Controlling the number of HIV infectives in a mobile population.

The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. We formulate various mathematical control problems for HIV spread in mobile heterosexual populations, and show how optimal regional control strategies can be obtained that minimize the national spread of HIV. We apply the cross-entropy method to solve these highly multi-modal and non-linear optimization problems. We demonstrate the effectiveness of the method via a range of experiments and illustrate how the form of the optimal control function depends on the mathematical model used for the HIV spread.

Stochastic models for the spread of HIV in a mobile heterosexual population.

An important factor in the dynamic transmission of HIV is the mobility of the population. We formulate various stochastic models for the spread of HIV in a heterosexual mobile population, under the assumptions of constant and varying population sizes. We also derive deterministic and diffusion analogues for these models, using a convenient rescaling technique, and analyze their stability conditions and equilibrium behavior. We illustrate the dynamic behavior of the models and their approximations via a range of numerical experiments.

IPCS conceptual framework for evaluating a mode of action for chemical carcinogenesis.

The International Programme on Chemical Safety (IPCS) is leading an activity to harmonize approaches to cancer risk assessment as a part of its larger project on the Harmonization of Approaches to the Assessment of Risk from Exposure to Chemicals. Through a series of workshops and the evaluation of case studies, a number of key components of risk assessments relating to harmonization were identified: transparency, terminology, weight of evidence, flexibility, and accessibility/communication. A major impediment to harmonization identified in the consideration of weight of evidence was the evaluation of mode of action. To address this need, a conceptual framework was developed, based on the general principles involved in considering the chemical induction of a specific tumor in animals. This is based partly on the Bradford Hill criteria for causality as modified by Faustman et al. (1997) for developmental toxicity. The framework is described in this paper followed by a worked example. It is recognized that the framework addresses only one stage in the overall characterization of hazard to humans of chemical carcinogens. Another important but separate step is the assessment of relevance to humans. This is a priority area for future work in this project.

Potency grading in carcinogen classification.

In 1992 the United Nations Conference on Environment and Development decided to harmonize carcinogen classification systems. A proposal for a harmonized classification system is currently being considered by the Organization for Economic Cooperation and Development (OECD). In many countries, classification of a chemical as carcinogenic triggers labeling requirements. Implicit in the labeling requirements are often restrictions on the sale of consumer products and workplace regulations. Many of the current classification systems for carcinogens use a single concentration limit for the minimum concentration of a carcinogen in a preparation (mixture) that requires labeling. For high-potency carcinogens, one concentration limit may not adequately express the hazard, whereas for low-potency carcinogens, one limit may overestimate the hazard caused by the carcinogen in the preparation (mixture). The potency grading system discussed consists of three potency groups: high-, medium-, and low-potency carcinogens. It is envisioned that the different classes will trigger different labeling requirements. In the process of potency grading, a preliminary conclusion as to whether a substance shows high, medium, or low potency is initially based on a tumorigenic dose descriptor. The preliminary potency evaluation may then be modified after due consideration of a number of additional elements. These may include evaluation of the dose-response curve; site-, species-, strain-, and sex-specific activity; mechanisms including genotoxicity; mechanistic relevance to humans; toxicokinetics; and other factors. The potency grading system discussed is applicable to most carcinogen classification systems, including that currently being considered by the OECD.

T25: a simplified carcinogenic potency index: description of the system and study of correlations between carcinogenic potency and species/site specificity and mutagenicity.

A simplified carcinogenic potency index, the T25, is proposed as a practical method for the inclusion of potency considerations in carcinogen classification systems. The T25 is the chronic daily dose in mg per kg bodyweight which will give 25% of the animals tumours at a specific tissue site, after correction for spontaneous incidence, within the standard life span of that species. Calculated T25 values of a set of 113 US National Cancer Institute/National Toxicology Program (NC/NTP) carcinogens showed excellent correlation (correlation coefficient 0.96, P < 0.0001) with the carcinogenic potency index TD50 of Peto et al. (1984). The mean of T25 values for 51 transspecies, multiple common site NCI/NTP carcinogens were 10-fold lower than those for 62 NCI/NTP single species, single site carcinogens. For these 113 carcinogens, the mean T25 values were approximately 3-fold lower for agents that were also mutagenic in Salmonella compared to the non-mutagenic agents.

Carcinogen classification systems: similarities and differences.

An overview of regulatory classification systems on carcinogens in the Organization for Economic Cooperation and Development (OECD) countries is presented based on a questionnaire study. Most OECD countries have implemented legislation including classification systems and lists of carcinogens. Basically, there are two types of classifications systems. The major difference between the two is that in one system carcinogens are classified according to the weight of evidence for carcinogenic effects in humans, whereas in the other carcinogens are allocated to various groups according to potency. Even if the classification systems may differ, the substances classified as carcinogens are to a large extent the same. Classification of carcinogens will in many countries require hazard labeling. This labeling, i.e., the limit for labeling of substances and preparations, and risk phrases show considerable similarities, but differ in certain aspects. Several countries have restrictions on sale and/or use of carcinogens. There is a trend toward introducing more mechanistic considerations in the classification of carcinogens.