Syndromic Surveillance Using Structured Telehealth Data: Case Study of the First Wave of COVID-19 in Brazil.

BACKGROUND: Telehealth has been widely used for new case detection and telemonitoring during the COVID-19 pandemic. It safely provides access to health care services and expands assistance to remote, rural areas and underserved communities in situations of shortage of specialized health professionals. Qualified data are systematically collected by health care workers containing information on suspected cases and can be used as a proxy of disease spread for surveillance purposes. However, the use of this approach for syndromic surveillance has yet to be explored. Besides, the mathematical modeling of epidemics is a well-established field that has been successfully used for tracking the spread of SARS-CoV-2 infection, supporting the decision-making process on diverse aspects of public health response to the COVID-19 pandemic. The response of the current models depends on the quality of input data, particularly the transmission rate, initial conditions, and other parameters present in compartmental models. Telehealth systems may feed numerical models developed to model virus spread in a specific region. OBJECTIVE: Herein, we evaluated whether a high-quality data set obtained from a state-based telehealth service could be used to forecast the geographical spread of new cases of COVID-19 and to feed computational models of disease spread. METHODS: We analyzed structured data obtained from a statewide toll-free telehealth service during 4 months following the first notification of COVID-19 in the Bahia state, Brazil. Structured data were collected during teletriage by a health team of medical students supervised by physicians. Data were registered in a responsive web application for planning and surveillance purposes. The data set was designed to quickly identify users, city, residence neighborhood, date, sex, age, and COVID-19-like symptoms. We performed a temporal-spatial comparison of calls reporting COVID-19-like symptoms and notification of COVID-19 cases. The number of calls was used as a proxy of exposed individuals to feed a mathematical model called "susceptible, exposed, infected, recovered, deceased." RESULTS: For 181 (43%) out of 417 municipalities of Bahia, the first call to the telehealth service reporting COVID-19-like symptoms preceded the first notification of the disease. The calls preceded, on average, 30 days of the notification of COVID-19 in the municipalities of the state of Bahia, Brazil. Additionally, data obtained by the telehealth service were used to effectively reproduce the spread of COVID-19 in Salvador, the capital of the state, using the "susceptible, exposed, infected, recovered, deceased" model to simulate the spatiotemporal spread of the disease. CONCLUSIONS: Data from telehealth services confer high effectiveness in anticipating new waves of COVID-19 and may help understand the epidemic dynamics.

Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.

The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction-diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction-diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction-diffusion model for describing local dynamics.

Data-Driven Simulation of Fisher-Kolmogorov Tumor Growth Models Using Dynamic Mode Decomposition.

The computer simulation of organ-scale biomechanistic models of cancer personalized via routinely collected clinical and imaging data enables to obtain patient-specific predictions of tumor growth and treatment response over the anatomy of the patient's affected organ. These patient-specific computational forecasts have been regarded as a promising approach to personalize the clinical management of cancer and derive optimal treatment plans for individual patients, which constitute timely and critical needs in clinical oncology. However, the computer simulation of the underlying spatiotemporal models can entail a prohibitive computational cost, which constitutes a barrier to the successful development of clinically-actionable computational technologies for personalized tumor forecasting. To address this issue, here we propose to utilize dynamic-mode decomposition (DMD) to construct a low-dimensional representation of cancer models and accelerate their simulation. DMD is an unsupervised machine learning method based on the singular value decomposition that has proven useful in many applications as both a predictive and a diagnostic tool. We show that DMD may be applied to Fisher-Kolmogorov models, which constitute an established formulation to represent untreated solid tumor growth that can further accommodate other relevant cancer phenomena (e.g., therapeutic effects, mechanical deformation). Our results show that a DMD implementation of this model over a clinically relevant parameter space can yield promising predictions, with short to medium-term errors remaining under 1% and long-term errors remaining under 20%, despite very short training periods. In particular, we have found that, for moderate to high tumor cell diffusivity and low to moderate tumor cell proliferation rate, DMD reconstructions provide accurate, bounded-error reconstructions for all tested training periods. Additionally, we also show that the three-dimensional DMD reconstruction of the tumor field can be leveraged to accurately reconstruct the displacement fields of the tumor-induced deformation of the host tissue. Thus, we posit the proposed data-driven approach has the potential to greatly reduce the computational overhead of personalized simulations of cancer models, thereby facilitating tumor forecasting, parameter identification, uncertainty quantification, and treatment optimization.

Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations.

Dynamic mode decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The classical procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion-reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD's ability to extrapolate in time (short-time future estimates).

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil.

The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models.

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.