Enteric disease surveillance under the AFHSC-GEIS: current efforts, landscape analysis and vision forward.

The mission of the Armed Forces Health Surveillance Center, Division of Global Emerging Infections Surveillance and Response System (AFHSC-GEIS) is to support global public health and to counter infectious disease threats to the United States Armed Forces, including newly identified agents or those increasing in incidence. Enteric diseases are a growing threat to U.S. forces, which must be ready to deploy to austere environments where the risk of exposure to enteropathogens may be significant and where routine prevention efforts may be impractical. In this report, the authors review the recent activities of AFHSC-GEIS partner laboratories in regards to enteric disease surveillance, prevention and response. Each partner identified recent accomplishments, including support for regional networks. AFHSC/GEIS partners also completed a Strengths, Weaknesses, Opportunities and Threats (SWOT) survey as part of a landscape analysis of global enteric surveillance efforts. The current strengths of this network include excellent laboratory infrastructure, equipment and personnel that provide the opportunity for high-quality epidemiological studies and test platforms for point-of-care diagnostics. Weaknesses include inconsistent guidance and a splintered reporting system that hampers the comparison of data across regions or longitudinally. The newly chartered Enterics Surveillance Steering Committee (ESSC) is intended to provide clear mission guidance, a structured project review process, and central data management and analysis in support of rationally directed enteric disease surveillance efforts.

Modeling electrocortical activity through improved local approximations of integral neural field equations.

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat "patchy" connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a "lattice-directed" traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.

A systematic analysis of average molecular weights and gelation conditions for branched immune complexes: the interaction between a multivalent antigen with distinct epitopes and many different types of bivalent antibodies.

A systematic model, based on standard equilibrium expressions and probability theory, is presented to calculate average molecular weights and gelation conditions for the immune system consisting of a single type of antigens with three (or more) different epitopes and three (or more) types of bivalent antibodies. Molecular weights Mn, Mw, Mz, and any other higher average molecular weights of formed branched antigen-antibody complexes in such an immune system are calculated directly without determining the whole distribution. The conditions for the formation of gel complexes also can be determined by this model.

Modeling the average molecular weights of antigen-antibody complexes by probability theory.

A method is presented to calculate average molecular weights for linear antigen-antibody complexes. Instead of determining the whole distributions and then using the distributions to calculate average properties, this method allows one to calculate the number-average, the weight-average, and the z-average molecular weights of the linear antigen-antibody complexes directly based on elementary probability theory and the recursive nature of antigen-antibody complexes.

Degenerate Hopf bifurcation and isolated periodic solutions of the Hodgkin-Huxley model with varying sodium ion concentration.

Points of degenerate Hopf bifurcation in the Hodgkin-Huxley model are found as parameters temperature T and voltage level of sodium VNa are varied. Local techniques of degenerate Hopf bifurcation analysis are used to show the existence of families of periodic solutions of the model: isolated branches of periodic solutions (i.e. branches not connected to the stationary branch) are found in addition to Hopf branches. Purely numerical techniques are used to show that the isolas persist for VNa up to a value slightly greater than 114 mV. Under some conditions there are multiple stable periodic solutions, so "jumping" between action potentials of different amplitudes might be observed.

Isolated periodic solutions of the Hodgkin-Huxley equations.

Periodic solutions of the current clamped Hodgkin-Huxley equations (Hodgkin & Huxley, 1952 J. Physiol. 117, 500) that arise by degenerate Hopf bifurcation were studied recently by Labouriau (1985 SIAM J. Math. Anal. 16, 1121, 1987 Degenerate Hopf Bifurcation and Nerve Impulse (Part II), in press). Two parameters, temperature T and sodium conductance gNa were varied from the original values obtained by Hodgkin & Huxley. Labouriau's work proved the existence of small amplitude periodic solution branches that do not connect locally to the stationary solution branch, and had not been previously computed. In this paper we compute these solution branches globally. We find families of isolas of periodic solutions (i.e. branches not connected to the stationary branch). For values of gNa in the range measured by Hodgkin & Huxley, and for physically reasonable temperatures, there are isolas containing orbitally asymptotically stable solutions. The presence of isolas of periodic solutions suggests that in certain current space clamped membrane experiments, action potentials could be observed even though the stationary state is stable for all current stimuli. Once produced, such action potentials will disappear suddenly if the current stimulus is either increased or decreased past certain values. Under some conditions, "jumping" between action potentials of different amplitudes might be observed.