On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

A cross-diffusion model of forest boundary dynamics

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction — diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction — cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.     

Bifurcation analysis of periodic SEIR and SIR epidemic models

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.     

Modelling the effect of treatment and behavioral change in HIV transmission dynamics

In this paper we analyze a model for the HIV-infection transmission in a male homosexual population. In the model we consider two types of infected individuals. Those that are infected but do not know their serological status and/or are not under any sort of clinical /therapeutical treatment, and those who are. The two groups of infectives differ in their incubation time, contact rate with susceptible individuals, and probability of disease transmission. The aim of this article is to study the roles played by detection and changes in sexual behavior in the incidence and prevalence of HIV. The analytical results show that there exists a unique endemic equilibrium which is globally asymptotically stable under a range of parameter values whenever a detection /treatment rate and an indirect measure of the level of infection risk are sufficiently large. However, any level of detection/ treatment rate coupled with a decrease of the transmission probability lowers the incidence rate and prevalence level in the population. In general, only significant reductions in the transmission probability (achieved through, for example, the adoption of safe sexual practices) can contain effectively the spread of the disease.     

Species composition of dabbling duck assemblages: ecomorphological patterns compared with null models

Ecomorphological patterns of breeding dabbling duck (Anas spp.) assemblages were studied in six regions in northern Europe. Observed spacings among species in terms of bill lamellar density and body length were compared with expected spacings based on null models incorporating different levels of constraints (regional species pools, species relative abundances, lake size and habitat requirements of species). Deviations of observed spacings from expected ones were compared with prey abundance and prey size diversity in the lakes. Observed spacings in terms of body length, but not in terms of bill lamellar density, were greater than expected on the basis of null models. The most abundant species were generally relatively more different than less abundant species in terms of body length but not in terms of bill lamellar density. Deviations between observed and expected spacings in terms of body length were more like those predicted by the competition hypothesis in lakes with low food abundance than in lakes with high food abundance. Patterns in bill lamellar spacings were not related to food abundance nor to food size diversity. In general, patterns in body length spacings were consistent with the competition hypothesis whether the null model used in comparisons was constrained or not.     

Simulation of nitrogen assimilation by heterotrophic soil microbial biomass

Assimilation of N by heterotrophic soil microbial biomass is associated with decomposition of organic matter in the soil. The form of N assimilated can be either low molecular weight organic N released from the breakdown of organic matter (direct assimilation), or NH⁺₄ and NO⁻₃ from the soil inorganic N pool, into which mineralized organic N is released (mineralization immobilization turnover). The kinetics of C and N turnover in soil is quantifiable by means of computer simulation models. NCSOIL was constructed to represent the two assimilation schemes. The rate of N assimilation depends on the rate of C assimilation and microbial C/N ratio, thereby rendering it independent of the assimilation scheme. However, if any of the N forms is labeled, a different amount of labeled N assimilation will be simulated by the different schemes. Experimental data on inorganic N and ¹⁵N and on organic ¹⁵N dynamics in soils incubated with ¹⁵N added as NH⁺₄ or organic N were compared with data simulated by different model schemes. Direct assimilation could not account for the amount of ¹⁵N assimilated in any of the experimental treatments. The best fit of the model to experimental data was obtained for the mineralization immobilization turnover scheme when both NH⁺₄ and NO⁻₃ were assimilated, in proportion to their concentration in the soil.     

水稻自然生长趋势的数学模型和动态分析

本研究以随机过程理论为基础,应用数理方法,在分期播种的基础上,提出了一个受遗传特性控制的水稻各生物学参量自然生长趋势的数学模型。并进行了重复验证,得到了不同生育时段各生物学参量的生长速度（一阶导数）和生长速度的变化率（二阶导数）,揭示了水稻生长的基本规律。并结合实测资料,通过相关分析,得到影响各生物学参量的关键气象因子,将水稻生长的研究建立在定量的基础上,有利于更加合理地采用各项高产栽培和农田管理措施。     

杭州西湖水质预测方法和结果分析

本文利用二维对流扩散模型对西湖水质总磷浓度进行预测,给出方程的理论基础,编制FORTRAN77程序,在386微机上实现预测,并对预测结果作了较为详细的分析．本模型对水质环境防治决策具有实际意义．     

Variability in the distribution and abundance of stream salmonids, and the associated use of habitat models

The effective management of salmonid fisheries requires that the factors influencing variation in the abundance of stream populations are understood. The use of habitat models to explain the spatial component of population variance offers potential for management, but has not previously been set in the context of long term variation in population abundance because of the lack of suitable data sets. This paper examines contributions of spatial and temporal factors lo fish density variance using a 10-year data set from five tributaries of the River Conwy, North Wales. Recently developed habitat models were applied to the data to test their ability to explain nominal spatial variance. Spatial variance accounted for between 21 and 62% of the overall variance of salmonid abundance, and habitat models explained up to 95% of the spatial variance component. Synchrony in population variation amongst sites within and between tributaries is described, and some of the factors that may influence this are discussed.     

The decline of tree diversity on newly isolated tropical islands: A test of a null hypothesis and some implications

Summary Six islands, each less than a hectare in area, were isolated in about 1913 from the mainland of central Panamá by the rising waters of Gatun Lake. By 1980, the diversity of trees on all but one of these islands was far lower than on mainland plots of comparable size. A restricted subset of tree species has spread on these islands, notablyProtium panamense, Scheelea zonensis, Oenocarpus panamanus andSwartzia simplex. We constructed a null model to predict how chance would change tree diversity and the similarity of tree species compositions of different islands, assuming that each mature tree has equal chances of dying and/or reproducing, regardless of its species. This model cannot account for the diminished diversity of the changes in vegetation on these islands: some factors must be favoring a particular set of tree species.Two factors, exposure to wind and absence of mammals, seem needed to bring about the vegetation changes observed on these small islands. Their vegetation shows many signs of wind damage and of adaptation to resist wind, reflecting its exposure to dry season winds and storm winds sweeping across the lake from the west. Their most common tree species appear to have spread because mammals rarely visit these small and isolated islands. Seed of these common species are normally much eaten by mammals and do not need burial by mammals to escape insect attack.A thorough grasp of plant—animal interactions is needed to understand the events that have taken place on these islands. Identifying those keystone animals essential for maintaining plant diversity is a necessary element of reserve design and forest management in the tropics.The US government has the right to retain a non-exclusive, royalty-free license in and to any copyright covering this paper.