Mathematical models for the transmission dynamics of HIV and its progression to AIDS in Ireland

Despite advances m understanding the basic biology of HIV the aetiological agent of AIDS, medica1, public health and health education planning is plagued by uncertainties Mathematical models of the dynamics of HIV transmission and its progression to AIDS can clarify what data must be collected in order to predict future prevalence, make predictions about the likely effect of future intervention pobcies and provide predictions for several decades ahead. The motivation of this research is to provide reliable estimates of the incidence of HIV infection and AIDS in the Irish population. In Chapters 1 and 2 we discuss the background to the disease in Ireland and the role of mathematical modelling in the spread AIDS. From this we show where key epidemiological data is lacking and how models to date have concentrated on the spread of the disease within the homosexual population. In Chapter 3 we describe the adjustment of the number of AIDS cases to allow for reporting delays Subsequently we consider the solution of the integral equation models generated by the back-projection method for the adjusted AIDS cases. In Chapter 4 we improve upon the estimates of the incidence of HIV infection found in Chapter 3 by evaluating the integral arising in back-projection, in terms of a gamma function plus a remainder in the form of a series in t. We also provide error bounds for the remainder. This new solution allows us to predict new and more reliable estimates of the level of HIV infection m Ireland. In Chapter 5 we provide estimates of the minimum number of deaths from AIDS, based on the number of AIDS cases known to the Department of Health and the distribution of the length of survival times after the onset of AIDS. The results of a HIV transmission survey are presented in Chapter 6 These provide detailed information on the habits and behaviour of those at risk of HIV infection and allow us to derive preliminary model parameters. Finally in Chapter 7 we develop and implement a nonlinear deterministic differential equation model for the spread of HIV and its progression to AIDS m the Irish IVDU and homosexual populations. We examine the effects of likely intervention policies on the extent and spread of the disease and we make recommendations based on our thesis findings

A mathematical model for measles epidemics in Ireland

The aim of this work is to establish a matnematical model for measles epidemics and to predict levels of vaccination coverage require! in Ireland in order to eradicate tne disease The emphasis througnout has oeen to derive the parameters of the model using data collected in Ireland. To achieve this a nonlinear differential equation model first oroposed by Anderson R M. and May R.M. has been adopted and adjusted to meet our application. In Chapter 1 we introduce the concept of mathematically modelling the dynamics of an infectious disease and we also propose a simple constant parameter model We then move on in Chapter 2 to discuss what is known as ”the force of the infection". This is then calculated for Ireland by testing over 100 blood samples for measles antibodies. In Chapter 3 we estimated the Irish interepidemic period using Hopf's bifurcation theorem. In Chapter 4 we move on to the more detailed model with age dependence. We also estimate the age dependent survival rate jj(a) for the Irish population. Finally, in Chapters 5 and 6, we look at immunisation and the results predicted by the model. In Chapter 5 we derive c(a), the Irish age dependent vaccination rate This is accomplished by computerising over 4,000 immunisations. We also predict how the reproductive rate, R , of the disease will change with vaccination. In Chapter 6 we numerically analyse the model with the Irish age dependent parameters and we predict the levels of vaccination required in order to eradicate measles in Ireland

Implications of two backward blood spatter models based on fluid dynamics for bloodstain pattern analysis

Bloodstain pattern analysis (BPA) is an integral part of crime scene investigation. For violent crimes involving gunshots, standard practice in police departments worldwide have some physical limitations. For instance, the effect of gravity and air drag on trajectories of blood droplets are neglected using current reconstruction methods, which results in a well-known overestimation of the height of the source of blood. As a consequence, more sophisticated models for blood spatter trajectory reconstruction are being developed, two of which are highlighted in the present work. They allow the prediction of bloodstain patterns produced from backward spattered blood droplets from blunt and sharp bullets. Our recent models attribute the splashing of blood to the Rayleigh-Taylor instability which arises when blood is accelerated towards lighter air. This physically-based description comes with the powerful predictive capability to correlate features of bloodstain patterns with the specific bullet and gun that produced them, as well as with the body position. The results of the numerical models were compared with four experiments simulating blood spatter deposition on a vertical wall through the number of stains produced, average stain area, and average impact angle at the surface, and the agreement found is fairly good. Moreover, further insight is obtained by probing and explaining the influence of observable parameters on the resulting spatter pattern, with the goal of aiding BPA experts evaluating a crime scene

Pattern and process in Amazon tree turnover, 1976-2001

Previous work has shown that tree turnover, tree biomass and large liana densities have increased in mature tropical forest plots in the late twentieth century. These results point to a concerted shift in forest ecological processes that may already be having significant impacts on terrestrial carbon stocks, fluxes and biodiversity. However, the findings have proved controversial, partly because a rather limited number of permanent plots have been monitored for rather short periods. The aim of this paper is to characterize regional-scale patterns of 'tree turnover' (the rate with which trees die and recruit into a population) by using improved datasets now available for Amazonia that span the past 25 years. Specifically, we assess whether concerted changes in turnover are occurring, and if so whether they are general throughout the Amazon or restricted to one region or environmental zone. In addition, we ask whether they are driven by changes in recruitment, mortality or both. We find that: (i) trees 10 cm or more in diameter recruit and die twice as fast on the richer soils of southern and western Amazonia than on the poorer soils of eastern and central Amazonia; (ii) turnover rates have increased throughout Amazonia over the past two decades; (iii) mortality and recruitment rates have both increased significantly in every region and environmental zone, with the exception of mortality in eastern Amazonia; (iv) recruitment rates have consistently exceeded mortality rates; (v) absolute increases in recruitment and mortality rates are greatest in western Amazonian sites; and (vi) mortality appears to be lagging recruitment at regional scales. These spatial patterns and temporal trends are not caused by obvious artefacts in the data or the analyses. The trends cannot be directly driven by a mortality driver (such as increased drought or fragmentation-related death) because the biomass in these forests has simultaneously increased. Our findings therefore indicate that long-acting and widespread environmental changes are stimulating the growth and productivity of Amazon forests

Characterizing generated charged inverse micelles with transient current measurements

We investigate the generation of charged inverse micelles in nonpolar surfactant solutions relevant for applications such as electronic ink displays and liquid toners. When a voltage is applied across a thin layer of a nonpolar surfactant solution between planar electrodes, the generation of charged inverse micelles leads to a generation current. From current measurements it appears that such charged inverse micelles generated in the presence of an electric field behave differently compared to those present in equilibrium in the absence of a field. To examine the origin of this difference, transient current measurements in which the applied voltage is suddenly increased are used to measure the mobility and the amount of generated charged inverse micelles. The mobility and the corresponding hydrodynamic size are found to be similar to those of charged inverse micelles present in equilibrium, which indicates that other properties determine their different behavior. The amplitude and shape of the transient currents measured as a function of the surfactant concentration confirm that the charged inverse micelles are generated by bulk disproportionation. A theoretical model based on bulk disproportionation with simulations and analytical approximations is developed to analyze the experimental transient currents

Rarity of monodominance in hyperdiverse Amazonian forests.

Tropical forests are known for their high diversity. Yet, forest patches do occur in the tropics where a single tree species is dominant. Such "monodominant" forests are known from all of the main tropical regions. For Amazonia, we sampled the occurrence of monodominance in a massive, basin-wide database of forest-inventory plots from the Amazon Tree Diversity Network (ATDN). Utilizing a simple defining metric of at least half of the trees ≥ 10 cm diameter belonging to one species, we found only a few occurrences of monodominance in Amazonia, and the phenomenon was not significantly linked to previously hypothesized life history traits such wood density, seed mass, ectomycorrhizal associations, or Rhizobium nodulation. In our analysis, coppicing (the formation of sprouts at the base of the tree or on roots) was the only trait significantly linked to monodominance. While at specific locales coppicing or ectomycorrhizal associations may confer a considerable advantage to a tree species and lead to its monodominance, very few species have these traits. Mining of the ATDN dataset suggests that monodominance is quite rare in Amazonia, and may be linked primarily to edaphic factors

Transmission Potential of Chikungunya Virus and Control Measures: The Case of Italy

During summer 2007 Italy has experienced an epidemic caused by Chikungunya virus – the first large outbreak documented in a temperate climate country – with approximately 161 laboratory confirmed cases concentrated in two bordering villages in North–Eastern Italy comprising 3,968 inhabitants. The seroprevalence was recently estimated to be 10.2%. In this work we provide estimates of the transmission potential of the virus and we assess the efficacy of the measures undertaken by public health authorities to control the epidemic spread. To such aim, we developed a model describing the temporal dynamics of the competent vector, known as Aedes albopictus, explicitly depending on climatic factors, coupled to an epidemic transmission model describing the spread of the epidemic in both humans and mosquitoes. The cumulative number of notified cases predicted by the model was 185 on average (95% CI 117–278), in good agreement with observed data. The probability of observing a major outbreak after the introduction of an infective human case was estimated to be in the range of 32%–76%. We found that the basic reproduction number was in the range of 1.8–6 but it could have been even larger, depending on the density of mosquitoes, which in turn depends on seasonal meteorological effects, besides other local abiotic factors. These results confirm the increasing risk of tropical vector–borne diseases in temperate climate countries, as a consequence of globalization. However, our results show that an epidemic can be controlled by performing a timely intervention, even if the transmission potential of Chikungunya virus is sensibly high