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, i.e. more likely to have cases?. 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 we label by i a particular neighborhood, the transmission risk index (TRi) measures the potential secondary cases caused by a host in that neighborhood. The vector transmission risk index (VTRi) measures the potential secondary cases caused by a vector. Finally, the vulnerability risk index (VRi) 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.

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In view of the serious health problems concerning infectious diseases in heavily populated areas, we followed the strategy of lead compound diversification to evaluate the near-by chemical space for new organic compounds. To this end, twenty derivatives of nitazoxanide (NTZ) were synthesized and tested for activity against Entamoeba histolytica parasites. To ensure drug-likeliness and activity relatedness of the new compounds, the synthetic work was assisted by a quantitative structure-activity relationships study (QSAR). Many of the inherent downsides – well-known to QSAR practitioners – we circumvented thanks to workarounds which we proposed in prior QSAR publication. To gain further mechanistic insight on a molecular level, ligand-enzyme docking simulations were carried out since NTZ is known to inhibit the protozoal pyruvate ferredoxin oxidoreductase (PFOR) enzyme as its biomolecular target.

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 ℝn+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 C2(Ω) ∩H1(Ω). The methodology roughly consists of first characterizing the admissible Cauchy data, then finding the minimum distance projection in the L2-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.

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