Modeling dynamics of an influenza pandemic with heterogeneous coping behaviors: case study of a 2009 H1N1 outbreak in Arizona

This paper aims to improve the accuracy of standard compartment models in modeling the dynamics of an influenza pandemic. Standard compartment models, which are commonly used in influenza simulations, make unrealistic assumptions about human behavioral responses during a pandemic outbreak. Existing simulation models with public avoidance also make a rigid assumption regarding the human behavioral response to influenza. This paper incorporates realistic assumptions regarding individuals’ avoidance behaviors in a standard compartment model. Both the standard and modified models are parameterized, implemented, and compared in the research context of the 2009 H1N1 influenza outbreak in Arizona. The modified model with heterogeneous coping behaviors forecasts influenza spread dynamics better than the standard model when evaluated against the empirical data, especially for the beginning of the 2009–2010 normal influenza season starting in October 2009 (i.e., the beginning of the second wave of 2009 H1N1). We end the paper with a discussion of the use of simulation models in efforts to help communities effectively prepare for and respond to influenza pandemics.     

A simulation case study to improve staffing decisions at mass immunization clinics for pandemic influenza

Mass immunization clinics (MICs) are an important component of pandemic influenza control strategies in many jurisdictions. Decisions about staffing levels at MICs affect several factors of concern to public health authorities: total vaccination volume, patient wait-times, operating costs, and intra-facility influenza transmission risk. We present a discrete-event simulation of an MIC to assess how strongly staffing changes affect these factors. The simulation is based on data from Canadian clinics responding to pandemic H1N1 in 2009. This study is the first to model flu transmission risk at an MIC, and the first to relate such risk to staffing decisions. We show that the marginal benefit of adding staff is greatly underestimated if indirect waiting costs and intra-facility infections are not considered.     

Simulation of alternative approaches to relieving congestion at locks in a river transportion system

We construct a discrete-event simulation model to investigate the impact of alternative decision rules and infrastructural improvements to relieve traffic congestion in a section of the Upper Mississippi River navigation system. The model covers a series of five locks that serve commercial tows with widely different barge configurations, as well as private recreational vessels. Mixes and intensities of vessel activity are highly dependent on the time of year, day of week and time of day. The model reveals that some improvement in performance (especially in peak periods) can be achieved by scheduling lock activity with priority given to vessels with shortest average processing and lock set-up times (tempered by the time that vessels have spent in queue). Greater improvement occurs with the use of helper boats and greatest improvement occurs with enlarged locks. The alternative remedies must be evaluated with consideration of their dramatically different capital costs.     

Reflective Pathways: Analysis of an Urban Science Teaching Field Experience on Noyce Scholar‐Science Education Awardees' Decisions to Teach Science in a High‐Need New York City School

Awardees of the National Science Foundation's Noyce Scholars funds are required to teach science in high‐need urban or rural school districts upon graduation. The purpose of this research was to analyze the reflective considerations that distinguish preservice Noyce Scholar science education majors committed to teaching in high‐need New York City (NYC) schools from those committed to high‐need rural careers. Essays designed to expose their (n = 22) considerations of teaching in NYC written before, immediately after, and two weeks following a one‐week cultural and science teaching internship experience were coded to reveal distinguishing reflective thought patterns. The results showed that those (16/22) whose final essay showed commitment to NYC teaching viewed themselves positively as NYC teachers and that increases in positive self‐perceptions were paralleled by increases in affinity toward living in NYC and NYC schools. Those not inclined to NYC teaching (6/22) expressed increasingly negative views of themselves as NYC teachers, NYC life, and urban education generally. The research provides insights into what Noyce Scholar undergraduates in science education think about when considering a teaching career in urban school districts.     

Teaching mathematics for Korean language learners based on ELL education models

The classroom culture of Korean schools has recently been changing as the population of linguistically and culturally diverse students increases. Students with multicultural backgrounds as well as Korea-born students returning from long residences in foreign countries have difficulties adjusting to Korean public schools due to a lack of Korean language proficiency and knowledge of Korean school culture. This study defines these students as Korean language learners (KLLs) and investigates both teacher and student perspectives on effective mathematics education for them. Cummins’ Quadrant model and the sheltered instruction observation protocol model, which were developed and used for English language learners (ELLs), are the frameworks used. The study explores various pedagogies for language learners and discusses the effectiveness and feasibility of ELL education models in a Korean school context based on the survey results of Korean elementary teachers and interviews of KLLs.     

基于生存分析的城市道路交通拥堵持续时间研究

根据北京市二环快速路的交通流数据,研究了城市道路交通拥堵持续时间的分布特性．采用生存分析方法,建立基于风险的交通拥堵持续时间模型,运用非参数方法对交通拥堵的持续时间进行估计,并对其时空分布规律进行了研究．结果表明二环各路段的拥堵持续时间70%在4min以内,89%在12min之内;当拥堵持续时间超过12min之后拥堵结束的可能性小于10%．工作日比双休日更容易发生拥堵;早高峰比晚高峰更容易发生拥堵,且当拥堵发生的前提下早高峰的拥堵持续时间更长;内环比外环更容易发生拥堵,但外环的拥堵持续时间更长;二环的4个方向上,西二环最容易发生拥堵,北二环的拥堵持续时间最长．     

Modeling passively Q-switched solid state lasers with multimode

Q-switching is considered as a favorable technology to generate short duration and high peak power pulses, which is widely used in industry. We derive a new model to simulate passively Q-switched solid state lasers in a three-dimensional (3D) space. In our model, several Gaussian modes are considered. Compared with single-mode models, 3D multimode models are much more capable of reflecting laser behaviors. In our modeling, the single-mode system is extended to a multimode system, which calculates photon numbers for different modes separately. In order to realize the numerical simulation of our multimode model, we apply a finite volume discretization respectively to the gain medium and saturable absorber, then the discretized multimode passively Q-switched laser system is obtained. The numerical results and applications of our model are shown at the end of the paper. The modeling and simulation of passively Q-switched solid state lasers can help to optimize laser designs.     

Assessing European primary school performance through a conditional nonparametric model

This paper uses a fully nonparametric framework to assess the efficiency of primary schools using data about schools in 16 European countries participating in PIRLS 2011. This study represents an original enterprise since most of the empirical research in the field is restricted to evaluations at regional or national level and focused on secondary education. For our purpose, we adapt the metafrontier framework to compare and decompose the technical efficiency of primary schools operating in heterogeneous contexts, which in our case is represented by different educational systems or countries. Similarly, we use an extension of the conditional nonparametric robust approach to test the potential influence of a mixed set of environmental school factors and variables representing cultural values of each country. Our results indicate that the intergenerational transmission of non-cognitive skills such as responsibility or perseverance are significantly related to school efficiency, whereas most school factors do not seem to have a significant influence on school performance.     

Residential location and school planning in a tightening urban economy

Facing worse fiscal plight, many municipalities in Sweden must today carefully reexamine their activities. In urban planning, this has resulted in a growing interest in how the urban development could be designed to support and facilitate the efficient use of existing public investments. This paper focuses on the school sector as being one of the most costly. A location-allocation model of the capacitated facility location type is formulated. A set of potential schools consisting of existing and new ones are considered. The school-age children are assigned to a subset of these schools so as to minimize the sum of the capital costs of this subset and the transportation costs of the children. The model is applied to the municipality of Uppsala in Sweden. Different future settlement structures proposed by the planners as well as different housing allocations generated by a separate optimization model are evaluated.     

A shift scheduling model for employees with different seniority levels and an application in healthcare

This paper addresses the problem of scheduling medical residents that arises in different clinical settings of a hospital. The residents are grouped according to different seniority levels that are specified by the number of years spent in residency training. It is required from the residents to participate in the delivery of patient care services directly by working weekday and weekend day shifts in addition to their regular daytime work. A monthly shift schedule is prepared to determine the shift duties of each resident considering shift coverage requirements, seniority-based workload rules, and resident work preferences. Due to the large number of constraints often conflicting, a multi-objective programming model has been proposed to automate the schedule generation process. The model is implemented on a real case in the pulmonary unit of a local hospital for a 6-month period using sequential and weighted methods. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules expending considerable effort and time. It is also shown that the employed weighting procedure based on seniority levels performs much better compared to the preemptive method in terms of computational burden.     

A method for reduction of human ventricular action potential model

ABSTRACT

Mathematical modelling and computer simulations are important tools in the field of cardiac electrophysiology. High computational costs of complex models make them difficult to apply in large-scale simulations like tissue. Therefore, model reduction are of particular importance in heart studies. In this paper, we introduce a technique for simplification of ventricular cell(VC) complex models. By using this technique, starting with a complex model of human VC including 17state variables, we reduce the number of state variables to two. Our simplified model is compared with the original one via several electrophysiological features and computational efficiency. Results show that the reduced model has acceptable behaviours in single cell and one-dimensional simulation, moreover, is 55 times faster than the original one. As the presented method does not depend on the reference model, it may be applied to every cardiac cell models or each complex excitable dynamical systems with the same dynamics as VC.     

A deterministic linear optimization model for allocating schools to zones

This paper presents a deterministic linear optimization model to support decisions on optimal allocation of schools to zones, its characterization and assignment of students, maximizing the social benefits of school owners and students. Students are assumed to show a multi-attribute behaviour, considering as important not only location, as is usual in the literature, but also quality of education and infrastructure, school costs and other attributes. There is heterogeneity of supply and demand. Students are classified by place of residence and socio-economic characteristics. Schools can be private, subsidized or free municipal ones. The model developed is applied to data of one of the municipalities of Santiago. The results obtained under different scenarios tend to confirm the expected demand's behaviour. This model could be used to guide decisions of both school owners or municipalities as well as students towards an equilibrium closer to a social optimum.     

Mathematical modelling of acute virus influenza A infections

This article models the immune system and the virus dynamics of acute influenza infection mathematically. We use the model to study the virus dynamics of some well-known and severe and mild types of viruses. Linkages to well-known models in the literature are illustrated. Simulations are compared with experimental results in vivo by comparing with results from infected ferrets where infection closely resembles those in humans. Good agreement is achieved between the model calculations and the experimental values for influenza A viruses. For the Spanish flu virus H1N1 peak virus load is high and virtually all cells are infected in the nostril. In general, the H1N1 viruses show much more prolonged infections than the H3N2 in the nostril. We suggest that the reason is that unspecific immunity attacks H3N2-budded viruses but not H1N1 viruses.     

Separate vs. joint replenishment policies with maximum storage requirement costs

Multi-item inventory problems give rise to the possibility of time-phasing the replenishments of different items over the inventory cycle. Such a policy reduces the peak storage requirement, compared to a policy of simultaneous replenishment. This, in turn, increases the amount of warehouse space which is permanently available for leasing throughout the cycle. However, where cost savings may be achieved through combining setups of different items, as in the well known joint replenishment problem, such a time-phasing policy may increase total setup costs. This paper considers the two item joint replenishment problem, where a cost (equivalent to the opportunity cost of warehouse space) attaches to the peak storage requirement which occurs within the inventory cycle. Existing joint replenishment models do not consider such costs, but their consideration suggests that joint replenishment is not always optimal. We analyze possible policies under both joint and separate replenishment, and provide optimal closed form solutions. A numerical example to illustrate the tradeoff between joint and separate replenishment is provided.     

Demand seasonality in retail inventory management

We investigate the value of accounting for demand seasonality in inventory control. Our problem is motivated by discussions with retailers who admitted to not taking perceived seasonality patterns into account in their replenishment systems. We consider a single-location, single-item periodic review lost sales inventory problem with seasonal demand in a retail environment. Customer demand has seasonality with a known season length, the lead time is shorter than the review period and orders are placed as multiples of a fixed batch size. The cost structure comprises of a fixed cost per order, a cost per batch, and a unit variable cost to model retail handling costs. We consider four different settings which differ in the degree of demand seasonality that is incorporated in the model: with or without within-review period variations and with or without across-review periods variations. In each case, we calculate the policy which minimizes the long-run average cost and compute the optimality gaps of the policies which ignore part or all demand seasonality. We find that not accounting for demand seasonality can lead to substantial optimality gaps, yet incorporating only some form of demand seasonality does not always lead to cost savings. We apply the problem to a real life setting, using Point-of-Sales data from a European retailer. We show that a simple distinction between weekday and weekend sales can lead to major cost reductions without greatly increasing the complexity of the retailer’s automatic store ordering system. Our analysis provides valuable insights on the tradeoff between the complexity of the automatic store ordering system and the benefits of incorporating demand seasonality.     

Solving a school bus scheduling problem with integer programming

In many rural areas in Germany pupils on the way to school are a large if not the largest group of customers in public transport. If all schools start more or less at the same time then the bus companies need a high number of vehicles to serve the customer peak in the morning rush hours. In this article, we present an integer programming model for the integrated coordination of the school starting times and the public bus services. We discuss preprocessing techniques, model reformulations, and cutting planes that can be incorporated into a branch-and-cut algorithm. Computational results show that in our test counties a much lower number of buses would be sufficient if the schools start at different times.     

Efficient Data Augmentation for Fitting Stochastic Epidemic Models to Prevalence Data

Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time evolution of an epidemic gives rise to a complicated latent variable problem in which the state space size of the epidemic grows large as the population size increases. This makes analytically integrating over the missing data infeasible for populations of even moderate size. We present a data augmentation Markov chain Monte Carlo (MCMC) framework for Bayesian estimation of stochastic epidemic model parameters, in which measurements are augmented with subject-level disease histories. In our MCMC algorithm, we propose each new subject-level path, conditional on the data, using a time-inhomogenous continuous-time Markov process with rates determined by the infection histories of other individuals. The method is general, and may be applied to a broad class of epidemic models with only minimal modifications to the model dynamics and/or emission distribution. We present our algorithm in the context of multiple stochastic epidemic models in which the data are binomially sampled prevalence counts, and apply our method to data from an outbreak of influenza in a British boarding school. Supplementary material for this article is available online.     

Teachers creating mathematical models to fairly distribute school funding

Our study aims to investigate what teachers do as they draw on their mathematical understanding and personal experiences to engage in social justice-oriented mathematical modeling. We analyze what ideas were expressed by teachers regarding their mathematical identities while they explore, wrestle with, and reconcile the underlying societal values that support mathematical models. We invited groups of teachers to make mathematical models for distributing school funding given real data from diverse, anonymized schools. Our results show that teachers created and refined diverse mathematical models to connect the mathematical world and societal space and these models reflected different societal values. Drawing on their own experiences, teachers expressed a sense of agency and critical consciousness while making decisions about school funding. This study delineates mathematical contents and processes necessary for advancing a societal goal of fairly distributing funds and we explore how teachers connect to this context as learners and members of society.     

Weekday dependence of German stock market returns

The so‐called ‘Monday effect’ has been found for various stock markets of the world. The empirical finding that Monday returns are significantly smaller than returns measured for the remaining days of the week calls the efficiency hypothesis for pricing processes operating on stock markets into question. Investigating an index series measured at the Frankfurt stock exchange the paper compares estimation results of parametric and non‐parametric autoregressive models with respect to possible weekday dependence of return data. Allowing for heteroskedastic error distributions the wild bootstrap is used to infer against time‐varying means and correlation of return data in parametric models and to obtain confidence bands for non‐parametric estimates. It is shown that time dependence is an important feature describing the dynamics of German stock market returns in the period 1960–1979. Within two subsamples obtained from the period 1980–1997 the evidence in favour of such effects is mitigated substantially. Copyright © 2000 John Wiley & Sons, Ltd.     

Production Planning in the New Zealand Dairy Industry

From 1977 onwards, D.S.I.R. has been developing an L.P. model to help the largest N.Z. dairy company plan its medium-term production. This time-staged model finds the most profitable daily production schedule of the various powder, casein, cheese and butter products. Computer reports and graphics show Company management how to allocate the milk available in the various farming regions to the Company's factories, and where to send the by-products for further processing.The L.P. models seasonal fluctuations in wholemilk availability and quality, as well as transport costs, factory capacities and costs, and product-yields and prices. Comparison runs have shown that the L.P. increases the profitability of the manual plan by over $5000 per day (because the computer can handle changing yields, factory costs and by-product processing). The model gives management the ability to adjust production plans quickly in response to improved information, new market opportunities and emergencies like plant breakdown.