key: cord-1044051-x7yb1rq0
authors: Jamshidi, B.; Jamshidi Zargaran, S.; Talaei-Khoei, A.; Kakavandi, M.
title: Modelling and Forecasting The Number of Confirmed Cases and Deaths from COVID-19 Pandemic in USA from April 12th to May 21st, 2020
date: 2020-11-04
journal: nan
DOI: 10.1101/2020.10.30.20223412
sha: 4c289cfa471a1aeec400fb72f4fd53060afe82a8
doc_id: 1044051
cord_uid: x7yb1rq0

In the present paper, our objective is to forecast the spread of the pandemic of COVID-19 in terms of the number of confirmed cases and deaths. The paper is based on a two-part to model the time series of the daily relative increments whose second part solely models the pattern of the death rate. All the simulations and calculations have been done in MatLab R2015b, and the average curves and confidence intervals are calculated based on 100 simulations of the fitted models. Our results establish that the cumulative number of confirmed cases reach 1464729 cases on 21 May 2020, with 80% confidence interval of [1375362 1540424], and the number of new confirmed cases decreases to the interval [12801 22578] with the probability of 80% (the point prediction is equal to 17551) on 21 May 2020. Finally, we forecast that the cumulative number of deaths from 18747 cases on 11 April increases to around 47000 cases on 21 May.

An epidemic disease of unknown cause, now called COVID-19, found in Wuhan, China was first reported to the World Health Organization Office in China on 31 December 2019. Shortly after, it was found that the ongoing pandemic is an infectious disease caused by 50 the coronaviruses, a large family of viruses that cause illness ranging from the common cold to more severe diseases such as MERS and SARS. The outbreak was declared as a Public Health Emergency worldwide on 30 January 2020. Based on its geographic spread, severity of illnesses it causes, and also its impact on society, on March (Biggerstaff et al., 2016) . Similar challenges was also organized for 100 Ebola (Viboud et al., 2018) , and Dengue (NOAA, 2016) . The literature in time series forecasting has used aberrancy-detection algorithms to identify temporal changes in the data. These temporal changes may be the indicator of epidemic outbreaks (Murphy and Burkom, 2008) . The . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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Early Aberration Reporting Systems from Centres for Disease Control 105 and Prevention utilizes C algorithms. However, C algorithms suffer from short-term prediction capabilities (Tokars et al., 2015) . General speaking, aberrancy-detection algorithms focuses on a single time point in a given time when the outbreaks occurs and they are limited to be used to forecast the number of confirmed cases in the future of outbreak 110 (Kass-Hout et al., 2012) . Zhang (2003) suggests the use of Autoregressive Integrated Moving Average (ARIMA) to address the shortfall of aberrancy-detection algorithms. ARIMA models have been largely used in forecasting infectious diseases such as dengue (Wongkoon et al., 2012) and tuberculosis (Rios et al., 2000) . ARIMA 115 models are committed to the assumption that in the Autoregressive model under the study, the present value of the time series is a linear function of the past values and random noise (Akaike, 1969) . Second, the present value of the time series is a linear function of present and past residuals in the moving average model (Haining, 1978) . Third, 120 ARIMA is based on both Autoregressive and moving average as well as the past values and residuals (Rojas et al., 2008) . These assumptions limit the flexibility of ARIMA models to reproduce the different stages of time series.

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The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101 https://doi.org/10. /2020 in the US, we can confirm that this is the case, See Day 0: 145 27 February 2020, Day 45: 12 April 2020. Figure 1 . Secondly, at any time, the time series of relative increase in the confirmed cases holds a normal distribution. The COVID-19 in the US demonstrates a normal distribution for the relative increase of the confirmed cases. Third, over time, the ratio of variance to mean 150 remains constant, which is the case for COVID-19 in the US.

The present paper relates to the recent articles attempting to model the spread of the COVID-19 19 (Berger et al., 2020; Kucharski et al., 2020; Read et al., 2020 CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101 https://doi.org/10. /2020 mainly looks at time series analysis to forecast the newly confirmed cases. 165 The rest of this paper is organized in the following way, Section 2 presents the proposed method. Section 3 presents the results of our forecast. Section 0 discusses the paper and provides some limitations as well as directions for future research. 

In this section, we will discuss the proposed model, and the estimations. We will also simulate the model and the estimation on the data from the US to forecast for the next 40 days. The . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10. 1101 /2020 February to 11 April 2020 and the paper forecasts from 12 April to 21May, 2020. ), which confirms the third assumption of our time series, See Section 1.

: The adjusting coefficient for the curve ‫ݐ‬ ି ఏ to fit the time series of the relative increment after the first period of the spread.

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The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10. 1101 /2020 The estimation of the proposed time series for the US Data of COVID-19 would be discussed in the next subsection. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

I n t h i s s e c t i o n , w e d i s c u s s o n h o w t h e t i m e s e r i e s e x p l a i n e d a b o v e w i l l f i t t o t h e C O V I D - 1 9 d a t a f r o m t h e U S . T o e s t i m a t e t h e 215 p a r a m e t e r s o f t h e m o d e l , t h e f o l l o w i n g p r a c t i c e s m u s t b e t a k e n : • t a k e ܾ a s t h e f i r s t p o i n t t h a t t h e g e o m e t r i c m e a n o f t h e r e l a t i v e i n c r e m e n t s i n t h e p r e v i o u s p o i n t s e x c e e d s 3 / 2 t i m e s t h e g e o m e t r i c m e a n o f t h e n e x t t h r e e p o i n t s . ܾ ൌ m i n ሼ ݊ | ‫ܩ‬ ݁ ‫‬ . ݉ ݁ ܽ ݊ ሺ ܺ ା ଵ , ܺ ା ଶ , ܺ ା ଷ ሻ ൏ 2 3 ‫ܩ‬ ݁ ‫‬ . ݉ ݁ ܽ ݊ ሺ ܺ ଵ , ܺ ଶ , … , ܺ ሻ ሽ which can be computed as 220 ܾ ൌ m i n ሼ ݊ | ඥ ሺ 1 ܺ ା ଵ ሻ ሺ 1 ܺ ା ଶ ሻ ሺ ܺ ା ଷ ሻ య െ 1 ൏ 2 3 ඥ ሺ 1 ܺ ଵ ሻ ሺ 1 ܺ ଶ ሻ … ሺ ܺ ሻ െ 1 ሽ G r a p h i c a l l y , t h i s t i m e c a n b e i d e n t i f i e d a

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The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101/2020.10.30.20223412 doi: medRxiv preprint . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10.1101/2020.10.30.20223412 doi: medRxiv preprint we use five different forecasting output variables, namely 80% lower bound, 80% upper bound, average and two possible realizations. In the first 10 days of April, the variable is fluctuate around 30000 while our prediction says that this variable decreases to [12801 22578] with the probability of 80% (the point prediction is equal to 17551) on 290 21 May 2020.

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The copyright holder for this preprint this version posted November 4, 2020. K .

It means we will encounter with about 1350 daily Mortalities on average over the studied period. The slope of the increasing graph for the cumulative number of Mortalities is falling as well as the graph of 305 the cumulative number of confirmed cases.

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The copyright holder for this preprint this version posted November 4, 2020. 117 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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cases in the US, from 12 April to 21 May, 2020.

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The copyright holder for this preprint this version posted November 4, 2020. ; https://doi.org/10. 1101 /2020 Day 0: 11 April 2020, Day 40: 21 May 2020. 

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