Guided waves in a fluid layer on an elastic irregular bottom

In this paper one considers the linearized problem to determine the movement of an ideal heavy fluid contained in an unbounded container withelastic walls. As initial data one knows the movement of both the bottom and the free surface of the fluid and also the strength of certain perturbation, strong enough to take the bottom out of its rest state. One important point to be considered regards the influence of the bottom's geometry on the propagation of superficial waves. This problem has been already studied in other works without considering the elastic properties of the bottom and considering a cilindrical container with bounded section

Vector-borne disease risk indexes in spatially structured populations

There are economic and physical limitations when applying prevention and control strategies for urban vector borne diseases. Consequently, there are increasing concerns and interest in designing efficient strategies and regulations that health agencies can follow in order to reduce the imminent impact of viruses like Dengue, Zika and Chikungunya. That includes fumigation, abatization, reducing the hatcheries, picking up trash, information campaigns. A basic question that arise when designing control strategies is about which and where these ones should focus. In other words, one would like to know whether preventing the contagion or decrease vector population, and in which area of the city, is more efficient. In this work, we propose risk indexes based on the idea of secondary cases from patch to patch. Thus, they take into account human mobility and indicate which patch has more chance to be a corridor for the spread of the disease and which is more vulnerable. They can also indicate the neighborhood where hatchery control will reduce more the number of potential cases. In order to illustrate the usefulness of these indexes, we run a set of numerical simulations in a mathematical model that takes into account the urban mobility and the differences in population density among the areas of a city. If i is a particular neighborhood, the transmission risk index TR_i measures the potential secondary cases caused by a host in that neighborhood. The vector transmission risk index VTR_i measures the potential secondary cases caused by a vector. Finally, the vulnerability risk index VR_i measures the potential secondary cases in the neighborhood. Transmission indexes can be used to give geographical priority to some neighborhoods when applying prevention and control measures. On the other hand, the vulnerability index can be useful to implement monitoring campaigns or public health investment.Comment: 16 pages, 5 figure

Increased efficiency in the second-hand tire trade provides opportunity for dengue control

Dengue fever is increasing in geographical range, spread by invasion of its vector mosquitoes. The trade in second-hand tires has been implicated as a factor in this process because they act as mobile reservoirs of mosquito eggs and larvae. Regional transportation of tires can create linkages between rural areas with dengue and disease-free urban areas, potentially giving rise to outbreaks even in areas with strong local control measures. In this work we sought to model the dynamics of mosquito transportation via the tire trade, in particular to predict its role in causing unexpected dengue outbreaks through vertical transmission of the virus across generations of mosquitoes. We also aimed to identify strategies for regulating the trade in second-hand tires, improving disease control. We created a mathematical model which captures the dynamics of dengue between rural and urban areas, taking into account the movement and storage time of tires, and mosquito diapause. We simulate a series of scenarios in which a mosquito population is introduced to a dengue-free area via movement of tires, either as single or multiple events, increasing the likelihood of a dengue outbreak. A persistent disease state can be induced regardless of whether urban conditions for an outbreak are met, and an existing endemic state can be enhanced by vector input. Finally we assess the potential for regulation of tire processing as a means of reducing the transmission of dengue fever using a specific case study from Puerto Rico. Our work demonstrates the importance of the second-hand tire trade in modulating the spread of dengue fever across regions, in particular its role in introducing dengue to disease-free areas. We propose that reduction of tire storage time and control of their movement can play a crucial role in containing dengue outbreaks

Guided waves in a fluid layer on an elastic irregular bottom

In this paper one considers the linearized problem to determine the movement of an ideal heavy fluid contained in an unbounded container withelastic walls. As initial data one knows the movement of both the bottom and the free surface of the fluid and also the strength of certain perturbation, strong enough to take the bottom out of its rest state. One important point to be considered regards the influence of the bottom's geometry on the propagation of superficial waves. This problem has been already studied in other works without considering the elastic properties of the bottom and considering a cilindrical container with bounded section

An optimal quasi solution for the cauchy problem for laplace equation in the framework of inverse ECG

The inverse ECG problem is set as a boundary data completion for the Laplace equation: at each time the potential is measured on the torso and its normal derivative is null. One aims at reconstructing the potential on the heart. A new regularization scheme is applied to obtain an optimal regularization strategy for the boundary data completion problem. We consider the R n+1 domain Ω. The piecewise regular boundary of Ω is defined as the union ∂Ω = Γ1 ∪ Γ0 ∪ Σ, where Γ1 and Γ0 are disjoint, regular, and n-dimensional surfaces. Cauchy boundary data is given in Γ0, and null Dirichlet data in Σ, while no data is given in Γ1. This scheme is based on two concepts: admissible output data for an ill-posed inverse problem, and the conditionally well-posed approach of an inverse problem. An admissible data is the Cauchy data in Γ0 corresponding to an harmonic function in C 2 (Ω) ∩ H 1 (Ω). The methodology roughly consists of first characterizing the admissible Cauchy data, then finding the minimum distance projection in the L 2-norm from the measured Cauchy data to the subset of admissible data characterized by given a priori information, and finally solving the Cauchy problem with the aforementioned projection instead of the original measurement

Time series of the model (8)–(12) for different values of the carrying capacity <i>C</i>, and the parameters values given in Table 1 with <i>β</i> = 0.67.

<p>Time series of the model <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e020" target="_blank">(8)</a>–<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e024" target="_blank">(12)</a> for different values of the carrying capacity <i>C</i>, and the parameters values given in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.t001" target="_blank">Table 1</a> with <i>β</i> = 0.67.</p

Dynamics of the infected population system-wide with control applied in different patches.

<p>(a) In a fully connected network the vector transmission index <i>VTR</i>_<i>i</i> is greater in patch 2. (b) In a Barabasi-Albert network the patch with largest vector transmissibility is number 4 as indicated by its <i>VTR</i>_<i>i</i>. The most effective strategy at the beginning of the outbreak is to reduce the carrying capacity in the patch with greatest <i>VTR</i>_<i>i</i>.</p

Description and estimated value of the model parameters ([30, 31]).

<p>Description and estimated value of the model parameters ([<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.ref030" target="_blank">30</a>, <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.ref031" target="_blank">31</a>]).</p

Time series of the multiple patch connected according to the dwell-time matrix <i>P</i>_{<i>e</i>.<i>g</i>.1} given in (19).

<p>Time series of the multiple patch connected according to the dwell-time matrix <i>P</i>_{<i>e</i>.<i>g</i>.1} given in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0006234#pntd.0006234.e037" target="_blank">(19)</a>.</p

Dynamics of the number of infected humans per patch in a network of 5 nodes for a fully connected network (a) and a Barabasi-Albert network (b).

<p>In (a) the vulnerability index <i>VR</i>_<i>i</i> indicates patch 3 (red line) as the most vulnerable and in (b) the most vulnerable as indicated by <i>VR</i>_<i>i</i> is patch 1 (red line). The most vulnerable patch corresponds to the one with more cases at the beginning of the epidemic (let say <i>t</i> ≤ 50).</p