Using the Kalman filter and dynamic models to assess the changing HIV/AIDS epidemic

Many factors, including therapy and behavioral changes, have modified the course of the HIV/AIDS epidemic in recent years. To include these modifications in HIV/AIDS models, in the absence of appropriate external data sources, changes over time in the parameters can be incorporated by a recursive estimation technique such as the Kalman filter. The Kalman filter accounts for stochastic fluctuations in both the model and the data and provides a means to assess any parameter modifications included in new observations. The Kalman filter approach was applied to a simple differential model to describe the observed HIV/AIDS epidemic in the homo/bisexual male community in Paris (France). This approach gave quantitative information on the time-evolution of some parameters of major epidemiological significance (average transmission rate, mean incubation rate, and basic reproduction rate), which appears quite consistent with the recent epidemiological literature.