Vector-borne epidemics are progressively becoming a global burden, especially those related to flaviviruses, and the effects of different factors such as climate change or the increase of human mobility can sensibly increase the population at risk worldwide. Such outbreaks are the result of the combination of different factors including crossed contagions between humans and vectors, their demographic distribution and human mobility among others. The current availability of information about all those ingredients demands their incorporation into current mathematical models for vector-borne disease transmission. Here, relying on a Markovian formulation of the metapopulation dynamics, we propose a framework that explicitly includes human-vector interactions, mobility, and demography. The analysis of the framework allows us not only to derive an expression of the epidemic threshold capturing the conditions for the onset of the epidemics but also to highlight some unseen features of vector-borne epidemics, such as abrupt changes in the unfolding patterns of the disease for small variations of the degree of mobility. Finally, driven by these insights, we obtain a prevalence indicator to rank populations according to their risk of being affected by a vector-borne disease. We illustrate the utility of this indicator by reproducing the spatial distribution Dengue cases reported in the city of Santiago de Cali (Colombia) from 2015 to 2016.

This paper develops a unified theory for establishing the local and q-superlinear convergence of quasi-Newton methods from the convex class when part of the Hessian matrix is known. One first proves the bounded deterioration principle due to Dennis (and popularized by Broyden, Dennis, and Moré) for the appropriate modifications of all update formulas in the convex Broyden class. Using standard conditions on the quasi-Newton updates, one then deduces local and q-superlinear convergence. Particular cases of these methods are the SQP augmented scale BFGS and DFP secant methods for constrained optimization problems introduced by Tapia and a generalization of the Al-Baali and Fletcher modification of the structured secant method considered by Dennis, Gay, and Welsch for the nonlinear least-squares problem. In all cases, bounded deterioration is proved for the approximate Hessian, not for its inverse.

The purpose of this paper is to study the Fishbone Warehouse layout. Fishbone layouts are non-traditional designs for warehouses that have shown to be more efficient under unit-load operations. This paper presents an analytical study of the design from an optimisation point of view. The authors gain an insight into the characteristics of the layout and present alternatives for different situations of interest in industrial environments. Finally, the authors compare the performance of Fishbone and traditional designs; presenting a formal conception of the expected savings. The authors focus on finding optimal conditions for the most important characteristic of the Fishbone design, which is the slope of the diagonal cross-aisle. The design decisions are modelled as a non-linear optimisation problem and solved using both numerical and exact methods, depending on the most convenient analysis. In addition, the robustness of the results is presented and their practical implications discussed

This paper focuses on the design and analysis of short-term control intervention measures seeking to suppress local populations of Aedes aegypti mosquitoes, the major transmitters of dengue and other vector-borne infections. Besides traditional measures involving the spraying of larvicides and/or insecticides, we include biological control based on the deliberate introduction of predacious species feeding on the aquatic stages of mosquitoes. From the methodological standpoint, our study relies on application of the optimal control modeling framework in combination with the cost-effectiveness analysis. This approach not only enables the design of optimal strategies for external control intervention but also allows for assessment of their performance in terms of the cost-benefit relationship. By examining numerous scenarios derived from combinations of chemical and biological control measures, we try to find out whether the presence of predacious species at the mosquito breeding sites may (partially) replace the common practices of larvicide/insecticide spraying and thus reduce their negative impact on non-target organisms. As a result, we identify two strategies exhibiting the best metrics of cost-effectiveness and provide some useful insights for their possible implementation in practical settings.