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Register a new userSystem inference for the spatio-temporal evolution of infectious diseases: Michigan in the time of COVID-19
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We extend the classical SIR model of infectious disease spread to account for time dependence in the parameters, which also include diffusivities. The temporal dependence accounts for the changing characteristics of testing, quarantine and treatment protocols, while diffusivity incorporates a mobile population. This model has been applied to data on the evolution of the COVID-19 pandemic in the US state of Michigan. For system inference, we use recent advances; specifically our framework for Variational System Identification (Wang et al., Comp. Meth. App. Mech. Eng., 356, 44-74, 2019; arXiv:2001.04816 [cs.CE]) as well as Bayesian machine learning methods.
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We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased (SIRD) compartmental model of epidemiology, which is achieved by replacing compartmental populations by their densities. Building on our recent work (Computational Mechanics, 66, 1177, 2020), we replace our earlier use of global polynomial basis functions with those having local support, as epitomized in the finite element method, for the spatial representation of the SIRD parameters. The time dependence is treated by inferring constant parameters over time intervals that coincide with the time step in semi-discrete numerical implementations. In combination, this amounts to a scheme of field inversion of the SIRD parameters over each time step. Applied to data over ten months of 2020 for the pandemic in the US state of Michigan and to all of Mexico, our system inference via field inversion infers spatio-temporally varying PDE SIRD parameters that replicate the progression of the pandemic with high accuracy. It also produces accurate predictions, when compared against data, for a three week period into 2021. Of note is the insight that is suggested on the spatio-temporal variation of infection, recovery and death rates, as well as patterns of the populations mobility revealed by diffusivities of the compartments.
A reasonable prediction of infectious diseases transmission process under different disease control strategies is an important reference point for policy makers. Here we established a dynamic transmission model via Python and realized comprehensive regulation of disease control measures. We classified government interventions into three categories and introduced three parameters as descriptions for the key points in disease control, these being intraregional growth rate, interregional communication rate, and detection rate of infectors. Our simulation predicts the infection by COVID-19 in the UK would be out of control in 73 days without any interventions; at the same time, herd immunity acquisition will begin from the epicentre. After we introduced government interventions, single intervention is effective in disease control but at huge expense while combined interventions would be more efficient, among which, enhancing detection number is crucial in control strategy of COVID-19. In addition, we calculated requirements for the most effective vaccination strategy based on infection number in real situation. Our model was programmed with iterative algorithms, and visualized via cellular automata, it can be applied to similar epidemics in other regions if the basic parameters are inputted, and is able to synthetically mimick the effect of multiple factors in infectious disease control.
The world evolution of the Severe acute respiratory syndrome coronavirus 2 (SARS-Cov2 or simply COVID-19) led the World Health Organization to declare it a pandemic. The disease appeared in China in December 2019, and it has spread fast around the world, specially in european countries like Italy and Spain. The first reported case in Brazil was recorded in February 26, and after that the number of cases growed fast. In order to slow down the initial growth of the disease through the country, confirmed positive cases were isolated to not transmit the disease. To better understand the early evolution of COVID-19 in Brazil, we apply a Susceptible-Infectious-Quarantined-Recovered (SIQR) model to the analysis of data from the Brazilian Department of Health, obtained from February 26, 2020 through March 25, 2020. Based on analyical and numerical results, as well on the data, the basic reproduction number is estimated to $R_{0}=5.25$. In addition, we estimate that the ratio unidentified infectious individuals and confirmed cases at the beginning of the epidemic is about $10$, in agreement with previous studies. We also estimated the epidemic doubling time to be $2.72$ days.
In this paper, we apply statistical methods for functional data to explain the heterogeneity in the evolution of number of deaths of Covid-19 over different regions. We treat the cumulative daily number of deaths in a specific region as a curve (functional data) such that the data comprise of a set of curves over a cross-section of locations. We start by using clustering methods for functional data to identify potential heterogeneity in the curves and their functional derivatives. This first stage is an unconditional descriptive analysis, as we do not use any covariate to estimate the clusters. The estimated clusters are analyzed as levels of alert to identify cities in a possible critical situation. In the second and final stage, we propose a functional quantile regression model of the death curves on a number of scalar socioeconomic and demographic indicators in order to investigate their functional effects at different levels of the cumulative number of deaths over time. The proposed model showed a superior predictive capacity by providing better curve fit at different levels of the cumulative number of deaths compared to the functional regression model based on ordinary least squares.
In this research, we study the propagation patterns of epidemic diseases such as the COVID-19 coronavirus, from a mathematical modeling perspective. The study is based on an extensions of the well-known susceptible-infected-recovered (SIR) family of compartmental models. It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world. As with all mathematical models, the predictive ability of the model is limited by the accuracy of the available data and to the so-called textit{level of abstraction} used for modeling the problem. In order to provide the broader audience of researchers a better understanding of spreading patterns of epidemic diseases, a short introduction on biological systems modeling is also presented and the Matlab source codes for the simulations are provided online.
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