Modelling the feedback effects of reconfiguring health services

The shift in the balance of health care, bringing services ‘closer to home’, is a well-established trend, which has been motivated by the desire to improve the provision of services. However, these efforts may be undermined by the improvements in access stimulating demand. Existing analyses of this trend have been limited to isolated parts of the system with calls to control demand with stricter clinical guidelines or to meet demand with capacity increases. By failing to appreciate the underlying feedback mechanisms, these interventions may only have a limited effect. We demonstrate the contribution offered by system dynamics modelling by presenting a study of two cases of the shift in cardiac catheterization services in the UK. We hypothesize the effects of the shifts in services and produce model output that is not inconsistent with real world data. Our model encompasses several mechanisms by which demand is stimulated. We use the model to clarify the roles for stricter clinical guidelines and capacity increases, and to demonstrate the potential benefits of changing the goals that drive activity.     

Oscillation and global attractivity in a periodic delay hematopoiesis model

In this paper we shall consider the nonlinear delay differential equation $$p'(t) = \frac{{\beta (t)}}{{1 + p^n (t - m\omega )}} - \delta (t)p(t),$$ wherem is a positive integer, β(t) and δ(t) are positive periodic functions of period ω. In the nondelay case we shall show that (*) has a unique positive periodic solution $\bar p(t)$ , and show that $\bar p(t)$ is a global attractor all other positive solutions. In the delay case we shall present sufficient conditions for the oscillation of all positive solutions of (*) about $\bar p(t)$ , and establish sufficient conditions for the global attractivity of $\bar p(t)$ . Our results extend and improve the well known results in the autonomous case.     

半导体与超晶格的数学模型及其分析Ⅰ:模型

本文论及半导体与超晶格的数学模型方法的一些新近发展动态。介绍了半导体与超晶格的一些背景材料并给出了半导体宏观模型间的层次框架。超晶格中载流子传输的SHE扩散模型也被观察。     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Modelling and Reality

Some authors have expressed concern about the concept of optimisation and the emphasis which is placed in the O.R. literature on the mathematical aspects of models. Case studies are often described as though the mathematical solutions were the most important parts and seldom does the opportunity arise to expose the more behavioural issues of a problem.The reason for the concentration on mathematics may be the form of the classical model of the process of O.R. and the inherent expectation that a study should conform to it. An earlier paper by this author is recognised to have been written in the mode of the classical model and now the issues of a non-mathematical nature are brought to the fore. It is suggested that there is scope for improving the classical model, which could in turn allow the introduction of greater realism into the case studies which are reported.     

Modelling Teams and Workgroups in Manufacturing

One of the major features of Japanese manufacturing techniques is the extensive use of teams, i.e., workers who as a group work together to produce sub-assemblies or finished products, or, alternatively, work together to accomplish a project. Many naive promoters of the team concept assume that the team members work together on the same tasks and activities and somehow accomplish them faster and better. However, observation of actual teams indicate that, unless a team member is new and quite inexperienced, teams split the required tasks or activities up so that each member has a unique task and most of the time members work independently. This paper develops models that try to describe the features of division of labour in teams and the way in which differences in capability between different team members impact performance. The models suggest that the advantage of teams probably lies primarily in the structure that enables faster/better workers to help out others.     

Modelling and forecasting mortality in Spain

Experience shows that static life tables overestimate death probabilities. As a consequence of this overestimation the premiums for annuities, pensions and life insurance are not what they actually should be, with negative effects for insurance companies or policy-holders. The reason for this overestimation is that static life tables, through being computed for a specific period of time, cannot take into account the decreasing mortality trend over time. Dynamic life tables overcome this problem by incorporating the influence of the calendar when graduating mortality. Recent papers on the topic look for the development of new methods to deal with this dynamism.     

A note on global attractivity in models of hematopoiesis

We consider the delay differential equations which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δ_j = δ_j(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δ_j] independently of β₀ and θ. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 5–12, January, 1998.     

Modelling take-up and profitability

We use response data collected by a lender to estimate the probabilities of loan offers being accepted by the applicants and the survival probabilities of default and of paying back early. Combining all those together we estimated the expected profit surface for the lender at the time of application before making an offer to an applicant. The results show how a lender could find the optimal interest rate to increase the expected profit or its market share. We also consider how different optimal decision policies could be applied to different market segments.     

Modelling Alternative Realities in Conflict and Negotiation

A framework is presented which provides a means of representing and relating the subjective perceptions of actors involved in a conflict or negotiation. Use is made of the method of cognitive mapping in setting down the components of a hierarchy of individual perceptions of a situation, and a formal definition of this overall structure, termed a hypermap, is given in the Appendix. A number of illustrative examples are used to demonstrate the approach and to indicate its potential, and some of its implications in practical applications are considered.     

Distributed Modelling

Budgeting, which can be defined as establishing medium-term control standards for an organisation as a whole and for each of its constituent parts, requires considerable amounts of both high-level management attention and also low-level data manipulation. In a large organisation, conventional methods of computerising the budgeting procedure tend merely to substitute one set of difficulties for another, and to alienate the managers in doing so. This paper describes the development and introduction of an interactive computer-based system in British Gas that successfully avoids such problems and assists the managers to improve their budgets while largely eliminating the requirement for low-level time and effort. The design principles of the system are outlined and the implementation history is described. It is concluded that with skilful use of existing computer techniques, significant improvements can be made in medium-term planning and control at little cost.