key: cord-346185-qmu1mrmx
authors: Velásquez, Ricardo Manuel Arias; Lara, Jennifer Vanessa Mejia
title: Forecast and evaluation of COVID-19 spreading in USA with Reduced-space Gaussian process regression
date: 2020-05-22
journal: Chaos Solitons Fractals
DOI: 10.1016/j.chaos.2020.109924
sha: 
doc_id: 346185
cord_uid: qmu1mrmx

In this report, we analyze historical and forecast infections for COVID-19 death based on Reduced-Space Gaussian Process Regression associated to chaotic Dynamical Systems with information obtained in 82 days with continuous learning, day by day, from January 21(th), 2020 to April 12(th). According last results, COVID-19 could be predicted with Gaussian models mean-field models can be meaning- fully used to gather a quantitative picture of the epidemic spreading, with infections, fatality and recovery rate. The forecast places the peak in USA around July 14(th) 2020, with a peak number of 132,074 death with infected individuals of about 1,157,796 and a number of deaths at the end of the epidemics of about 132,800. Late on January, USA confirmed the first patient with COVID-19, who had recently traveled to China, however, an evaluation of states in USA have demonstrated a fatality rate in China (4%) is lower than New York (4.56%), but lower than Michigan (5.69%). Mean estimates and uncertainty bounds for both USA and his cities and other provinces have increased in the last three months, with focus on New York, New Jersey, Michigan, California, Massachusetts,... (January e April 12(th)). Besides, we propose a Reduced-Space Gaussian Process Regression model predicts that the epidemic will reach saturation in USA on July 2020. Our findings suggest, new quarantine actions with more restrictions for containment strategies implemented in USA could be successfully, but in a late period, it could generate critical rate infections and death for the next 2 month.

able on the Center for Systems Science and Engineering at Johns Hopkins University [6] , the available data analyzed is considered between January 21 th 2020 and April 39 12 th 2020, included, with a feedback process in a neural network applied; it allows 40 to examined the information in real time in each state, at Fig. 1 • . With COVID-19, the spatial representation of the disease by using GIS plat-73 form allows to verified the "material, population and social psychology at three 74 scales: individual,group and regional" [9] ; in this case, with GIS technology is 75 necessary to implement big data techniques, for cross validations and analysis. 

• Associated to GPR the idea is to "utilize nonlinear diffusion map coordinates 79 and formulate a deterministic dynamical system on the system manifold" [12] .

A interesting approach has a reduced-space data-driven dynamical system with 81 an evaluation, with efficiency with low intrinsic dimensionality.

• An "advantage of employing GPR to reconstruct the reduced-order dynamics 83 is the simultaneous estimation of the dynamics and the associated uncertaint" with an input xn ∈ R and "noisy scalar output yn" [11] . For infection population, 

Where: 

Where: 119

θ 1 : Is a hyper-parameter with maximum covariance in chaotic systems. 132

In Eq. (9), Bayes rule is written with a normalized process to find (f, f * ) in Eq. (10).

In Eq. (11), associates to "conditioning the joint Gaussian prior distribution on 134 the observations, resulting in the closed-form Gaussian distribution" [12] . With Eq.

(12), f * , the mean and covariance should be directly added to obtain Eq. (13).

136

Finally, in Eq.(14) makes feasible to use up to more than twelve thousands of training x ∈ R

In the Eq. (16), individually node in the hidden layer has "linear combination" [18] 152 with a chain events. The hidden layers are composed as following: 

In Eq. (18) describes a matrix of weights, it is analogous to regression coefficient in

Where:

172 h: it is a description of the hidden layer, due to restriction of the "linearly trans-173 formed and passed to the output layer". However, China has implemented robust strategies for distancing control and quar-206 antine around this country, therefore, the recovery rate is 90%. Far away from New 207 York, with recovery rate of 9.42% and on the other hand, cities as Texas is 13.09%.

Besides, Hawaii has different rate of 56.79% for the restrictions initiated with more 209 influence in their population.

Combining a mathematical model with multiple datasets, Fig. 6 and Fig. 7 , we 211 found that the median daily Rt of COVID-19 in USA probably varied between 2.6 212 and 5.6 in April, 2020, before 3 weeks of travel restrictions were introduced. We In traditional methods, we detect mistakes in the forecast associated to old pan-269 demic researches, and as we can see, the COVID-19 has behaved in unpredictable 270 and changing ways, according to the factors used in its treatment. Therefore, we 271 think that the pandemic behaves as a dynamic-chaotic system, which sets new start-272 ing points that do not intersect and changes its behavior according to the way it 273 is treated. Consequently, this study could be a real contribution for understanding 274 this problem with a good tool of processing a systematic review. As we can see 275 in the Fig. 9 , the example started with three countries, with three initial states. 276 Hence they have been evolving together until some days, but after a month, they 

Grants/financial support.

None.

Credit authorship contribution statement. Conflict of interest.

There is no conflict of interest in this work. 

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Acknowledgments.
