Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

An approximate mathematical model for solidification of a flowing liquid in a microchannel

A mathematical model is developed to analyse the combined flow and solidification of a liquid in a small pipe or two-dimensional channel. In either case the problem reduces to solving a single equation for the position of the solidification front. Results show that for a large range of flow rates the closure time is approximately constant, and the value depends primarily on the wall temperature and channel width. However, the ice shape at closure will be very different for low and high fluxes. As the flow rate increases the closure time starts to depend on the flow rate until the closure time increases dramatically, subsequently the pipe will never close.

A Health Economics Model. The cost benefits of the Physical Activity Strategy for Northern Ireland - a summary of key findings

This summary report follows on from the publication of the Northern Ireland physical activity strategy in 1996 and the subsequent publication of the strategy action plan in 1998. Within this strategy action plan a recommendation was made for the health sector, that research should be carried out to evaluate and compare the cost of investing in physical activity programmes against the cost of treating preventable illness. To help in the development of this key area, the Department of Health, Social Services and Public Safety's Economics Branch agreed to develop a model that would seek to establish the extent of avoidable deaths from physical inactivity and, as a consequence, the avoidable economic and healthcare costs for Northern Ireland.

Re: Cost effectiveness of strategies to combat cardiovascular disease, diabetes, and tobacco use in sub-Saharan Africa and South East Asia: mathematical modelling study.

Rapid response to: Ortegón M, Lim S, Chisholm D, Mendis S. Cost effectiveness of strategies to combat cardiovascular disease, diabetes, and tobacco use in sub-Saharan Africa and South East Asia: mathematical modelling study. BMJ. 2012 Mar 2;344:e607. doi: 10.1136/bmj.e607. PMID: 22389337.

Understanding the Economics of Investments in the Social Determinants of Health

Briefing 9 - Understanding the economics of investments in the social determinants of health This document, commissioned by Public Health England, and written by the UCL Institute of Health Equity, examines how to use measures of economic investment to improve and increase local investment in the social determinants of health. The paper provides information to support decision-making on actions to address the social determinants of health and the development of business cases for investment. It supplements the evidence reviews in this series, which include information on the economic impacts of actions on health inequalities, and should help the reader to be an intelligent customer and commissioner of economic analyses and to understand their limitations. The paper covers: - The rationale for understanding, measuring and taking into account the economic impact of decisions and interventions that impact on the social determinants of health.- The benefits and limitations of various ‘economic measures of impact’ – commonly used terms which can be confusing, sometimes leading to misinterpretation of which measure of economic impact is appropriate for what purpose.- What is currently known about the economic impact of intervening in the social determinants of health.- Good practice and further resources which will support better decisions. The briefing is available to download above. This document is part of a series. An overview document which provides an introduction to this and other documents in the series, and links to the other topic areas, is available on the ‘Local Action on health inequalities’ project page. A video of Michael Marmot introducing the work is also available on our videos page.

An Introduction to Health Economics & Economic Evaluations

- Overview of Economic Evaluation - Stages in Economic Evaluation  

Introduction to Evaluation and Health Economics

A video summary by Orla Doyle

Lifelong dynamics of human CD4+CD25+ regulatory T cells: insights from in vivo data and mathematical modeling.

Despite their limited proliferation capacity, regulatory T cells (T(regs)) constitute a population maintained over the entire lifetime of a human organism. The means by which T(regs) sustain a stable pool in vivo are controversial. Using a mathematical model, we address this issue by evaluating several biological scenarios of the origins and the proliferation capacity of two subsets of T(regs): precursor CD4(+)CD25(+)CD45RO(-) and mature CD4(+)CD25(+)CD45RO(+) cells. The lifelong dynamics of T(regs) are described by a set of ordinary differential equations, driven by a stochastic process representing the major immune reactions involving these cells. The model dynamics are validated using data from human donors of different ages. Analysis of the data led to the identification of two properties of the dynamics: (1) the equilibrium in the CD4(+)CD25(+)FoxP3(+)T(regs) population is maintained over both precursor and mature T(regs) pools together, and (2) the ratio between precursor and mature T(regs) is inverted in the early years of adulthood. Then, using the model, we identified three biologically relevant scenarios that have the above properties: (1) the unique source of mature T(regs) is the antigen-driven differentiation of precursors that acquire the mature profile in the periphery and the proliferation of T(regs) is essential for the development and the maintenance of the pool; there exist other sources of mature T(regs), such as (2) a homeostatic density-dependent regulation or (3) thymus- or effector-derived T(regs), and in both cases, antigen-induced proliferation is not necessary for the development of a stable pool of T(regs). This is the first time that a mathematical model built to describe the in vivo dynamics of regulatory T cells is validated using human data. The application of this model provides an invaluable tool in estimating the amount of regulatory T cells as a function of time in the blood of patients that received a solid organ transplant or are suffering from an autoimmune disease.

Mathematical modeling and analysis of the interaction of populations of bacteria and bacteriophages within chicken intestine

Vegeu el resum a l'inici del document de l'arxiu adjunt

Ideas, Possibilities and Limitations of Sustainable Economic Policy – the Example of Ecological Economics

A mesura que el suport del creixement econòmic constitueix un objectiu fonamental de la formulació de polítiques econòmiques, cal assenyalar que aquest tipus de creixement està limitat naturalment per un planeta finit. Aquest article argumenta que, des del punt de vista de la justícia intergeneracional, la realització d'un concepte de desmaterialització i, com a efecte, d'una economia que no creix (en el sentit de dissociació absoluta del creixement econòmic i consum d'energia i materials) es pot justificar. Per tant, el creixement pot ser també entesa com la millora de la qualitat de vida sobretot en comptes d'ampliar quantitats escarpats de sortida. Per tant, una dràstica reducció del cabal de material es necessita, sobretot en els països d'alts ingressos. Després de presentar alguns crítica de les propostes, en el focus d'aquest article es dibuixen en els arguments de per què la política econòmica en el futur han de ser etiquetats com "ecològic" i, a continuació, les opcions de posar en acció les idees del teòric presentat marc en tasques manejables polítiques seran discutides. En aquest cas, s'argumentarà que l'enfocament clàssic de internalització d'efectes externs sovint seguides de decisions de política econòmica ortodoxa no és completament capaç de reflectir canvis ecològics en les estructures de preus dels mercats. Per tant, formal (industrial i l'establiment de la política de consum) i institucions informals (llars) representen punts clau de la política econòmica sostenible, assenyalant l'individu com així com la responsabilitat col · lectiva per omplir aquest buit substancial.

New perspectives in the use of ink evidence in forensic science: Part II. Development and testing of mathematical algorithms for the automatic comparison of ink samples analysed by HPTLC

In the first part of this research, three stages were stated for a program to increase the information extracted from ink evidence and maximise its usefulness to the criminal and civil justice system. These stages are (a) develop a standard methodology for analysing ink samples by high-performance thin layer chromatography (HPTLC) in reproducible way, when ink samples are analysed at different time, locations and by different examiners; (b) compare automatically and objectively ink samples; and (c) define and evaluate theoretical framework for the use of ink evidence in forensic context. This report focuses on the second of the three stages. Using the calibration and acquisition process described in the previous report, mathematical algorithms are proposed to automatically and objectively compare ink samples. The performances of these algorithms are systematically studied for various chemical and forensic conditions using standard performance tests commonly used in biometrics studies. The results show that different algorithms are best suited for different tasks. Finally, this report demonstrates how modern analytical and computer technology can be used in the field of ink examination and how tools developed and successfully applied in other fields of forensic science can help maximising its impact within the field of questioned documents.

Crises as a disease of the body politick: a metaphor in the history of nineteenth century economics

This paper examines the use of the medical metaphor in the early theories of crises. It first considers the borrowing of medical terminology and generic references to disease which, notwithstanding their relatively trivial character, illustrate how crises were originally conceived as disturbances (often of a political nature) to a naturally healthy system. Then it shows how a more specific metaphor, the fever of speculation, shifted the emphasis by treating prosperity as the diseased phase, to which crises are a remedy. The metaphor of the epidemic spreading of the disease introduced the theme of the cumulative character of both upswing and downswing, while the similitude with intermittent fevers accounted for the recurring nature of crises. Finally, the paper examines how the medical reflections on the causality of diseases contributed to the epistemology of crises theory, and reflects on the metaphisical shift accompanying the transition from the theories of crises to the theories of cycles.