Fig 1 - uploaded by Kevin E. M. Church
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Schematic drawing of a solution of the relay model in the case α = 0. The two vector fields are drawn simultaneously, corresponding respectively to β 0 (green arrows) and β 1 (blue arrows). The upper and lower black lines respectively represent I = I C and I = I R . On black dashed lines the solution satisfies σ = 0 and on the dotted line it satisfies σ = 1. Between each switching, the solution follows the vector field corresponding to the value of σ.
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Moving averages and other functional forecasting models are used to inform policy in pandemic response. In this paper, we analyze an infectious disease model in which the contact rate switches between two levels when the moving average of active cases crosses one of two thresholds. The switching mechanism naturally forces the existence of periodic...
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Citations
... Traditional mathematical models use compartmental models to study the transmission dynamics of COVID-19, such as SIR and SEIR models and their variants, see Gao et al. [3], Church [4], Neves and Guerrero [5], Ng and Gui [6]. Miranda et al. [7] construct a hybrid ODE-network model for the COVID-19 pandemic accounting for certain spatial aspects. ...
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... Proof. To complete the proof, one can first run the script [9] proof cycle.m in MATLAB with an INTLAB license (tested on v11) installed. In order, this script performs the following steps. ...
Moving averages and other functional forecasting models are used to inform policy in pandemic response. In this paper, we analyze an infectious disease model in which the contact rate switches between two levels when the moving average of active cases crosses one of two thresholds. The switching mechanism naturally forces the existence of periodic orbits. In order to make unbiased comparisons between periodic orbits in this model and a traditional one where the contact rate switches based on more simplistic pointwise evaluations of active cases, we use a rigorous homotopy continuation method. We develop computer-assisted proofs that can validate the continuation and prove that the branch of periodic orbits has no folds and is isolated in the space of periodic solutions. This allows a direct, rigorous comparison between the geometric and quantitative properties of the cycles with a moving average threshold and a pointwise threshold. We demonstrate the effectiveness of the method on a sample problem modeled off of the COVID-19 pandemic in the City of Montreal.
The rapid spread of COVID-19 disease has had a significant impact on the world. In this paper, we study COVID-19 data interpretation and visualization using open-data sources for 351 cities and towns in Massachusetts from December 6, 2020 to September 25, 2021. Because cities are embedded in rather complex transportation networks, we construct the spatio-temporal dynamic graph model, in which the graph attention neural network is utilized as a deep learning method to learn the pandemic transition probability among major cities in Massachusetts. Using the spectral graph wavelet transform (SGWT), we process the COVID-19 data on the dynamic graph, which enables us to design effective tools to analyze and detect spatio-temporal patterns in the pandemic spreading. We design a new node classification method, which effectively identifies the anomaly cities based on spectral graph wavelet coefficients. It can assist administrations or public health organizations in monitoring the spread of the pandemic and developing preventive measures. Unlike most work focusing on the evolution of confirmed cases over time, we focus on the spatio-temporal patterns of pandemic evolution among cities. Through the data analysis and visualization, a better understanding of the epidemiological development at the city level is obtained and can be helpful with city-specific surveillance.
