Undesirable facility location with minimal covering objectives

An undesirable facility is to be located within some feasible region of any shape in the plane or on a planar network. Population is supposed to be concentrated at a finite number n of points. Two criteria are taken into account: a radius of influence to be maximised, indicating within which distance from the facility population disturbance is taken into consideration, and the total covered population, i.e. lying within the influence radius from the facility, which should be minimised. Low complexity polynomial algorithms are derived to determine all nondominated solutions, of which there are only O(n³) for a fixed feasible region or O(n²) when locating on a planar network. Once obtained, this information allows almost instant answers and a trade-off sensitivity analysis to questions such as minimising the population within a given radius (minimal covering problem) or finding the largest circle not covering more than a given total population.     

A mathematical-model approach to human population explosions caused by migration

If the human population density becomes extremely high in a small area, then we say that a population explosion occurs in the area. Geographical movements of human population can form a regional overconcentration of population. If such an overconcentration becomes excessive, then it often forms a population explosion. In this paper, by taking a mathematical-model approach to human population explosions caused by migration, we obtain a sufficient condition for population to explode. It is known in sociodynamics that geographical population movements are described by a nonlinear integro-partial differential equation whose unknown function denotes the population density. This equation is called the master equation, and has its origin in statistical physics. We express a population explosion as a blow-up solution to the initial-value problem for this equation. We will study a population explosion as an interdisciplinary subject among human population dynamics, statistical physics, and the theory of nonlinear functional equations. The principal result is as follows: if a human population migrates within a sufficiently small domain, if the gradient of initial population density is sufficiently large, if the population gravitates strongly toward densely populated areas, and if a cost incurred in moving is sufficiently small, then a population explosion occurs.     

How does within‐host dynamics affect population‐level dynamics? Insights from an immuno‐epidemiological model of malaria

Malaria is one of the most common mosquito‐borne diseases widespread in the tropical and subtropical regions. Few models coupling the within‐host malaria dynamics with the between‐host mosquito‐human dynamics have been developed. In this paper, by adopting the nested approach, a malaria transmission model with immune response of the host is formulated. Applying age‐structured partial differential equations for the between‐host dynamics, we describe the asymptomatic and symptomatic infectious host population for malaria transmission. The basic reproduction numbers for the within‐host model and for the coupled system are derived, respectively. The existence and stability of the equilibria of the coupled model are analyzed. We show numerically that the within‐host model can exhibit complex dynamical behavior, possibly even chaos. In contrast, equilibria in the immuno‐epidemiological model are globally stable and their stabilities are determined by the reproduction number. Increasing the activation rate of the within‐host immune response “dampens” the sensitivity of the population level reproduction number and prevalence to the increase of the within‐host reproduction of the pathogen. From public health perspective this means that treatment in a population with higher immunity has less impact on the population‐level reproduction number and prevalence than in a population with less immunity.     

Genetic learning in strategic form games

We analyze the learning behavior of a Simple Genetic Algorithm in symmetric 3 × 3 Strategic-Form-Games. In cases of contests within one population and also between two populations the behavior of the SGA is compared with the behavior of the replicator dynamics and is analyzed with respect to equilibrium concepts in evolutionary game theory. Furthermore conservative non-adaptive strings are added to the population which lead to convergence to an equilibrium even in “GA-deceptive” games where the equilibrium can not be reached by GAs using only selection and crossover.     

Competitive carbon emission yields the possibility of global self-control

Despite many international climate meetings such as Copenhagen 2009, it is still unclear how annual global emissions can be reduced without requiring governments to micro-manage the emitting companies within their individual jurisdictions. Here we examine a simple, yet highly non-trivial, computer model of carbon emission which is consistent with recent activity in the European carbon markets. Our simulation results show that the ongoing daily competition to emit CO₂ within a population of emitters, can lead to a form of collective self-control over the aggregated emissions. We identify regimes in which such a population spontaneously hits its emissions target with minimal fluctuations. We then focus on the emission dynamics induced by a governing body which chooses to actively manage the capping level. Finally we lay some formal stepping stones toward a complete analytic theory for carbon emissions fluctuations within this model framework – in so doing, we also connect this problem to more familiar theoretical terrain within computer science.     

Final attack ratio in SIR epidemic models for multigroup populations

We analyse an SIR epidemic model in a closed population subdivided in n groups. Population mixing occurs at two levels: within each group, and uniformly in the population. We prove that, if within-group transmission rates are large enough and not all identical to each other, then the final attack ratio is lower than what would occur in a population mixing homogeneously with the average transmission rate. We also show that the opposite may hold for certain parameter values and explore numerically the parameter regions in which the final attack ratio is higher or lower than in the corresponding homogeneous model. Finally, we analyse simulations of the corresponding stochastic model with finite group size, studying how well final attack ratio is approximated by the deterministic outcome and its relations with exponential growth rate.     

System Dynamics modeling of Chlamydia infection for screening intervention planning and cost-benefit estimation

^** Corresponding author. Email: P.R.Harper{at}maths.soton.ac.uk Genital Chlamydia trachomatis infection is the most common sexuallytransmitted infection in the UK. It constitutes a major publichealth problem given that the majority of infections are asymptomaticwhich can lead to serious long-term medical consequences ifnot treated. This paper describes a System Dynamics model forcapturing Chlamydia infection dynamics within a population,incorporating the behaviour of different risk groups, and providesa cost-benefit study for screening using data collected fromthe Department of Health opportunistic Chlamydia screening programmein Portsmouth. Furthermore, we demonstrate that high-risk groupsare key in determining the overall infection dynamics of thesystem, and quantify screening rates required to manage infectionprevalence within the wider population.     

An Approach to Optimal Recruitment and Transition Strategies for Manpower Systems using Dynamic Programming

In this paper, concepts of dynamic programming are used within a discrete time Markovian model for the development of a graded population. Optimal recruitment and transition patterns are determined by minimizing expected discrepancies between actual states and preferred goals.     

U.S. national population projections methods: A view from four forecasting traditions

Four traditions — judgmental, time series, demographic accounting, and explanatory — represent different approaches to national population projections. The U.S. Census Bureau's methodology for national population projections is mainly within the demographic accounting tradition incorporating selected aspects of the other three traditions. Several avenues for combining the best methods from each of the four forecasting traditions in future projections activities are outlined.     

Using population of models to investigate and quantify gas production in a spatially heterogeneous coal seam gas field

In this work, we discuss the use of a local model developed previously [1] that describes the multiphase flow of gaseous species and liquid water within a single coal seam to investigate the gas production from a spatially heterogeneous production field. The field is located within the Surat Basin in Queensland, and is composed of a total of 80 production wells spread over a region covering approximately 36 km². However, not every well is producing gas at any one time and so in this work we take a subset of 42 wells that are the top-producing wells in terms of total gas volume.We utilise a population of models approach to understand the variability in the underlying physical processes, and as a mechanism for dealing with the spatial heterogeneity that arises due to geological variation across the field. We are able to simultaneously obtain a family of parameter sets for each of these wells, in which each set in the family yields a predicted cumulative total gas production curve that matches the measured cumulative production curve for a given well to within an allowable limit of error.By analysing the results of this population of models approach we can identify the similarities between wells based on the parameter distributions, and understand the sensitivity of key model parameters. We show by example that high correlation between wells based on their parameter values may be an indicator of their similarity. A combinatorial sum of the predicted gas production is compared against the individual gas volumes (given in terms of percentage of the total volume) measured at the compression facility as a way of further calibrating a subpopulation of models.     

An Age-structured Mathematical Model for the Within Host Dynamics of Malaria and the Immune System

In the paper, we use a mathematical model to study the population dyna mics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are then integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.      

Wave features of a hyperbolic prey–predator model

A hyperbolic predator–prey model is proposed within the context of extended thermodynamics. The nature of the steady state solutions for the uniform and non‐uniform perturbations are analyzed. The existence of smooth traveling wave‐like solutions, related to the invasion of the predator population into a prey‐only state is discussed. Validation of the model in point is also accomplished by searching for numerical solutions of the system, which also points out limit cycles in the populations. Copyright © 2010 John Wiley & Sons, Ltd.     

具有HollingⅡ型功能反应和Allee效应的捕食系统模型

利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性.通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态,探索研究参数的变化对种群大小的影响,阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性.研究结果表明:1)当处理时间处于有效区间内时,处理时间越大种群的稳定共存参数域越大;2)Allee效应的引入使种群的动态行为更为复杂,从而增加了捕食者种群的灭绝风险;3)系统受强Allee效应的影响,种群会出现提前分叉现象,如果继续增加Allee效应就会导致种群灭绝;4)强Allee效应更容易使种群趋向灭绝.所得结论在丰富生态学理论的同时,提出了保护生态学的重要依据.     

Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions

This work is motivated by a study of a population of multiple sclerosis (MS) patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to identify active brain lesions. At each visit, a contrast agent is administered intravenously to a subject and a series of images are acquired to reveal the location and activity of MS lesions within the brain. Our goal is to identify the enhancing lesion locations at the subject level and lesion enhancement patterns at the population level. We analyze a total of 20 subjects scanned at 63 visits (～30Gb), the largest population of such clinical brain images. After addressing the computational challenges, we propose possible solutions to the difficult problem of transforming a qualitative scientific null hypothesis, such as “this voxel does not enhance,” to a well-defined and numerically testable null hypothesis based on the existing data. We call such procedure “soft null” hypothesis testing as opposed to the standard “hard null” hypothesis testing. This problem is fundamentally different from: (1) finding testing statistics when a quantitative null hypothesis is given; (2) clustering using a mixture distribution; or (3) setting a reasonable threshold with a parametric null assumption. Supplementary materials are available online.     

Apportionment methods and the Liu–Layland problem

The Liu–Layland periodic scheduling problem can be solved by the house monotone quota methods of apportionment. This paper shows that staying within the quota is necessary for any apportionment divisor method to solve this problem. As a consequence no divisor method, or equivalently no population monotone method, solves the Liu–Layland problem.     

A theory of liberal churches

There is a counterintuitive gap in the club theory of religion. While it elegantly accounts for the success of strict sectarian religious groups in recruiting members and maintaining commitment, it is less satisfactory when attempting to account for groups requiring neither extreme nor zero sacrifice. Moderate groups are always a suboptimal choice for rational, utility maximizing agents within the original representative agent model. The corner solutions of zero and absolute sacrifice, however, are rarely observed empirically compared to the moderate intermediate. In this paper, we extend the original model to operate within an agent-based computational context, with a distribution of heterogeneous agents occupying coordinates in a two dimensional lattice, making repeated decisions over time. Our model offers the possibility of successful moderate groups, including outcomes wherein the population is dominated by moderate groups. The viability of moderate groups is dependent on extending the model to accommodate agent heterogeneity, not just within the population of agents drawn from, but heterogeneity within groups. Moderate sacrifice rates mitigate member free riding and serve as a weak screening device that permits a range of agent types into the group. Within-group heterogeneity allows agents to benefit from the differing comparative advantages of their fellow members.     

Global properties of a two-scale network stochastic delayed human epidemic dynamic model

Complex population structure and the large-scale inter-patch connection human transportation underlie the recent rapid spread of infectious diseases of humans. Furthermore, the fluctuations in the endemicity of the diseases within patch dwelling populations are closely related with the hereditary features of the infectious agent. We present an SIR delayed stochastic dynamic epidemic process in a two-scale dynamic structured population. The disease confers temporary natural or infection-acquired immunity to recovered individuals. The time delay accounts for the time-lag during which naturally immune individuals become susceptible. We investigate the stochastic asymptotic stability of the disease free equilibrium of the scale structured mobile population, under environmental fluctuations and the impact on the emergence, propagation and resurgence of the disease. The presented results are demonstrated by numerical simulation results.     

Low dimensional homeochaos in coevolving host–parasitoid dimorphic populations: Extinction thresholds under local noise

A discrete time model describing the population dynamics of coevolution between host and parasitoid haploid populations with a dimorphic matching allele coupling is investigated under both determinism and stochastic population disturbances. The role of the properties of the attractors governing the survival of both populations is analyzed considering equal mutation rates and focusing on host and parasitoid growth rates involving chaos. The purely deterministic model reveals a wide range of ordered and chaotic Red Queen dynamics causing cyclic and aperiodic fluctuations of haplotypes within each species. A Ruelle–Takens–Newhouse route to chaos is identified by increasing both host and parasitoid growth rates. From the bifurcation diagram structure and from numerical stability analysis, two different types of chaotic sets are roughly differentiated according to their size in phase space and to their largest Lyapunov exponent: the Confined and Expanded attractors. Under the presence of local population noise, these two types of attractors have a crucial role in the survival of both coevolving populations. The chaotic confined attractors, which have a low largest positive Lyapunov exponent, are shown to involve a very low extinction probability under the influence of local population noise. On the contrary, the expanded chaotic sets (with a higher largest positive Lyapunov exponent) involve higher host and parasitoid extinction probabilities under the presence of noise. The asynchronies between haplotypes in the chaotic regime combined with low dimensional homeochaos tied to the confined attractors is suggested to reinforce the long-term persistence of these coevolving populations under the influence of stochastic disturbances. These ideas are also discussed in the framework of spatially-distributed host–parasitoid populations.     

On the correlation of a group of rankings with an external ordering relative to the internal concordance

A method is presented for comparing the strength of agreement of a group rankings with an external ordering to the corresponding measure of concordance within the group. While the procedure is not model dependent, we illustrate the characteristics of interest using an existing model for a nonnull distribution for a population of rankings. U-statistics and a jackknife with adjusted degrees of freedom are employed to set approximate confidence intervals on the contrast between the two measures of rank order agreement.     

Maintenance of diversity in a hierarchical host–parasite model with balancing selection and reinfection

Inspired by DNA data of the human cytomegalovirus we propose a model of a two-type parasite population distributed over its hosts. The parasite is capable to persist in its host till the host dies, and to reinfect other hosts. To maintain type diversity within a host, balancing selection is assumed.For a suitable parameter regime we show that in the limit of large host and parasite populations the host state frequencies follow a dynamical system with a globally stable equilibrium, guaranteeing that both types are maintained in the parasite population for a long time on the host time scale.