Has wild poliovirus been eliminated from Nigeria?

Wild poliovirus type 3 (WPV3) has not been seen anywhere since the last case of WPV3-associated paralysis in Nigeria in November 2012. At the time of writing, the most recent case of wild poliovirus type 1 (WPV1) in Nigeria occurred in July 2014, and WPV1 has not been seen in Africa since a case in Somalia in August 2014. No cases associated with circulating vaccine-derived type 2 poliovirus (cVDPV2) have been detected in Nigeria since November 2014. Has WPV1 been eliminated from Africa? Has WPV3 been eradicated globally? Has Nigeria interrupted cVDPV2 transmission? These questions are difficult because polio surveillance is based on paralysis and paralysis only occurs in a small fraction of infections. This report provides estimates for the probabilities of poliovirus elimination in Nigeria given available data as of March 31, 2015. It is based on a model of disease transmission that is built from historical polio incidence rates and is designed to represent the uncertainties in transmission dynamics and poliovirus detection that are fundamental to interpreting long time periods without cases. The model estimates that, as of March 31, 2015, the probability of WPV1 elimination in Nigeria is 84%, and that if WPV1 has not been eliminated, a new case will be detected with 99% probability by the end of 2015. The probability of WPV3 elimination (and thus global eradication) is >99%. However, it is unlikely that the ongoing transmission of cVDPV2 has been interrupted; the probability of cVDPV2 elimination rises to 83% if no new cases are detected by April 2016. Added July 10, 2015: On June 26, a cVDPV2 case was confirmed by the Global Polio Laboratory Network. The date of paralysis was May 16. The case provides new information about cVDPV2 prevalence that is useful for assessing the accuracy of previous predictions and informing an updated forecast for the time to cVDPV2 elimination.Comment: Added model validation section and updated cVDPV2 forecast in response to new case data; expanded material on surveillance sensitivity; additional minor edits; and references added. 24 pages, 4 figure

Implications of single-neuron gain scaling for information transmission in networks

Summary: 

Many neural systems are equipped with mechanisms to efficiently encode sensory information. To represent natural stimuli with time-varying statistical properties, neural systems should adjust their gain to the inputs' statistical distribution. Such matching of dynamic range to input statistics has been shown to maximize the information transmitted by the output spike trains (Brenner et al., 2000, Fairhall et al., 2001). Gain scaling has not only been observed as a system response property, but also in single neurons in developing somatosensory cortex stimulated with currents of different amplitude (Mease et al., 2010). While gain scaling holds for cortical neurons at the end of the first post-natal week, at birth these neurons lack this property. The observed improvement in gain scaling coincides with the disappearance of spontaneous waves of activity in cortex (Conheim et al., 2010).

We studied how single-neuron gain scaling affects the dynamics of signal transmission in networks, using the developing cortex as a model. In a one-layer feedforward network, we showed that the absence of gain control made the network relatively insensitive to uncorrelated local input fluctuations. As a result, these neurons selectively and synchronously responded to large slowly-varying correlated input--the slow build up of synaptic noise generated in pacemaker circuits which most likely triggers waves. Neurons in gain scaling networks were more sensitive to the small-scale input fluctuations, and responded asynchronously to the slow envelope. Thus, gain scaling both increases information in individual neurons about private inputs and allows the population average to encode the slow fluctuations in the input. Paradoxically, the synchronous firing that corresponds to wave propagation is associated with low information transfer. We therefore suggest that the emergence of gain scaling may help the system to increase information transmission on multiple timescales as sensory stimuli become important later in development. 

Methods:

Networks with one and two layers consisting of hundreds of model neurons were constructed. The ability of single neurons to gain scale was controlled by changing the ratio of sodium to potassium conductances in Hodgkin-Huxley neurons (Mainen et al., 1995). The response of single layer networks was studied with ramp-like stimuli with slopes that varied over several hundreds of milliseconds. Fast fluctuations were superimposed on this slowly-varying mean. Then the response to these networks was tested with continuous stimuli. Gain scaling networks captured the slow fluctuations in the inputs, while non-scaling networks simply thresholded the input. Quantifying information transmission confirmed that gain scaling neurons transmit more information about the stimulus. With the two-layer networks we simulated a cortical network where waves could spontaneously emerge, propagate and degrade, based on the gain scaling properties of the neurons in the network

Feature selection in simple neurons: how coding depends on spiking dynamics

The relationship between a neuron's complex inputs and its spiking output defines the neuron's coding strategy. This is frequently and effectively modeled phenomenologically by one or more linear filters that extract the components of the stimulus that are relevant for triggering spikes, and a nonlinear function that relates stimulus to firing probability. In many sensory systems, these two components of the coding strategy are found to adapt to changes in the statistics of the inputs, in such a way as to improve information transmission. Here, we show for two simple neuron models how feature selectivity as captured by the spike-triggered average depends both on the parameters of the model and on the statistical characteristics of the input.Comment: 23 Pages, LaTeX + 4 Figures. v2 is substantially expanded and revised. v3 corrects minor errors in Sec. 3.

Probabilistic Neural Coding from Deterministic Neural Dynamics: mathematics and biophysics of adaptive single neuron computation

Thesis (Ph.D.)--University of Washington, 2012The basic unit of computation in the nervous system is the transformation of input into output spikes performed by an individual neuron. The spiking response of the neuron to a complex, time-varying input can be characterized with two different classes of models: nonlinear dynamical systems represent the detailed biophysical properties a neuron, and probabilistic black box coding models identify abstract representations of the computation performed. However, the relationships between biophysical mechanisms and neural coding properties have very rarely been resolved. Here, the focus is on the task of feature selection, where a neuron extracts and encodes from its complex inputs a small number of relevant signal components. Feature selection is generally adaptive: both the relevant features and the encoding depend on the background statistical context in which the signal appears. This thesis presents a theory of conditional dynamical processes that associate abstract representations of the signal with sub-ensembles of states of the corresponding dynamical system. The theory provides a bridge to use meth- ods from either coding or dynamics to simultaneously study both. The unifying framework is used to derive how the interactions of the statistical properties of the input and the neural dynamics determine which features of the input are encoded by spikes. Adaptation of the encoding to changes in input statistics is shown to arise from corresponding changes in how the state space of the nonlinear system is probed by the input. First, we identify the mechanisms of adaptive feature selection in integrate-and-fire mod- els. Then, we demonstrate that integrate-and-fire models without any additional currents can perform a novel type of stochastically-emergent perfect contrast gain control--a sophis- ticated adaptive computation. We identify the general dynamical principles responsible and design from first principles a nonlinear dynamical model that implements automatic gain control. We conclude by fitting models to experimental data and relating the models to measurable biophysical properties to demonstrate that our proposed theoretical mechanism is consistent with the adaptive gain control observed in the developing cortex

Historical polio incidence in Nigeria.

<p>Polio case counts in 3 month bins: WPV1 (A), WPV3 (C), cVDPV2 (E). Inferred growth rate (and reproductive number for <i>μ</i> = 26 yr⁻¹): WPV1 (B), WPV3 (D), cVDPV2 (F). Note that while the overall case counts vary over time by two orders of magnitude, the reproductive number mean and range are stable. This motivates the assumption that transmission dynamics are stable among the populations that support ongoing transmission even as the number of such populations is lower now than a decade ago.</p

Model results for elimation and time to next case.

<p>Probability of elimination assuming no new cases are observed: WPV1 (A), WPV3 (C), cVDPV2 (E). Probability of observing a new case if elimination doesn’t occur, WPV1 (B), WPV3 (D), cVDPV2 (F). Fig prepared March 31, 2015 (black dashed line). In each panel, the horizontal axis origin is the time of the most recent case, the solid blue curve shows the scenario with mean <i>R</i>_eff = 1 and perfect surveillance, the green curve shows a less conservative scenario with mean <i>R</i>_eff < 1 and perfect surveillance, and the dashed blue curve shows a conservative scenario with mean <i>R</i>_eff = 1 and 50% surveillance sensitivity. For cVDPV2 (C,F), the orange curve depicts an optimistic scenario in which the mean <i>R</i>_eff is held at the lowest value ever observed and the standard deviation is reduced to one-fourth of its observed value.</p