Nonstandard finite difference method revisited and application to the Ebola virus disease transmission dynamics

We provide effective and practical guidelines on the choice of the complex denominator function of the discrete derivative as well as on the choice of the nonlocal approximation of nonlinear terms in the construction of nonstandard finite difference (NSFD) schemes. Firstly, we construct nonstandard one-stage and two-stage theta methods for a general dynamical system defined by a system of autonomous ordinary differential equations. We provide a sharp condition, which captures the dynamics of the continuous model. We discuss at length how this condition is pivotal in the construction of the complex denominator function. We show that the nonstandard theta methods are elementary stable in the sense that they have exactly the same fixed-points as the continuous model and they preserve their stability, irrespective of the value of the step size. For more complex dynamical systems that are dissipative, we identify a class of nonstandard theta methods that replicate this property. We apply the first part by considering a dynamical system that models the Ebola Virus Disease (EVD). The formulation of the model involves both the fast/direct and slow/indirect transmission routes. Using the specific structure of the EVD model, we show that, apart from the guidelines in the first part, the nonlocal approximation of nonlinear terms is guided by the productive-destructive structure of the model, whereas the choice of the denominator function is based on the conservation laws and the sub-equations that are associated with the model. We construct a NSFD scheme that is dynamically consistent with respect to the properties of the continuous model such as: positivity and boundedness of solutions; local and/or global asymptotic stability of disease-free and endemic equilibrium points; dependence of the severity of the infection on self-protection measures. Throughout the paper, we provide numerical simulations that support the theory.     

Birds movement impact on the transmission of West Nile virus between patches

Spatial heterogeneity plays an important role in the distribution and persistence of many infectious disease. In the paper, a multi-patch model for the spread of West Nile virus among $n$ discrete geographic regions is presented that incorporates a mobility process. In the mobility process, we assume that the birds can move among regions, but not the mosquitoes based on scale-space. We show that the movement of birds between patches is sufficient to maintain disease persistence in patches. We compute the basic reproduction number $R_{0}$. We prove that if $R_{0}<1$, then the disease-free equilibrium of the model is globally asymptotically stable. When $R_{0}>1$, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain. Finally, numerical simulations demonstrate that the disease becomes endemic in both patches when birds move back and forth between two regions.     

Assessing the effects of poverty in tuberculosis transmission dynamics

Tuberculosis (TB) transmission is enhanced by poor living conditions. In this study, a deterministic model was developed to assess the impact of socioeconomic conditions on TB transmission, taking into account heterogeneous mixing patterns. The epidemic thresholds known as the reproduction numbers, as well as equilibria for the model, are determined and stabilities analysed. Results from the study suggest that TB transmission is more common in poverty-stricken communities than in rich communities, supporting the argument that TB is a disease of the poor. The outcome is significantly dependent on the probability of latency, so that if the number of fast TB cases could be reduced, the epidemic would significantly improve. Interestingly, our results illustrate that heterogeneous mixing of the rich and poor will make the epidemic worse, but homogenous mixing will slightly improve the outcome. Further, even when all other factors are equal, the poor contact rate will have more impact than the rich contact rate. It follows that the rich community can help themselves by helping those less fortunate.     

Global analysis of an environmental disease transmission model linking within-host and between-host dynamics

In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R₀ for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R₀ < 1, and the endemic equilibrium is globally asymptotically stable when R₀ > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load.     

Regulatory impact of environmental standards on the eco-efficiency of firms

In this paper, we propose an approach to implement environmental standards into Data Envelopment Analysis (DEA) and in this way to measure their regulatory impact on eco-efficiency of firms. One standard feature of basic DEA models lies in the exogeneity of inputs, desirable and undesirable outputs. Taking into account the environmental constraints, we therefore apply the bounded variable DEA model. The regulatory impact is assessed as difference in eco-efficiency scores before and after fictive introduction of an environmental standard. Furthermore, we distinguish between weak and strong disposability of undesirable outputs and develop corresponding models. Assessing the regulatory impact of environmental standards in advance provides support for environmental policymakers in choosing appropriate instruments and in adjusting the intensity of regulation.     

Assessing the impact of inventory inaccuracies within a Newsvendor framework

This paper examines a Newsvendor framework in which a wholesaler who sells products to retailers is subject to inaccuracies in inventory data. The wholesaler’s decision regarding the management of his warehouse inventory is based on inventory data recorded in the information system. We assume that the wholesaler uses barcode labels and scanners in order to gather information concerning the available inventory in the warehouse. Because of errors arising during the manual barcode scanning process, the information on the available inventory level can deviate from the physical quantity and can result in an additional cost. This paper quantifies the economic impact of having uncertainty on the inventory level. We first analyze the case of a wholesaler that is not aware of inventory errors or chooses to ignore them in order to evaluate the efficiency loss due to errors compared with an error free situation. We then assess the effect of various actions enabling to tackle the inventory inaccuracy issue with a particular focus on actions such as the deployment of a new data capture technology.     

Assessing the impact of derived behavior information on customer attrition in the financial service industry

The value of the customer has been widely recognized in terms of financial planning and efficient resource allocation including the financial service industry. Previous studies have shown that directly observable information can be used in order to make reasonable predictions of customer attrition probabilities. However, these studies do not take full account of customer behavior information. In this paper, we demonstrate that efficient use of information can add value to financial services industry and improve the prediction of customer attrition. To achieve this, we apply an orthogonal polynomial approximation analysis to derive unobservable information, which is then used as explanatory variables in a probit–hazard rate model. Our results show that derived information can help our understanding of customer attrition behavior and give better predictions. We conclude that both researchers and the financial service industry should gather and use derived financial information in addition to directly observable information.     

Assessing the impact of educational campaigns on controlling HCV among women in prison settings

Prior studies have shown that imprisonment is a major risk factor for hepatitis C infection, with the risk of infection directly proportional to the length of incarceration. Women are at least twice as likely as men to contract HCV as they have limited access to information, health services and safe intravenous drug injecting equipments. We develop a mathematical model to assess the impact of educational campaigns on controlling HCV among women in prison settings. Equilibria for the model are determined and their stability are examined. Population-level effects of increased educational campaigns to encourage safe injecting practices among women in prison are evaluated through numerical simulations. The results suggest that educating women prisoners about abstaining from intravenous drug misuse may significantly reduce HCV prevalence among women in prison settings. Targeted education campaigns, which are effective at stopping transmission of HCV more than 80% of the time, will be highly effective at controlling the disease among women in prisons.     

Mathematical model for assessing the impact of vaccination and treatment on measles transmission dynamics

A deterministic model for the transmission dynamics of measles in a population with fraction of vaccinated individuals is designed and rigorously analyzed. The model with standard incidence exhibits the phenomenon of backward bifurcation, where a stable disease‐free equilibrium coexists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. This phenomenon can be removed if either measles vaccine is assumed to be perfect or disease related mortality rates are negligible. In the latter case, the disease‐free equilibrium is shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, the model has a unique endemic equilibrium whenever the reproduction threshold exceeds unity. This equilibrium is shown, using a nonlinear Lyapunov function of Goh‐Volterra type, to be globally asymptotically stable for a special case.     

The impact of environmental regulations on forest product trade in China

Forest product trade plays an important role in the development of the Chinese forest industry. The trading value of forest product has shown a yearly growth rate of 12% during the last five recent years. Stringent environmental regulations in China have a profound impact on raw material supplies and industrial production in the forest sector; however, their impact on the forest product trade is still unclear. This study applies fixed and random effects models as well as a seemingly unrelated regression model to investigate the impact of environmental regulations on the trade of forest product from 2002 to 2015. The results indicate that the stringent environmental regulations promoted the import but restricted the export of forest product in general. Specifically, the stringent environmental regulations stimulated the import but had an ambiguous impact on the export of the paper product. The stringent environmental regulations had also stimulated the import of wood product but inhibited the export. In contrast, wooden furniture had been affected minimally; only export got slightly negatively affected by environmental regulations. Recommendations for resource managers:

• Trade‐offs between economic growth and environmental regulations are needed to smoothly promote the forest product trade in China.
• Paper and wooden furniture product sectors are less likely to be affected by stringent environmental regulations, because high value‐added products could compensate for environmental costs.
• The wood product sector is more likely to be negatively affected by stringent environmental regulations because environmental costs could severely impact the competitiveness of low value‐added products.

     

Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus

In this note, we report on the formulation and mathematical analysis of single and multiple group models for the spread of the human immuno-deficiency virus (HIV), which is the etiological agent for the acquired immunodeficiency syndrome (AIDS). Results on the robustness of a single group model are stated for specific and arbitrary survivorship functions. In addition, we provide results that show that multiple group models can have multiple endemic equilibria.     

Assessing the risk of vCJD transmission via surgery: models for uncertainty and complexity

Variant Creutzfeldt–Jakob disease (vCJD) is a fatal degenerative brain disease, which probably passed into humans from cattle infected with bovine spongiform encephalopathy (BSE) or ‘mad cow disease’. Whatever its origins, the question arises of whether vCJD could be spread from person to person. Any such risk is very difficult to quantify, not least because the number of people already infected is unknown. This paper reflects on a study assessing the risk of transmission via instruments used in hospital surgery. The study underpinned a number of policy initiatives, including a £200?m programme to improve instrument decontamination. The methodology had to meet two major challenges. That of dealing with very large and multiple uncertainties was initially addressed using simple spreadsheet-based models to generate alternative scenarios. The complexity in the possible dynamics of vCJD within the population was then tackled. This paper outlines the models built and their use in eliciting expert judgement and informing risk management policy.     

Assessing the heterogeneity of a disease spread through a community

A multivariate non-parametric test and a semi-parametric regression model via counting process are proposed for detecting the heterogeneity of a disease spread through a community. The infection rates are allowed to depend on time in an arbitrary manner. Infectious data usually are not completely observed, nevertheless only partial information of the epidemic is needed for the suggested methods. The testing procedures and the associated methods of analysis are illustrated with reference to epidemics of respiratory disease on the Island of Tristan da Cunha in the South Atlantic     

Assessing the impact of problem structuring methods in multi-organizational settings: an empirical investigation

Problem structuring methods (PSMs) have most commonly been employed with groups operating within single-organizational contexts. This paper argues that PSMs are by their nature also appropriate for supporting the work of multi-organizational groups (MOGs) operating within a partnership context. An experience of the use of a PSM in this context is reported and evaluated. The research findings suggest that there is indeed scope for the use of PSMs with MOGs, and that these methods do appear to have a positive role in achieving some of the products claimed for PSM interventions. In particular, the experience as a whole tends to demonstrate that mutual accommodations between the organizations represented in the MOG can be the result of the use of PSMs. The paper concludes with a discussion of the significance of the experience, and proposes some directions for further research.     

条件(Q)条件(PT)对推出图及Rees商的传递性

研究了条件(Q)、条件(PT)对推出图、Rees商的传递性,证明了在推出图(1)中P满足条件(Q)当且仅当Y满足条件(Q)并且f是酉的.     

The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model

Dengue has grown dramatically in recent decades globally. In order to investigate the spread of dengue with vector control, especially, the impact of Wolbachia on dengue transmission, a mathematical model is established and analyzed to study dengue transmission between humans and mosquitoes. Firstly, model qualitative analysis including the existence and local asymptotic stability of dengue-free equilibria and endemic equilibria is done. It is found that dengue will disappear when the basic reproduction number is less than one, and dengue will prevail when the basic reproduction number is larger than one. More important finding is that the persistence of Wolbachia is determined by its fitness effect on mosquitoes, and Wolbachia can drastically reduce dengue fever transmission. All the results are verified by numerical simulation. Secondly, sensitivity analysis is done to explore the relative importance of different parameters on the system. It is obtained that parameters with strong sensitivity and controllability are the biting rate, the probability of dengue infection between mosquitoes and humans and the recovery rate of infectious humans. Finally, the control methods are discussed.     

How to measure the impact of environmental factors in a nonparametric production model

The measurement of technical efficiency allows managers and policy makers to enhance existing differentials and potential improvements across a sample of analyzed units. The next step involves relating the obtained efficiency estimates to some external or environmental factors which may influence the production process, affect the performances and explain the efficiency differentials. Recently introduced conditional efficiency measures (,  and ), including conditional FDH, conditional DEA, conditional order-m and conditional order-α, have rapidly developed into a useful tool to explore the impact of exogenous factors on the performance of Decision Making Units in a nonparametric framework. This paper contributes in a twofold fashion. It first extends previous studies by showing that a careful analysis of both full and partial conditional measures allows the disentangling of the impact of environmental factors on the production process in its two components: impact on the attainable set and/or impact on the distribution of the efficiency scores. The authors investigate these interrelationships, both from an individual and a global perspective. Second, this paper examines the impact of environmental factors on the production process in a new two-stage type approach but using conditional measures to avoid the flaws of the traditional two-stage analysis. This novel approach also provides a measure of inefficiency whitened from the main effect of the environmental factors allowing a ranking of units according to their managerial efficiency, even when facing heterogeneous environmental conditions. The paper includes an illustration on simulated samples and a real data set from the banking industry.     

The impact of zidovudine (AZT) therapy on the survivability of those with the progressive HIV infection

An analysis of the data regarding the impact of zidovudine therapy on the Survivability of those with progressive HIV disease demonstrates that this therapy extends longevity for perhaps 5.5 months on the average but does not prevent the disease from eventually being fatal. All of the benefits of zidovudine therapy in extending survivability appear to accrue within a relatively short treatment period, perhaps within a few months, but the effectiveness of this drug wanes in time, suggesting that zidovudine therapy could eventually be stopped without influencing survivability. Since the efficacy of zidovudine therapy in extending survivability appears to be independent of the stage of the HIV infection in infecteds whose CD4 T-cell densities fall below 200 cells/mm³, zidovudine therapy should be initiated when the patient's infection reaches a potentially fatal stage. Zidovudine therapy may be viewed as causing the HIV infection to regress to a previous stage of the disease, but the infection's progression promptly resumes and follows a course similar to one uninfluenced by zidovudine.