紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。     

Modeling the influence of social networks and environment on energy balance and obesity

The influence of social networks on the development of obesity has been demonstrated, and several models have been proposed. However, these models are limited since they consider obesity as a ‘contagious’ phenomenon that can be caught if most social contacts are deemed obese. Furthermore, social networks were proposed as a means to mitigate the obesity epidemic, but the interaction of social networks with environmental factors could not yet be explored as it was not accounted for in the current models. We propose a new model of obesity to face these limitations. In our model, individuals influence each other with respect to food intake and physical activity, which may lead to changes depending on the environment, and will impact energy balance and weight. We illustrate the potential of our model via two questions: could we focus on social networks and neglect environmental sources of influence, at least from a modelling viewpoint? Are some social structures less prone to be influenced by their environment? We performed a factorial analysis based on both synthetic and real-world social networks, and found that the environment was a key component behind changes in weight but its contribution was mitigated by structural properties of the population. Furthermore, the contribution of the environment was not dictated by macro-level properties (small-world and scale-free), which suggests that particular patterns of social ties at the micro-level are involved in making populations more resilient to change and less influenced by the environment.     

A dynamical systems model of intrauterine fetal growth

ABSTRACT

The underlying mechanisms for how maternal perinatal obesity and intrauterine environment influence foetal development are not well understood and thus require further understanding. In this paper, energy balance concepts are used to develop a comprehensive dynamical systems model for foetal growth that illustrates how maternal factors (energy intake and physical activity) influence foetal weight and related components (fat mass, fat-free mass, and placental volume) over time. The model is estimated from intensive measurements of foetal weight and placental volume obtained as part of Healthy Mom Zone (HMZ), a novel intervention for managing gestational weight gain in obese/overweight women. The overall result of the modelling procedure is a parsimonious system of equations that reliably predicts foetal weight gain and birth weight based on a sensible number of assessments. This model can inform clinical care recommendations as well as how adaptive interventions, such as HMZ, can influence foetal growth and birth outcomes.     

Airport noise modelling and aircraft scheduling so as to minimize community annoyance

A mathematical model of the annoyance created at an airport by aircraft operations is developed. The model incorporates population distribution considerations around an airport and the annoyance caused by aircraft noise. The objective function of this model corresponds to seeking to minimize total population annoyance created by all aircraft operations in a 24-hour period. Several factors are included in this model as constraint relationships. Aircraft operations by type and time period are upper bounded. Demand for flight services is incorporated by including lower bounds on the number of operations by type of aircraft, runway used and time period. Also upper bounds on the number of operations for each runway are included. The mathematical model as formulated is recognized as corresponding to a nonlinear integer mathematical programming problem.The solution technique selected makes use of a successive linear approximation optimization algorithm. An especially attractive feature of this solution algorithm is that it is capable of obtaining solutions to large problems. For example, it would be feasible to attempt the solution of problems involving several thousand variables and over 500 linear constraints. This suggested solution algorithm was implemented on a computer and computational results obtained for example problems.     

Complicated endemics of an SIRS model with a generalized incidence under preventive vaccination and treatment controls

In this paper, we propose and study an SIRS epidemic model that incorporates: a generalized incidence rate function describing mechanisms of the disease transmission; a preventive vaccination in the susceptible individuals; and different treatment control strategies depending on the infective population. We provide rigorous mathematical results combined with numerical simulations of the proposed model including: treatment control strategies can determine whether there is an endemic outbreak or not and the number of endemic equilibrium during endemic outbreaks, in addition to the effects of the basic reproduction number; the large value of the preventive vaccination rate can reduce or control the spread of disease; and the large value of the psychological or inhibitory effects in the incidence rate function can decrease the infective population. Some of our interesting findings are that the treatment strategies incorporated in our SIRS model are responsible for backward or forward bifurcations and multiple endemic equilibria; and the infective population decreases with respect to the maximal capacity of treatment. Our results may provide us useful biological insights on population managements for disease that can be modeled through SIRS compartments.     

Modeling the depletion of dissolved oxygen due to algal bloom in a lake by taking Holling type-III interaction

In this paper a non-linear mathematical model for depletion of dissolved oxygen due to algal bloom in a lake is proposed and analyzed. The model is formulated by considering four variables namely, cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen. In the modeling process it is assumed that nutrients are continuously coming with a constant rate to the lake through water runoff from agricultural fields and domestic drainage. The Holling type-III interaction between nutrients and algal population is considered. Equilibrium values have been obtained and their stability analysis has also been performed. Numerical simulations are carried out to explain the mathematical results.     

Probabilistic stability analysis of social obesity epidemic by a delayed stochastic model

Sufficient conditions for stability in probability of the equilibrium point of a social obesity epidemic model with distributed delay and stochastic perturbations are obtained. The obesity epidemic model is demonstrated on the example of the Region of Valencia, Spain. The considered nonlinear system is linearized in the neighborhood of the positive point of equilibrium and a sufficient condition for asymptotic mean square stability of the zero solution of the constructed linear system is obtained.     

Modelling and simulation of heat exchange and moisture content in a cereal storage silo

ABSTRACT

In this paper, a mathematical model is developed based on the heat transfer of stored grains aerated in a cylindrical silo. This work is a part of study that aims to model the whole process of cereal storage system including a dehumidifier. The use of dehumidifier is intended to remove excess moisture from the airflow injected by the ventilator system in the silo filled with wheat, and to keep hygroscopic properties of grain in safe level during the storage period. Temperature and humidity are the two important variables coupled to control the process and to preserve grain quality. The laboratory device permitted us to achieve several tests for different conditions of grain stored in silo without aeration. A simulation of the airflow through the thermal space of the silo and grain parameters has been carried out. The results are reasonably in agreement with experiments and other published data. The system performance is evaluated at critical conditions of storage boundaries.     

Modelling and stability analysis in human population genetics with selection and mutation

Population genetics is a scientific discipline that has extensively benefitted from mathematical modelling; since the Hardy‐Weinberg law (1908) to date, many mathematical models have been designed to describe the genotype frequencies evolution in a population. Existing models differ in adopted hypothesis on evolutionary forces (such as, for example, mutation, selection, and migration) acting in the population. Mathematical analysis of population genetics models help to understand if the genetic population admits an equilibrium, ie, genotype frequencies that will not change over time. Nevertheless, the existence of an equilibrium is only an aspect of a more complex issue concerning the conditions that would allow or prevent populations to reach the equilibrium. This latter matter, much more complex, has been only partially investigated in population genetics studies. We here propose a new mathematical model to analyse the genotype frequencies distribution in a population over time and under two major evolutionary forces, namely, mutation and selection; the model allows for both infinite and finite populations. In this paper, we present our model and we analyse its convergence properties to the equilibrium genotype frequency; we also derive conditions allowing convergence. Moreover, we show that our model is a generalisation of the Hardy‐Weinberg law and of subsequent models that allow for selection or mutation. Some examples of applications are reported at the end of the paper, and the code that simulates our model is available online at https://www.ding.unisannio.it/persone/docenti/del-vecchio for free use and testing.     

Mathematical modeling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines based on a thermodynamic multi zone model

The main purpose of the current study is mathematical modelling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines. A validated multi-zone model coupled to a semi-detailed chemical kinetics is used to predict homogeneous charge compression ignition combustion and emissions. Heat and Mass transfer submodels are linked to the multi-zone model. Bulk flow and diffusion mass transfer between zones are considered. The results indicate that the diffusion mass transfer is negligible in homogeneous charge compression ignition engines. Bulk flow mass transfer plays a critical role in homogeneous charge compression ignition simulation and applying it in the multi-zone model leads to accurate prediction of the start of combustion, peak pressure and exhaust emissions. The results show that the maximum error changes from 90% to 5% in carbon monoxide prediction and from 98% to 14% in unburned hydrocarbons prediction, using the mass transfer submodel.     

Transmission dynamics and the control of hepatitis B in China: a population dynamics view

Though the prevalence of hepatitis B began to decline for the first time in 2010, it remains unclear whether this downward trend is permanent and the disease will be eradicated in mainland China under the current measures. Because a large number of hepatitis B virus (HBV) carriers and unknown HBV infections is characteristic of HBV infections in China, a mathematical model was designed and fitted to the reported hepatitis B data. The estimated basic reproduction number is 1.2861 (95\% confidence interval (CI) 1.2386-1.3302), which remains greater than one. Thus, the decline in 2010 may be part of the temporary benefits of public policy measures and should not be interpreted as indicative of successful intervention, although interventions do provide some benefits. To assess the effects of various interventions, the global uncertainty and sensitivity analyses revealed that the contribution of carriers is always greater than that of acute infections, and the prevalence of hepatitis B in China may be primarily a result of transmission by unknown patients. Therefore, strategies for controlling the HBV endemic, which target known patients, are unlikely to be highly effective. Additionally, three feasible strategies are proposed, although the benefits of these strategies may change radically over time.     

A two-stage approach to multi-period allocation of savings among investment plans

This paper presents a two-stage multi-period decision model for allocation of the individual's savings into several investment plans. Although the U.S. economy is used as the background, the modelling methods are general enough to accommodate any tax law. The first stage of the model uses an asset-allocation method based on the single-index model. Because this method is static and does not provide for tax considerations and other constraints, it alone is not enough. The output of this optimal selection is used as exogenous parameters and controls for the second stage of the model which is an integer program. The IP includes fixed charges, statutory and budgetary constraints, a discount rate, and the risk level. We provide an example of this approach to illustrate how an individual can achieve his goals of terminal accumulations while maintaining the risk level, measured by the aggregate beta, he prefers. A linear programming relaxation of the IP model is utilized for sensitivity analysis to examine whether future adjustments in investment strategies are required. The model remains tractable enough for implementation by individuals who may not be experts in mathematical programming and financial planning.     

Studying the sensitivity of pollutants’ concentrations caused by variations of chemical rates

A systematic procedure for sensitivity analysis of a case study in the area of air pollution modeling has been performed. Contemporary mathematical models should include a large set of chemical and photochemical reactions to be established as a reliable simulation tool. The Unified Danish Eulerian Model is in the focus of our investigation as one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes.Variance-based methods are one of the most often used approaches for providing sensitivity analysis. To measure the extent of influence of the variation of the chemical rate constants in the mathematical model over pollutants’ concentrations the Sobol’ global sensitivity indices are estimated using efficient techniques for small sensitivity indices to avoid a loss of accuracy. Studying relationships between input parameters and the model’s output as well as internal mechanisms is very useful for a verification and an improvement of the model and also for development of monitoring and control strategies of harmful emissions, for a reliable prediction of the final output of scenarios when the concentration levels of pollutants are exceeded. The proposed procedure can also be applied when other large-scale mathematical models are used.     

Population needs assessment and access modelling for cardiac services

The National Service Framework (NSF) for Coronary Heart Disease (CHD), recently published by the Department of Health, specifies Government target rates for different cardiac procedures. This paper describes how the Eastern Regional Office of the Department of Health, with current rates approximately half the NSF target levels, designed a strategy to plan rationally for increases in service provision. A bottom-up needs assessment model was used to predict the population requirements for these CHD procedures and accounts for the effects of demographic change, anticipated reduction in the incidence of heart disease due to primary prevention programmes and the expected improvement in cardiology and cardiac surgery technologies. It is predicted that excess procedures would be required across the region over the next 20 years, and so a geographical access model was developed and used to recommend the building and location of a new tertiary cardiac centre to meet the increased demand. These tools have successfully been used in the Eastern Region to plan long-term increases in CHD rates in order to achieve Department of Health targets.     

PREDICTING GULL/HUMAN CONFLICTS WITH MATHEMATICAL MODELS: A TOOL FOR MANAGEMENT

Abstract Gulls are highly adaptable animals that thrive in proximity to humans. Although gulls enjoy legal protection in North America, England, and Europe, they often conflict with human interests by spreading disease, transporting contaminants, fouling public areas with droppings, and colliding with aircraft. Of particular concern are aggregates of “loafing” gulls that gather on parking lots, rooftops, and airport runways. Loafing in birds is a general state of immobility that involves behaviors such as sleeping, sitting, standing, resting, preening, and defecating. The ability to predict the incidence of aggregated loafing provides a first step toward the amelioration of bird/human conflicts. We used mathematical models to predict the aggregate loafing behavior of gulls as a function of environmental conditions and tested model portability across years, phase of breeding cycle, loafing location, and species. Because groups of loafing birds quickly reassemble after disturbance, algebraic models for the steady‐state dynamics can be obtained from the differential equations using time‐scale analysis. The accessible management tool requires data collection on an appropriate time scale and information‐theoretic model selection from a suite of alternative algebraic models.     

‘New mathematics’ and teaching

Inside the scientific world it is not always understood that the mood of mathematics, which is a product and a part of culture, can change with time. This is partly why many have been surprised by the coming of the so‐called new mathematics.

In the truly creative mathematical mind two opposite tendencies coexist: the logical and the imaginative. Apparently it seems that new mathematics can be reduced to a purely logical machinery. In fact it contains as much imaginative contributions as classical mathematics. But it is difficult to show simultaneously the logical sequence of propositions and the clumsy progression of research itself. Mathematical exposition does not always follow the ‘ most natural slopes’ of the mind. Unfamiliar presentations often give an impression of ‘ abstraction ‘, more familiar ones an impression of concreteness ‘.

So it appears that difficulties with new mathematics are mostly of psychological origin. Misuses of it can easily raise up intolerance reactions and emotional blocks. Perhaps insisting upon the fact that, here as elsewhere, it is important to be able to guess, to realize that intuition and imagination are essential, could help to make new mathematics better understood, more useful and more able to be considered as a unifing element among sciences.     

一类非线性动力系统的数值分析及控制策略研究

根据艾滋病在新疆的流行特点,建立了一个非线性动力系统的数学模型来研究艾滋病在新疆高危人群中传播的规律.通过查阅大量的统计数据和文献资料,确定了模型中部分参数的具体数值,然后通过数据拟合的方法得到了各个高危人群中的HIV病毒的传染性系数.在模型中,选择2004年底(2005年初)作为系统的初始点,预测了艾滋病未来几年内在新疆的流行趋势.最后,提出并比较遏止艾滋病传播的各项干预措施.     

A METHOD FOR PREDICTING HARBOR SEAL (PHOCA VITULINA) HAULOUT AND MONITORING LONG‐TERM POPULATION TRENDS WITHOUT TELEMETRY

Monitoring population trends in harbor seals (Phoca vitulina) generally involves two steps: (i) a census obtained from aerial surveys of haul‐out sites, and (ii) an upward correction based on the proportion of seals hauled out as estimated from a sample of telemetry‐tagged seals. Here we present a mathematical method for obtaining site‐specific correction factors without telemetry. The method also determines site‐specific environmental factors associated with haulout and provides algebraic equations that predict diurnal haul‐out numbers and correction factors as functions of these variables. We applied the method at a haul‐out site on Protection Island, Washington, USA. The haul‐out model and correction factor model were functions of tide height, current velocity, and time of day, and the haul‐out model explained 46% of the observed variability in diurnal haul‐out dynamics. Although the particular models are site‐specific, the general model and methods are portable. A suite of such models for haul‐out sites of a regional stock would allow managers to monitor long‐term population trends without telemetry.     

一个胎儿体重预测的数学模型

利用B型超声对520例胎儿的股骨长度、腹围的测量数据,建立多元非线性回归模型,并用此模型对982例胎儿进行实例验证、分析,得到精确度极高的预测结果,为临床应用提供了新的胎儿体重预测方法.     

教学管理中的数学模型

针对教学管理的需要 ,在总体服从正态分布的假设下 ,通过控制总体的某项指标 (均值 y或及格率 r) ,分别给出了相应的加分数学模型 .该模型具有合理性、普适性、保序性以及实用性 .通过对模型的检验表明 ,效果相当令人满意 .