On the dynamics of a class of multi-group models for vector-borne diseases

The resurgence of vector-borne diseases is an increasing public health concern, and there is a need for a better understanding of their dynamics. For a number of diseases, e.g. dengue and chikungunya, this resurgence occurs mostly in urban environments, which are naturally very heterogeneous, particularly due to population circulation. In this scenario, there is an increasing interest in both multi-patch and multi-group models for such diseases. In this work, we study the dynamics of a vector borne disease within a class of multi-group models that extends the classical Bailey-Dietz model. This class includes many of the proposed models in the literature, and it can accommodate various functional forms of the infection force. For such models, the vector-host/host-vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases. Under the assumption that the contact network is strongly connected, we can define the basic reproductive number $\mathcal{R}_0$ and show that this system has only two equilibria: the so called disease free equilibrium (DFE); and a unique interior equilibrium---usually termed the endemic equilibrium (EE)---that exists if, and only if, $\mathcal{R}_0>1$. We also show that, if $\mathcal{R}_0\leq1$, then the DFE equilibrium is globally asymptotically stable, while when $\mathcal{R}_0>1$, we have that the EE is globally asymptotically stable

Enhancing Nervous System Recovery through Neurobiologics, Neural Interface Training, and Neurorehabilitation.

After an initial period of recovery, human neurological injury has long been thought to be static. In order to improve quality of life for those suffering from stroke, spinal cord injury, or traumatic brain injury, researchers have been working to restore the nervous system and reduce neurological deficits through a number of mechanisms. For example, neurobiologists have been identifying and manipulating components of the intra- and extracellular milieu to alter the regenerative potential of neurons, neuro-engineers have been producing brain-machine and neural interfaces that circumvent lesions to restore functionality, and neurorehabilitation experts have been developing new ways to revitalize the nervous system even in chronic disease. While each of these areas holds promise, their individual paths to clinical relevance remain difficult. Nonetheless, these methods are now able to synergistically enhance recovery of native motor function to levels which were previously believed to be impossible. Furthermore, such recovery can even persist after training, and for the first time there is evidence of functional axonal regrowth and rewiring in the central nervous system of animal models. To attain this type of regeneration, rehabilitation paradigms that pair cortically-based intent with activation of affected circuits and positive neurofeedback appear to be required-a phenomenon which raises new and far reaching questions about the underlying relationship between conscious action and neural repair. For this reason, we argue that multi-modal therapy will be necessary to facilitate a truly robust recovery, and that the success of investigational microscopic techniques may depend on their integration into macroscopic frameworks that include task-based neurorehabilitation. We further identify critical components of future neural repair strategies and explore the most updated knowledge, progress, and challenges in the fields of cellular neuronal repair, neural interfacing, and neurorehabilitation, all with the goal of better understanding neurological injury and how to improve recovery

A non-standard evolution problem arising in population genetics

We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries, supplemented by a pair of conservation laws. It is readily shown that no classical or standard weak solution definition yields solvability of the problem. We provide an appropriate definition of weak solution for the problem, for which we show existence and uniqueness. The solution displays a very distinctive structure and, for large time, we show convergence to a unique stationary solution that turns out to be a singular measure supported at the endpoints. An exponential rate of convergence to this steady state is also proved.Comment: 16 pages. Proposition 4 statement and proof corrected. Also a number of typos has been fixe

Topology counts: force distributions in circular spring networks

Filamentous polymer networks govern the mechanical properties of many biological materials. Force distributions within these networks are typically highly inhomogeneous and, although the importance of force distributions for structural properties is well recognized, they are far from being understood quantitatively. Using a combination of probabilistic and graph-theoretical techniques we derive force distributions in a model system consisting of ensembles of random linear spring networks on a circle. We show that characteristic quantities, such as mean and variance of the force supported by individual springs, can be derived explicitly in terms of only two parameters: (i) average connectivity and (ii) number of nodes. Our analysis shows that a classical mean-field approach fails to capture these characteristic quantities correctly. In contrast, we demonstrate that network topology is a crucial determinant of force distributions in an elastic spring network.Comment: 5 pages, 4 figures. Missing labels in Fig. 4 added. Reference fixe

Wire mesh design

We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods

Adherence to artemether/lumefantrine treatment in children under real-life situations in rural Tanzania.

A follow-up study was conducted to determine the magnitude of and factors related to adherence to artemether/lumefantrine (ALu) treatment in rural settings in Tanzania. Children in five villages of Kilosa District treated at health facilities were followed-up at their homes on Day 7 after the first dose of ALu. For those found to be positive using a rapid diagnostic test for malaria and treated with ALu, their caretakers were interviewed on drug administration habits. In addition, capillary blood samples were collected on Day 7 to determine lumefantrine concentrations. The majority of children (392/444; 88.3%) were reported to have received all doses, in time. Non-adherence was due to untimeliness rather than missing doses and was highest for the last two doses. No significant difference was found between blood lumefantrine concentrations among adherent (median 286 nmol/l) and non-adherent [median 261 nmol/l; range 25 nmol/l (limit of quantification) to 9318 nmol/l]. Children from less poor households were more likely to adhere to therapy than the poor [odds ratio (OR)=2.45, 95% CI 1.35-4.45; adjusted OR=2.23, 95% CI 1.20-4.13]. The high reported rate of adherence to ALu in rural areas is encouraging and needs to be preserved to reduce the risk of emergence of resistant strains. The age-based dosage schedule and lack of adherence to ALu treatment guidelines by health facility staff may explain both the huge variability in observed lumefantrine concentrations and the lack of difference in concentrations between the two groups