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Incidence vs. Cumulative Cases (ICC) curves are introduced and shown to provide a simple framework for parameter identification in the case of the most elementary epidemiological model, consisting of susceptible, infected, and removed compartments. This novel methodology is used to estimate the basic reproduction ratio of recent outbreaks, including those associated with the ongoing COVID-19 pandemic.

Since 2013, the Centers for Disease Control and Prevention (CDC) has hosted an annual influenza season forecasting challenge. The 2015–2016 challenge consisted of weekly probabilistic forecasts of multiple targets, including fourteen models submitted by eleven teams. Forecast skill was evaluated using a modified logarithmic score. We averaged submitted forecasts into a mean ensemble model and compared them against predictions based on historical trends. Forecast skill was highest for seasonal peak intensity and short-term forecasts, while forecast skill for timing of season onset and peak week was generally low. Higher forecast skill was associated with team participation in previous influenza forecasting challenges and utilization of ensemble forecasting techniques. The mean ensemble consistently performed well and outperformed historical trend predictions. CDC and contributing teams will continue to advance influenza forecasting and work to improve the accuracy and reliability of forecasts to facilitate increased incorporation into public health response efforts.

We present artificial neural networks as a feasible replacement for a mechanistic model of mosquito abundance. We develop a feed-forward neural network, a long short-term memory recurrent neural network, and a gated recurrent unit network. We evaluate the networks in their ability to replicate the spatiotemporal features of mosquito populations predicted by the mechanistic model, and discuss how augmenting the training data with time series that emphasize specific dynamical behaviors affects model performance. We conclude with an outlook on how such equation-free models may facilitate vector control or the estimation of disease risk at arbitrary spatial scales.

Background : Emerging pathogens such as Zika, chikungunya, Ebola, and dengue viruses are serious threats to national and global health security. Accurate forecasts of emerging epidemics and their severity are critical to minimizing subsequent mortality, morbidity, and economic loss. The recent introduction of chikungunya and Zika virus to the Americas underscores the need for better methods for disease surveillance and forecasting. Methods : To explore the suitability of current approaches to forecasting emerging diseases, the Defense Advanced Research Projects Agency (DARPA) launched the 2014–2015 DARPA Chikungunya Challenge to forecast the number of cases and spread of chikungunya disease in the Americas. Challenge participants ( n =38 during final evaluation) provided predictions of chikungunya epidemics across the Americas for a six-month period, from September 1, 2014 to February 16, 2015, to be evaluated by comparison with incidence data reported to the Pan American Health Organization (PAHO). This manuscript presents an overview of the challenge and a summary of the approaches used by the winners. Results : Participant submissions were evaluated by a team of non-competing government subject matter experts based on numerical accuracy and methodology. Although this manuscript does not include in-depth analyses of the results, cursory analyses suggest that simpler models appear to outperform more complex approaches that included, for example, demographic information and transportation dynamics, due to the reporting biases, which can be implicitly captured in statistical models. Mosquito-dynamics, population specific information, and dengue-specific information correlated best with prediction accuracy. Conclusion : We conclude that with careful consideration and understanding of the relative advantages and disadvantages of particular methods, implementation of an effective prediction system is feasible. However, there is a need to improve the quality of the data in order to more accurately predict the course of epidemics.

This article discusses numerical and analytical results on grain boundaries, which are line defects that separate roll patterns oriented in different directions. The work is set in the context of a canonical pattern-forming system, the Swift–Hohenberg (SH) equation, and of its phase diffusion equation, the regularized Cross–Newell equation. It is well known that, as the angle made by the rolls on each side of a grain boundary is decreased, dislocations appear at the core of the defect. Our goal is to shed some light on this transition, which provides an example of defect formation in a system that is variational. Numerical results of the SH equation that aim to analyse the phase structure of far-from-threshold grain boundaries are presented. These observations are then connected to properties of the associated phase diffusion equation. Outcomes of this work regarding the role played by phase derivatives in the creation of defects in pattern-forming systems, about the role of harmonic analysis in understanding the phase structure in such systems, and future research directions are also discussed. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

We propose an improved Aedes aegypti (L.) abundance model that takes into account the effect of relative humidity (RH) on adult survival, as well as rainfall-triggered egg hatching. The model uses temperaturedependent development rates described in the literature as well as documented estimates for mosquito survival in environments with high RH, and for egg desiccation. We show that combining the two additional components leads to better agreement with surveillance trap data and with dengue incidence reports in various municipalities of Puerto Rico than incorporating either alone or neither. Capitalizing on the positive association between disease incidence and vector abundance, this improved model is therefore useful to estimate incidence of Ae. aegypti-borne diseases in locations where the vector is abundant year-round.

This article discusses numerical and analytical results on grain boundaries, which are line defects that separate roll patterns oriented in different directions. The work is set in the context of a canonical pattern-forming system, the Swift–Hohenberg (SH) equation, and of its phase diffusion equation, the regularized Cross–Newell equation. It is well known that, as the angle made by the rolls on each side of a grain boundary is decreased, dislocations appear at the core of the defect. Our goal is to shed some light on this transition, which provides an example of defect formation in a system that is variational. Numerical results of the SH equation that aim to analyse the phase structure of far-from-threshold grain boundaries are presented. These observations are then connected to properties of the associated phase diffusion equation. Outcomes of this work regarding the role played by phase derivatives in the creation of defects in pattern-forming systems, about the role of harmonic analysis in understanding the phase structure in such systems, and future research directions are also discussed. This article is part of the theme issue ‘Stability of nonlinear waves and patterns and related topics’.

We describe a third-year undergraduate course that focuses on multiscale modeling and protein folding and has as its primary goal the encouragement of students to integrate thinking across and beyond disciplinary boundaries. The ability to perform innovative and successful research work in STEM (science, technology, engineering, and mathematics) fields is often dependent on being aware of the multiple connections between the sciences, but how to develop such an integrated perspective is rarely taught in college classes. Designed for STEM majors, the course combines laboratory sessions and lectures, assessed through student journals and oral presentations. We report on some of the activities we developed for this course and on the associated outcomes. A syllabus, an assessment, and interview questions, as well as examples of student responses, are provided as supplementary materials. The course topics discussed in this article include an analogy between desiccated corn starch and basaltic columns, a discussion of the size of trees, diffusion at the microscopic and macroscopic levels, and computational aspects of protein folding. Teaching materials, including handouts, experimental methods, and MATLAB codes, as well as student journals, are available from the course website.

This article corrects [Collective behaviors in two-dimensional systems of interacting particles, SIAM J. Appl. Dyn. Syst., 10 (2011), pp. 1213--1231]. [PUBLICATION ABSTRACT]