Robert G. McLeod

Could Condoms Stop the AIDS Epidemic

Although therapeutic treatment strategies appear promising for retarding the progression of HIV-related diseases, prevention remains the most effective strategy against the HIV/AIDS epidemic. This paper focuses on the effect of condom use as a single-strategy approach in HIV prevention in the absence of any treatment. There are two primary factors in the use of condoms to halt the HIV/AIDS epidemic: condom efficacy and compliance. Our study is focused on the effect of these factors in stopping the epidemic by constructing a new deterministic mathematical model. The current estimate of condom effectiveness against HIV transmission, based on the latest meta-analysis, is 60–96%, with a mean of 87%. Since the parameter estimates are subject to different kinds of uncertainty, to achieve adequate quality assurance in predictions, uncertainty and sensitivity analyses are carried out using latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCCs). Using stability and sensitivity analyses, based on a plausible range of parameter values, key parameters that govern the persistence or eradication of HIV are identified. This analysis shows that the product of efficacy and compliance, which we call ‘preventability’ (p), has a negative effect on the epidemic; as increasing p decreases the level of epidemicity. It is also shown that the threshold preventability (pc) increases with increasing average number of HIV-infected partners of susceptible individuals, especially those in the AIDS stage. For populations where the average number of HIV-infected partners is large, the associated preventability threshold is high and perhaps unattainable, suggesting that for such a population, HIV may not be controlled using condoms alone. On the other hand, for a population where the average number of HIV-infected partners is low (within a reasonable range), it is shown that pc is about 75%, suggesting that the epidemic could be stopped using condoms. Thus, for such a population, public health measures that can bring preventability above the threshold and continuous quantitative monitoring to make sure it stays there, are what would be necessary. In other words, for populations with reasonable average numbers of HIV-infected partners, given the will and effort, it is within our means to halt this epidemic using condoms.

The Design of Blocked Fractional Factorial Split-Plot Experiments

In industrial screening experiments, if some factors are hard to vary and others are easy to vary, randomization restrictions may lead to the use of fractional factorial split-plot (FFSP) designs. Blocked FFSP (BFFSP) designs arise when all runs cannot be performed under homogeneous conditions. This article introduces three approaches for blocking FFSP designs. A catalog of designs is presented in which BFFSP designs are ranked according to the minimum aberration criterion. In addition, additional optimality criteria are used to assist in the ranking procedure. The case study that motivated this research is also discussed in detail.

Blocked Fractional Factorial Split-Plot Experiments for Robust Parameter Design

Fractional factorial experiments are commonly used for robust parameter design and, for ease of use, such experiments are often run as split-plot designs. If the control factors are at the subplot level and the noise factors are at the whole-plot level, this also results in gains in efficiency. If all runs of the fractional factorial split-plot design cannot be run under homogeneous conditions, such designs are frequently blocked. In this paper, we explore the choice of blocked fractional factorial split-plot designs for use in robust parameter design. A ranking scheme for such designs is developed and, using a search algorithm, a catalog of 32-run optimal designs is provided. Two situations are considered, one in which the control factors are at the subplot level and one in which the control factors are at the whole-plot level. An example from the aerospace sector is used to illustrate the concepts.

MATHEMATICAL STUDY OF THE IMPACT OF QUARANTINE, ISOLATION AND VACCINATION IN CURTAILING AN EPIDEMIC

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small basic reproduction number and transmission coefficient of asymptomatically-infected individuals. If asymptomatic individuals transmit at a rate that is at least 20% that of symptomatic individuals, quarantine is always more effective. The study further shows that the reduction in disease burden obtained from a combined quarantine and isolation program can be comparable to that obtained by a vaccination program, if the former is implemented quickly enough after the onset of the outbreak. If the implementation of such a quarantine/isolation program is delayed, however, even for a short while, its effectiveness decreases rapidly.

Optimal Foldover Plans for Two-Level Fractional Factorial Split-Plot Designs

We consider the construction of foldovers of two-level fractional factorial split-plot designs. As a follow-up strategy, the foldover technique is useful when the objective is to systematically de-alias effects of interest after the initial fractional factorial split-plot design has been run. Due to the sequential nature in which the runs of the initial and foldover designs are conducted, the resulting combined design (the design consisting of both the initial design and its foldover) is a blocked fractional factorial split-plot design. Using the minimum aberration criterion for blocked fractional factorial split-plot designs, in conjunction with other optimality criteria, we provide a catalog of optimal foldover plans for initial minimum aberration fractional factorial split-plot designs consisting of 16 and 32 runs.

Quality by Experimental Design, Third Edition

A major strength of IRM is its collection of exercises and data sets. Exercises at the ends of chapters provide a good mix of applied and theoretical problems, leaning more toward the applied. A problem with some regression textbooks is their overuse of the same data sets in exercises. In contrast, the data sets used in the exercises and examples of IRM are numerous and come from a wide variety of fields. The data files are provided on a CD that comes with the book and on a web site. The names of the data files are highlighted in bold in the exercises to make them easier to locate.