BackgroundAcellular pertussis vaccine studies postulate that waning protection, particularly after the adolescent booster, is a major contributor to the increasing US pertussis incidence. However, these studies reported relative (ie, vs a population given prior doses of pertussis vaccine), not absolute (ie, vs a pertussis vaccine naïve population) efficacy following the adolescent booster. We aim to estimate the absolute protection offered by acellular pertussis vaccines.MethodsWe conducted a systematic review of acellular pertussis vaccine effectiveness (VE) publications. Studies had to comply with the US schedule, evaluate clinical outcomes, and report VE over discrete time points. VE after the 5-dose childhood series and after the adolescent sixth-dose booster were extracted separately and pooled. All relative VE estimates were transformed to absolute estimates. VE waning was estimated using meta-regression modeling.FindingsThree studies reported VE after the childhood series and four after the adolescent booster. All booster studies reported relative VE (vs acellular pertussis vaccine-primed population). We estimate initial childhood series absolute VE is 91% (95% CI: 87% to 95%) and declines at 9.6% annually. Initial relative VE after adolescent boosting is 70% (95% CI: 54% to 86%) and declines at 45.3% annually. Initial absolute VE after adolescent boosting is 85% (95% CI: 84% to 86%) and declines at 11.7% (95% CI: 11.1% to 12.3%) annually.InterpretationAcellular pertussis vaccine efficacy is initially high and wanes over time. Observational VE studies of boosting failed to recognize that they were measuring relative, not absolute, VE and the absolute VE in the boosted population is better than appreciated.

We develop a new neural network architecture for projective clustering of data sets that incorporates adaptive transmission delays and signal transmission information loss. The resultant selective output signaling mechanism does not require the addition of multiple hidden layers but instead is based on the assumption that the signal transmission velocity between input processing neurons and clustering neurons is proportional to the similarity between the input pattern and the feature vector (the top-down weights) of the clustering neuron. The mathematical model governing the evolution of the signal transmission delay, the short-term memory traces, and the long-term memory traces represents a new class of large-scale delay differential equations where the evolution of the delay is described by a nonlinear differential equation involving the similarity measure already noted. We give a complete description of the computational performance of the network for a wide range of parameter values.

In this paper we propose a new framework for designing a delay differential equation (DDE) solver which works with any supplied initial value problem (IVP) solver that is based on a standard step-by-step approach, such as Runge-Kutta or linear multi-step methods, and can provide dense output. This is done by treating a general DDE as a special example of a discontinuous IVP. Using this interpretation we develop an efficient technique to solve the resulting discontinuous IVP. We also give a more clear process for the numerical techniques used when solving the implicit equations that arise on a time step, such as when the underlying IVP solver is implicit or the delay vanishes.The new modular design for the resulting simulator we introduce, helps to accelerate the utilization of advances in the different components of an effective numerical method. Such components include the underlying discrete formula, the interpolant for dense output, the strategy for handling discontinuities and the iteration scheme for solving any implicit equations that arise.

In this paper, we derive an equation governing the dynamics of firstorder forward sensitivities for a general system of parametric neutral delay differential equations (NDDEs). We also derive a formula which identifies the size of jumps that appear at discontinuity points when the sensitivity equations are integrated. The formula leads to an algorithm which can compute sensitivities for various types of parameters very accurately and efficiently.