A Bayesian approach for estimating bioterror attacks from patient data.

Terrorist attacks using an aerosolized pathogen have gained credibility as a national security concern after the anthrax attacks of 2001. Inferring some important details of the attack quickly, for example, the number of people infected, the time of infection, and a representative dose received can be crucial to planning a medical response. We use a Bayesian approach, based on a short time series of diagnosed patients, to estimate a joint probability density for these parameters. We first test the formulation with idealized cases and then apply it to realistic scenarios, including the Sverdlovsk anthrax outbreak of 1979. We also use simulated outbreaks to explore the impact of model error, as when the model used for generating simulated epidemic curves does not match the model subsequently used to characterize the attack. We find that in all cases except for the smallest attacks (fewer than 100 infected people), 3-5 days of data are sufficient to characterize the outbreak to a specificity that is useful for directing an emergency response.

Spectral methods for parametric sensitivity in stochastic dynamical systems.

Stochastic dynamical systems governed by the chemical master equation find use in the modeling of biological phenomena in cells, where they provide more accurate representations than their deterministic counterparts, particularly when the levels of molecular population are small. The analysis of parametric sensitivity in such systems requires appropriate methods to capture the sensitivity of the system dynamics with respect to variations of the parameters amid the noise from inherent internal stochastic effects. We use spectral polynomial chaos expansions to represent statistics of the system dynamics as polynomial functions of the model parameters. These expansions capture the nonlinear behavior of the system statistics as a result of finite-sized parametric perturbations. We obtain the normalized sensitivity coefficients by taking the derivative of this functional representation with respect to the parameters. We apply this method in two stochastic dynamical systems exhibiting bimodal behavior, including a biologically relevant viral infection model.