A syringe-sharing model for the spread of HIV: application to Omsk, Western Siberia.

A system of two differential equations is used to model the transmission dynamics of human immunodeficiency virus between 'persons who inject drugs' (PWIDs) and their syringes. Our vector-borne disease model hinges on a metaphorical urn from which PWIDs draw syringes at random which may or may not be infected and may or may not result in one of the two agents becoming infected. The model's parameters are estimated with data mostly from the city of Omsk in Western Siberia. A linear trend in PWID prevalence in Omsk could only be fitted by considering a time-dependent version of the model captured through a secular decrease in the probability that PWIDs decide to share a syringe. A global sensitivity analysis is performed with 14 parameters considered random variables in order to assess their impact on average numbers infected over a 50-year projection. With obvious intervention implications the drug injection rate and the probability of syringe-cleansing are the only parameters whose coefficients of correlations with numbers of infected PWIDs and infected syringes have an absolute value close to or larger than 0.40.

A Leslie matrix model for Sicyopterus lagocephalus in La Réunion: sensitivity, uncertainty and research prioritization.

We propose a Leslie matrix model for the population dynamics of Sicyopterus lagocephalus in La Réunion. In order to capture both the amphidromous and the seasonal natures of the species' life history the model has four stages (sea+three river sites) and is cyclical with a 12 month period. Baseline parameters (age-specific fecundity, spatial dispersion patterns and survival rates) were chosen in such a way that the dominant eigenvalue of the year-on-year projection matrix is 1. Large uncertainties on the parameter values preclude the use of the model for management purpose. A sensitivity/uncertainty analysis sheds light on the parameters that cause much of the output to vary and that are poorly known: the life expectancy in rivers and the mortality both at river mouths and during the drift of larvae to sea. The aim is to help policymakers and researchers prioritize data acquisition efforts. The ultimate goal is a sustainable management of Sicyopterus lagocephalus in La Réunion.

Consistent partnership formation: application to a sexually transmitted disease model.

We apply a consistent sexual partnership formation model which hinges on the assumption that one gender's choices drives the process (male or female dominant model). The other gender's behavior is imputed. The model is fitted to UK sexual behavior data and applied to a simple incidence model of HSV-2. With a male dominant model (which assumes accurate male reports on numbers of partners) the modeled incidences of HSV-2 are 77% higher for men and 50% higher for women than with a female dominant model (which assumes accurate female reports). Although highly stylized, our simple incidence model sheds light on the inconsistent results one can obtain with misreported data on sexual activity and age preferences.

A parity-structured matrix model for tsetse populations.

A matrix model is used to describe the dynamics of a population of female tsetse flies structured by parity (i.e., by the number of larvae laid). For typical parameter values, the intrinsic growth rate of the population is zero when the adult daily survival rate is 0.970, corresponding to an adult life expectancy of 1/0.030 = 33.3 days. This value is plausible and consistent with results found earlier by others. The intrinsic growth rate is insensitive to the variance of the interlarval period. Temperature being a function of the time of the year, a known relationship between temperature and mean pupal and interlarval times was used to produce a time-varying version of the model which was fitted to temperature and (estimated) population data. With well-chosen parameter values, the modeled population replicated at least roughly the population data. This illustrates dynamically the abiotic effect of temperature on population growth. Given that tsetse flies are the vectors of trypanosomiasis ("sleeping sickness") the model provides a framework within which future transmission models can be developed in order to study the impact of altered temperatures on the spread of this deadly disease.

Back-calculation and projection of the HIV/AIDS epidemic among homosexual/ bisexual men in three European countries: evalution of past projections and updates allowing for treatment effects.

This study critically evaluates the quality of 1990 back-calculations and long-term projections of the HIV/AIDS epidemic for homosexual/bisexual men in France, the Federal Republic of Germany, and the UK. The projection captured the general pattern observed in all three countries although the observed AIDS incidence peaked 2-3 years later and declined faster than had been projected. Total AIDS incidences from 1989 to 2000 were overestimated by 38.5% in France, and underestimated by 23.9 and 17.5% in western Germany and the UK. Updated back-calculations and projections to 2020 use AIDS incidence data up to 2000. The procedure incorporates an asymmetric long-tailed cumulative HIV curve as well as the increase in the median incubation period brought about by new therapies introduced during the 1990s. The results suggest that: (i) The rapid decrease in cases during the late 1990s was caused by a median incubation period that increased from 10 years to 21-23 years by the late 1990s. (ii) An imminent bottoming out followed by a protracted increase in AIDS cases from 2000 to at least 2010 could be the consequence of a leveling off of the median incubation period. (iii) A low variant of the projections shows that at least 40,000 homosexual men could develop AIDS in the three countries after 2000.