Quantitative Biology

We present a new mathematical model to explicitly capture the effects that the three restriction measures: the lockdown date and duration, social distancing and masks, and, schools and border closing, have in controlling the spread of COVID-19 infections i(r,t) . Before restrictions were introduced, the random spread of infections as described by the SEIR model grew exponentially. The addition of control measures introduces a mixing of order and disorder in the system's evolution which fall under a different mathematical class of models that can eventually lead to critical phenomena. A generic analytical solution is hard to obtain. We use machine learning to solve the new equations for i(r,t) , the infections i in any region r at time t and derive predictions for the spread of infections over time as a function of the strength of the specific measure taken and their duration. The machine is trained in all of the COVID-19 published data for each region, county, state, and country in the world. It utilizes optimization to learn the best-fit values of the model's parameters from past data in each region in the world, and it updates the predicted infections curves for any future restrictions that may be added or relaxed anywhere. We hope this interdisciplinary effort, a new mathematical model that predicts the impact of each measure in slowing down infection spread combined with the solving power of machine learning, is a useful tool in the fight against the current pandemic and potentially future ones.

The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ( S ) and two different infectious groups ( I 1 and I 2 ). Once infected, an individual becomes a member of one of these infectious groups which have different clinical forms of infection. In addition, during the progress of the illness, an infected individual in group I 1 may pass to the infectious group I 2 which has a higher mortality rate. In this study, positiveness of the solutions for the model is proved. Stability analysis of species extinction, I 1 -free equilibrium and endemic equilibrium as well as disease-free equilibrium is studied. Relation between the basic reproduction number of the disease and the basic reproduction number of each infectious stage is examined. The model is investigated under a specific condition and its exact solution is obtained.

Dry eye disease (DED) affects approximately half of the United States population. DED is characterized by dryness on the corena surface due to a variety of causes. This study fills the spatiotemporal gaps in DED epidemiology by using Google Trends as a novel epidemiological tool for geographically mapping DED in relation to environmental risk factors. We utilized Google Trends to extract DED-related queries estimating user intent from 2004-2019 in the United States. We incorporated national climate data to generate heat maps comparing geographic, temporal, and environmental relationships of DED. Multi-variable regression models were constructed to generate quadratic forecasts predicting DED and control searches. Our results illustrated the upward trend, seasonal pattern, environmental influence, and spatial relationship of DED search volume across US geography. Localized patches of DED interest were visualized along the coastline. There was no significant difference in DED queries across US census regions. Regression model 1 predicted DED searches over time (R^2=0.97) with significant predictors being control queries (p=0.0024), time (p=0.001), and seasonality (Winter p=0.0028; Spring p<0.001; Summer p=0.018). Regression model 2 predicted DED queries per state (R^2=0.49) with significant predictors being temperature (p=0.0003) and coastal zone (p=0.025). Importantly, temperature, coastal status, and seasonality were stronger risk factors of DED searches than humidity, sunshine, pollution, or region as clinical literature may suggest. Our work paves the way for future exploration of geographic information systems for locating DED and other diseases via online search query metrics.

In this paper, we formulate a Nonlinear Model Predictive Control (NMPC) to plan appropriate social distancing measures (and relaxations) in order to mitigate the COVID-19 pandemic effects, considering the contagion development in Brazil. The NMPC strategy is designed upon an adapted data-driven Susceptible-Infected-Recovered-Deceased (SIRD) contagion model, which takes into account the effects of social distancing. Furthermore, the adapted SIRD model includes time-varying auto-regressive contagion parameters, which dynamically converge according to the stage of the pandemic. This new model is identified through a three-layered procedures, with analytical regressions, Least-Squares optimization runs and auto-regressive model fits. The data-driven model is validated and shown to adequately describe the contagion curves over large forecast horizons. In this model, control input is defined as finitely parametrized values for social distancing guidelines, which directly affect the transmission and infection rates of the SARS-CoV-2 virus. The NMPC strategy generates piece-wise constant quarantine guidelines which can be relaxed/strengthen as each week passes. The implementation of the method is pursued through a search mechanism, since the control is finitely parametrized and, thus, there exist a finite number of possible control sequences. Simulation essays are shown to illustrate the results obtained with the proposed closed-loop NMPC strategy, which is able to mitigate the number of infections and progressively loosen social distancing measures. With respect to an "open-loop"/no control condition, the number of deaths still could be reduced in up to 30 %. The forecast preview an infection peak to September 2nd, 2020, which could lead to over 1.5 million deaths if no coordinate health policy is enacted. The framework serves as guidelines for possible public health policies in Brazil.

The outbreaks of Coronavirus Disease 2019 (COVID-19) have impacted the world significantly. Modeling the trend of infection and real-time forecasting of cases can help decision making and control of the disease spread. However, data-driven methods such as recurrent neural networks (RNN) can perform poorly due to limited daily samples in time. In this work, we develop an integrated spatiotemporal model based on the epidemic differential equations (SIR) and RNN. The former after simplification and discretization is a compact model of temporal infection trend of a region while the latter models the effect of nearest neighboring regions. The latter captures latent spatial information. %that is not publicly reported. We trained and tested our model on COVID-19 data in Italy, and show that it out-performs existing temporal models (fully connected NN, SIR, ARIMA) in 1-day, 3-day, and 1-week ahead forecasting especially in the regime of limited training data.

In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by countries and the state of Texas in the USA. The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot. Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions. Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures. We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020. By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease.

Governments around the world have implemented preventive measures against the spread of the coronavirus disease (COVID-19). In this study, we consider a multivariate discrete-time Markov model to analyze the propagation of COVID-19 across 33 provincial regions in China. This approach enables us to evaluate the effect of mobility restriction policies on the spread of the disease. We use data on daily human mobility across regions and apply the Bayesian framework to estimate the proposed model. The results show that the spread of the disease in China was predominately driven by community transmission within regions and the lockdown policy introduced by local governments curbed the spread of the pandemic. Further, we document that Hubei was only the epicenter of the early epidemic stage. Secondary epicenters, such as Beijing and Guangdong, had already become established by late January 2020, and the disease spread out to connected regions. The transmission from these epicenters substantially declined following the introduction of human mobility restrictions across regions.

Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of infection models correspond to three chemical species. Areal densities emerge as the key variables, thus capturing the effect of spatial density. We derive expressions for the kinetics of the infection rates and for the important parameter R0, that include areal density and its spatial distribution. Coupled with mobility the model allows the study of various effects. We first present results for a batch reactor, the chemical process equivalent of the SIR model. Because density makes R0 a decreasing function of the process extent, the infection curves are different and smaller than for the standard SIR model. We show that the effect of the initial conditions is limited to the onset of the epidemic. We derive effective infection curves for a number of cases, including a back-and-forth commute between regions of low and high R0 environments. We then consider spatially distributed systems. We show that diffusion leads to traveling waves, which in 1-D geometries propagate at a constant speed and with a constant shape, both of which are sole functions of R0. The infection curves are slightly different than for the batch problem, as diffusion mitigates the infection intensity, thus leading to an effective lower R0. The dimensional wave speed is found to be proportional to the product of the square root of the diffusivity and of an increasing function of R0, confirming the importance of restricting mobility in arresting the propagation of infection. We examine the interaction of infection waves under various conditions and scenarios, and extend the wave propagation analysis to 2-D heterogeneous systems.

In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while minimizing the costs incurred by the introduction of societal control measures (such as closing schools, social distancing, lockdowns, etc.), under the constraint that the infected fraction of the population does never exceed a certain maximum corresponding to public health system capacity. Optimality is derived and verified by variational and numerical methods for a number of model cost functions. The effects of immune response decay after recovery are taken into account and discussed in terms of the feasibility of strategies based on herd immunity.

Movement is fundamental to life, shaping population dynamics, biodiversity patterns, and ecosystem structure. Recent advances in tracking technology have enabled fundamental questions about movement to be tackled, leading to the development of the movement ecology framework (MEF), considered a milestone in the field [1]. The MEF introduced an integrative theory of organismal movement, linking internal state, motion capacity and navigation capacity to external factors. Here, a decade later, we investigated the current state of research in the field. Using a text mining approach on >8000 peer-reviewed papers in movement ecology, we explored the main research topics, evaluated the impact of the MEF, and assessed changes in the use of technological devices, software and statistical methods. The number of publications has increased considerably and there have been major technological changes in the past decade (i.e.~increased use of GPS devices, accelerometers and video cameras, and a convergence towards R), yet we found that research focuses on the same questions, specifically, on the effect of environmental factors on movement and behavior. In practice, it appears that movement ecology research does not reflect the MEF. We call on researchers to transform the field from technology-driven to embrace interdisciplinary collaboration, in order to reveal key processes underlying movement (e.g.~navigation), as well as evolutionary, physiological and life-history consequences of particular strategies.