Aedes-AI: Neural network models of mosquito abundance.

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.

EpiCovDA: a mechanistic COVID-19 forecasting model with data assimilation.

We introduce a minimalist outbreak forecasting model that combines data-driven parameter estimation with variational data assimilation. By focusing on the fundamental components of nonlinear disease transmission and representing data in a domain where model stochasticity simplifies into a process with independent increments, we design an approach that only requires four core parameters to be estimated. We illustrate this novel methodology on COVID-19 forecasts. Results include case count and deaths predictions for the US and all of its 50 states, the District of Columbia, and Puerto Rico. The method is computationally efficient and is not disease- or location-specific. It may therefore be applied to other outbreaks or other countries, provided case counts and/or deaths data are available.

Parameter estimation from ICC curves.

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.

Collaborative efforts to forecast seasonal influenza in the United States, 2015-2016.

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.

Summary results of the 2014-2015 DARPA Chikungunya challenge.

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.

The phase structure of grain boundaries.

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'.

Aedes aegypti (Diptera: Culicidae) Abundance Model Improved With Relative Humidity and Precipitation-Driven Egg Hatching.

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 temperature-dependent 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.

Effect of Temperature Thresholds on Modeled Aedes aegypti (Diptera: Culicidae) Population Dynamics.

Dynamic simulation models provide vector abundance estimates using only meteorological data. However, model outcomes may heavily depend on the assumptions used to parameterize them. We conducted a sensitivity analysis for a model of Aedes aegypti (L.) abundance using weather data from two locations where this vector is established, La Margarita, Puerto Rico and Tucson, Arizona. We tested the effect of simplifying temperature-dependent development and mortality rates and of changing development and mortality thresholds as compared with baselines estimated using biophysical models. The simplified development and mortality rates had limited effect on abundance estimates in either location. However, in Tucson, where the vector is established but has not transmitted viruses, a difference of 5 °C resulted in populations either surviving or collapsing in the hot Arizona mid-summer, depending on the temperature thresholds. We find three important implications of the observed sensitivity to temperature thresholds. First, this analysis indicates the need for better estimates of the temperature tolerance thresholds to refine entomologic risk mapping for disease vectors. Second, our results highlight the importance of extreme temperatures on vector survival at the marginal areas of this vector's distribution. Finally, the model suggests that adaptation to warmer temperatures may shift regions of pathogen transmission.

Data-driven outbreak forecasting with a simple nonlinear growth model.

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Projection of Climate Change Influences on U.S. West Nile Virus Vectors.

While estimates of the impact of climate change on health are necessary for health care planners and climate change policy makers, models to produce quantitative estimates remain scarce. We describe a freely available dynamic simulation model parameterized for three West Nile virus vectors, which provides an effective tool for studying vector-borne disease risk due to climate change. The Dynamic Mosquito Simulation Model is parameterized with species specific temperature-dependent development and mortality rates. Using downscaled daily weather data, we estimate mosquito population dynamics under current and projected future climate scenarios for multiple locations across the country. Trends in mosquito abundance were variable by location, however, an extension of the vector activity periods, and by extension disease risk, was almost uniformly observed. Importantly, mid-summer decreases in abundance may be off-set by shorter extrinsic incubation periods resulting in a greater proportion of infective mosquitoes. Quantitative descriptions of the effect of temperature on the virus and mosquito are critical to developing models of future disease risk.

Reduced models for the pacemaker dynamics of cardiac cells.

We introduce three- and two-dimensional biophysical models of cardiac excitability derived from a 14-dimensional model of the sinus venosus [Rasmusson, R., et al., 1990. Am. J. Physiol. 259, H352-369]. The reduced models capture normal pacemaking dynamics with a small complement of ionic currents. The two-dimensional model bears some similarities with the Morris-Lecar model [Morris, C., Lecar, H., 1981. Biophysical Journal, 35, 193-213]. Because they were reduced from a biophysical model, both models depend on parameters that were obtained from experimental data. Even though the correspondence with the original model is not exact, parameters may be adjusted to tune the reductions to fit experimental traces. As a consequence, unlike other generic low-dimensional models, the models introduced here provide a means to relate physiologically relevant characteristics of pacemaker potentials such as diastolic depolarization, plateau, and action potential frequency, to biophysical variables such as the relative abundance of membrane channels and channel kinetic rates. In particular, these models can lead to an explicit description of how the shape of cardiac action potentials depends on the relative contributions and states of inward and outward currents. By being physiologically derived and computationally efficient, the models presented in this article are useful tools for theoretical studies of excitability at the cellular and network levels.