hyphae and their functions in growth and metabolism are described. The population model and the morphologically structured model are interrelated by a branching function and a differentiation function. In the model, the growth rate of immature apical compartment is distinguished from those of matured ones, branching is proposed to occur only in the subapical region, and the hyphal compartment is assumed to synthesize secondary metabolites. The model is successfully applied to simulate the batch fermentation process of streptomycin production. The growth characteristics of filamentous microorganisms are also discussed using the model predictions.     

Reliability Analysis of the Groundwater Conceptual Model

The hydrologic model is the foundation of water resource management and planning. Conceptual model is the essential component of groundwater model. Due to limited understanding of natural hydrogeological conditions, the conceptual model is always constructed incompletely. Therefore, the uncertainty in the model's output is evitable when natural groundwater field is simulated by a single groundwater model. A synthetic groundwater model is built and regarded as the true model, and three alternative conceptual models are constructed by considering incomplete hydrogeological conditions. The outputs (groundwater budget terms from boundary conditions) of these groundwater models are analyzed statistically. The results show that when the conceptual model is closer to the true hydrogeological conditions, the distributions of outputs of the groundwater model are more concentrated on the true outputs. Therefore, the more reliable the structure of the conceptual model is, the more reliable the output of the groundwater model is. Moreover, the uncertainty caused by the conceptual model cannot be compensated by parameter uncertainty.     

Ecological interpretations of the mid-domain effect

The suggestion that spatial gradients in species richness are influenced by geometric constraints resulting in the mid‐domain effect has been investigated by null models. The technical aspects of making such null models are well explored, but the implicit ecological assumptions behind these models are less explored. Four ecological models that all assume that species ranges are constrained by hard boundaries are made: evolutionary model, source‐sink model, dynamic‐environment model, and range‐size model. These models give different predictions that make it possible to separate the models from each other, and from a model that assumes that hard boundaries are not important.     

A nonparametric mixture model for cure rate estimation

Nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis. In this paper, we study a general nonparametric mixture model. The proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured. The EM algorithm, the marginal likelihood approach, and multiple imputations are employed to estimate parameters of interest in the model. This model extends models and improves estimation methods proposed by other researchers. It also extends Cox's proportional hazards regression model by allowing a proportion of event-free patients and investigating covariate effects on that proportion. The model and its estimation method are investigated by simulations. An application to breast cancer data, including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers, confirms the conclusions from the parametric model but not those from the existing nonparametric model.     

An experimental study of the dielectric dispersion of solutions of cytochrome c at medium ionic strengths

In this paper, the results are presented of measurements of the dielectric dispersions of horse heart cytochrome c molecules in various buffers. The data are fitted to the Cole-Cole relaxation model. The influence of the concentration and the ionic strength on the parameters that result from the Cole-Cole model is determined. The measured data are compared with calculations based on the model presented previously. Good agreement is found between the model and the observed data.     

A Pseudo-Markov Model for Series of Neuronal Spike Events

Spike trains of spontaneous neuronal activity in the rabbit brain are submitted to statistical analyses based on the following pseudo-Markov model. The nerve cell is supposed to alternate between a bursting and a resting state. The numbers of consecutive spikes within each state are assumed to be independent integer-valued random variables with discrete probability distributions. Given the state, the interspike intervals are independent real-valued random variables. The two state semi-Markov model is obtained as a special case when the discrete distributions are geometrical. Statistical second-order properties of recorded spike trains are compared with those predicted by the model on the basis of known first-order properties. For that purpose, serial correlation coefficients and intensity functions for spike trains produced by the model are computed. A comparison between observed and predicted results for the spontaneous activity of 17 brain cells yields a good fit in eight cells and discloses some salient features of the statistical structure in the activity of six other cells. By making it feasible to compute theoretical correlograms, the model may advance the understanding of empirical correlograms. The possibilities for integrating this statistical model of spike trains with a model of the mechanism of spike train production are discussed.     

An Evaluation of Beta-Binomial and Dirichlet-Trinomial Models for the Analysis of Reproductive and Developmental Effects

The common endpoints for the evaluation of reproductive and developmental toxic effects are the number of dead/resorbed fetuses, the number of malformed fetuses, and the number of normal fetuses for each litter. The joint distribution of the three endpoints could be modelled by a Dirichlettrinomial distribution or by a product of two-beta-binomial distributions. A simulation experiment is used to investigate the biases of the maximum likelihood estimate (MLE) for the probability of adverse effects under the Dirichlet-trinomial model and the beta-binomial model. Also, the type I errors and powers of the likelihood ratio test for comparing the difference between treatment and control are evaluated for the two underlying models. In estimation, the two MLE's are comparable, the bias estimates are small. In testing, the likelihood ratio test is generally more powerful under the Dirichlet-trinomial model than the beta-binomial model. The type I error rate is greater than the nominal level using the Dirichlet-trinomial model in some cases, when the data are generated from the two-beta-binomial model, and it is less than the nominal level using the beta-binomial model in other cases, when the data are generated from the Dirichlet-trinomial model.     

Modeling of nitrogen in river water using a detailed and a simplified model

To model catchment surface water quantity and quality, different model types are available. They vary from detailed physically based models to simplified conceptual and empirical models. The most appropriate model type for a certain application depends on the project objectives and the data availability. The detailed models are very useful for short-term simulations of representative events. They cannot be used for long-term statistical information or as a management tool. For those purposes, more simplified (conceptual or meta-) models must be used. In this study, nitrogen dynamics are modeled in a river in Flanders. Nitrogen sources from agricultural leaching and domestic point sources are considered. Based on this input, concentrations of ammonium (NH4-N) and nitrate (NO3-N) in the river water are modeled in MIKE 11 by taking into consideration advection and dispersion and the most important biological and chemical processes. Model calibration was done on the basis of available measured water quality data. To this detailed model, a more simplified model was calibrated with the objective to more easily yield long-term simulation results that can be used in a statistical analysis. The results show that the conceptual simplified model is 1800 times faster than the MIKE 11 model. Moreover the two models have almost the same accuracy. The detailed models are recommended for short-term simulations unless there are enough data for model input and model parameters. The conceptual simplified model is recommended for long-term simulations.     

A discrete-time model with vaccination for a measles epidemic.

A discrete-time, age-independent SIR-type epidemic model is formulated and analyzed. The effects of vaccination are also included in the model. Three mathematically important properties are verified for the model: solutions are nonnegative, the population size is time-invariant, and the epidemic concludes with all individuals either remaining susceptible or becoming immune (a property typical of SIR models). The model is applied to a measles epidemic on a university campus. The simulated results are in good agreement with the actual data if it is assumed that the population mixes nonhomogeneously. The results of the simulations indicate that a rate of immunity greater than 98% may be required to prevent an epidemic in a university population. The model has applications to other contagious diseases of SIR type. Furthermore, the simulated results of the model can easily be compared to data, and the effects of a vaccination program can be examined.     

Does a reduction in the price of rhino horn prevent poaching?

Rhino poaching around the world has increased inordinately, to the extent that concerns exist over the possible survival of the species. An open access rhino poaching model is developed for South African rhino. The model is a hybrid dynamical model, as both a system dynamics model as well as a Bayesian network model are developed. The system dynamics model is used to estimate the unknown parameter values (through optimisation) and also to determine the intervals for the parameters. These intervals are then used in the Bayesian Belief Network model to assess uncertainty. Hybrid approaches improve the ability to validate models compared with conventional modelling. The resultant model indicates that reducing the price of rhino horn would not be effective at curbing poaching, unless poacher costs are also increased. However, increasing poacher costs is not a realistic policy option since these costs are largely beyond the control of decision-makers. The insensitivity of price to poaching effort has implications for methods proposed to reduce the value of rhinos, such as introducing synthetic rhino horn and the de-horning of rhinos.     

A Variance Components Model for Analyzing Repeated Measures Designs with Non-Stationary Error Structure

When data are collected in the form of multiple measurements on several subjects, they are often analyzed as repeated measures data with some stationary error structure assumed for the errors. For data with non-stationary error structure, the multivariate model is often used. The multivariate model imposes restrictions that are often not met in practice by data of such type. At the same time, they ignore valuable information in the data that are related to time dependencies and time relations. In this paper, we propose a model that is a reparametrization of the multivariate model and is suitable to analyze general repeated measures designs with non-stationary error structure. The model is shown to be a variance components model whose components are estimated using the method of maximum likelihood. Several other properties of the model are derived and discussed including tests of significance. Finally, an example on neurological data is included to demonstrate its application in biological sciences.     

A Multidimensional Multispecies Continuum Model for Heterogeneous Biofilm Development

We propose a multidimensional continuum model for heterogeneous growth of biofilm systems with multiple species and multiple substrates. The new model provides a deterministic framework for the study of the interactions between several spe1cies and their effects on biofilm heterogeneity. It consists of a system of partial differential equations derived on the basis of conservation laws and reaction kinetics. The derivation and key assumptions are presented. The assumptions used are a combination of those used in the established one dimensional model, due to Wanner and Gujer, and for the viscous fluid model, of Dockery and Klapper. The work of Wanner and Gujer in particular has been extensively used through the years, and thus this new model is an extension to several spatial dimensions of an already proven working model. The model equations are solved using numerical techniques, for purposes of simulation and verification. The new model is applied to two different biofilm systems in several spatial dimensions, one of which is equivalent to a system originally studied by Wanner and Gujer. Dimensionless formulations for these two systems are given, and numerical simulation results with varying initial conditions are presented. An erratum to this article can be found at     

周期性静滴给药的稳态动力学研究

对线性一定模型的药物,周期静滴给药的动力学模型为一分段连续函数,本文对其动态动力学特征进行了研究,得到了稳态浓度的ｃ－ｔ方程以及一次给药和多次给药动力学参数之间的关系。为预测稳态浓度提供了依据,在此基础上对给药方案的拟定进行了讨论。     

A fuzzy-genetic model for estimating forces from electromyographical activity of antagonistic muscles due to planar lower arm movements: the effect of nonlinear muscle properties

The aim of this paper is to create a model for mapping the surface electromyogram (EMG) signals to the force that generated by human arm muscles. Because the parameters of each person's muscle are individual, the model of the muscle must have two characteristics: (1) The model must be adjustable for each subject. (2) The relationship between the input and output of model must be affected by the force-length and the force-velocity behaviors are proven through Hill's experiments. Hill's model is a kinematic mechanistic model with three elements, i.e. one contractile component and two nonlinear spring elements.In this research, fuzzy systems are applied to improve the muscle model. The advantages of using fuzzy system are as follows: they are robust to noise, they prove an adjustable nonlinear mapping, and are able to model the uncertainties of the muscle.Three fuzzy coefficients have been added to the relationships of force-length (active and passive) and force-velocity existing in Hill's model. Then, a genetic algorithm (GA) has been used as a biological search method that can adjust the parameters of the model in order to achieve the optimal possible fit.Finally, the accuracy of the fuzzy genetic implementation Hill-based muscle model (FGIHM) is invested as following: the FGIHM results have 12.4% RMS error (in worse case) in comparison to the experimental data recorded from three healthy male subjects. Moreover, the FGIHM active force-length relationship which is the key characteristics of muscles has been compared to virtual muscle (VM) and Zajac muscle model. The sensitivity of the FGIHM has been evaluated by adding a white noise with zero mean to the input and FGIHM has proved to have lower sensitivity to input noise than the traditional Hill's muscle model.     

Sex-structured HIV/AIDS model to analyse the effects of condom use with application to Zimbabwe

We present a sex-structured model for heterosexual transmission of HIV/AIDS in a community. The model is formulated using integro-differential equations, which are shown to be equivalent to delay differential equations with a time delay due to incubation period. The sex-structured HIV/AIDS model divides the population into a two sex-structure consisting of females and males. The threshold and equilibria for the model are determined and stabilities are examined. We extend the model to focus on the effects of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. Initially we model the use of male condoms and further extend the model to incorporate the use of both female and male condoms. The model includes two primary factors in condom use to control HIV that are condom efficacy and compliance. The exposure risk of infection after each intervention is obtained. Basic reproductive numbers for these models are computed and compared to assess the effectiveness of male and female condom use in a community. The models are numerically analysed to assess the effectiveness of condom use on the transmission dynamics of HIV/AIDS using demographic and epidemiological parameters for Zimbabwe. The study demonstrates the use of sex-structured HIV/AIDS models in assessing the effectiveness of female and male condom use as a preventative strategy in a heterosexually active population. Z. Mukandavire would like to acknowledge financial support given by the National University of Science and Technology through a Staff Development Scholarship. The authors are grateful to Eagle Insurance Company of Zimbabwe for financial support.     

Simulation of bracken cover in forested areas in Victoria in response to season,overstorey and fire conditions

Abstract A computer-based model is presented that brings together the existing knowledge about the dynamics of bracken in eucalypt forests in south-eastern Australia. The average length of the growing season, the timing and extent of logging, and the timing and severity of fire are major inputs to the model. The model is predominantly deterministic, but has a stochastic environmental component. The model is validated with four independent sets of data. The model successfully predicts the trends in the data. The interactions between bracken, other understorey species and eucalypt regeneration are explored with the model. The likely effect of different silvicultural and fire management practices on the cover of bracken are investigated using the model. Year to year variation can mask the effects of disturbance if bracken cover is viewed in any one year in isolation. Bracken cover trends can only be seen over a period of 10 years or more. The model reinforces the importance of site productivity as measured by length of growing season and the degree of tree removal on bracken cover.     

The species-area relation III. A third model for a delimited community

Summary A mathematical model of the species-area relation is described for a group of limited species. This model is a modification of that proposed earlier (Kobayashi, 1975), being assumed that the limited species are expected to occur in a habitat under consideration. The model equation gives a sigmoid species-log area curve implying that few rare species are found in a group of species. The good agreement between observation and this model is exemplified with the data of plant and arthropod communities. The implication of parameters involved are examined in connection with those of the preceding model, and the underlying ecology of the model is discussed. Contribution from the Laboratory of Applied Zoology, Yamagata University, No. 83.