Mathematical analysis of a stochastic model for spread of Coronavirus

Babaei, Afshin; Jafari, Hossein; Banihashemi, Seddigheh; Ahmadi, M.

doi:10.1016/j.chaos.2021.110788

Cited by 43 publications

(19 citation statements)

References 24 publications

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“… [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] .…”

Section: Uncited Referencesunclassified

Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods

et al. 2021

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The first known case of Coronavirus disease 2019 (COVID-19) was identified in December 2019. It has spread worldwide, leading to an ongoing pandemic, imposed restrictions and costs to many countries. Predicting the number of new cases and deaths during this period can be a useful step in predicting the costs and facilities required in the future. The purpose of this study is to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days. The motivation for predicting every n days (instead of just every day) is the investigation of the possibility of computational cost reduction and still achieving reasonable performance. Such a scenario may be encountered in real-time forecasting of time series. Six different deep learning methods are examined on the data adopted from the WHO website. Three methods are LSTM, Convolutional LSTM, and GRU. The bidirectional extension is then considered for each method to forecast the rate of new cases and new deaths in Australia and Iran countries. This study is novel as it carries out a comprehensive evaluation of the aforementioned three deep learning methods and their bidirectional extensions to perform prediction on COVID-19 new cases and new death rate time series. To the best of our knowledge, this is the first time that Bi-GRU and Bi-Conv-LSTM models are used for prediction on COVID-19 new cases and new deaths time series. The evaluation of the methods is presented in the form of graphs and Friedman statistical test. The results show that the bidirectional models have lower errors than other models. A several error evaluation metrics are presented to compare all models, and finally, the superiority of bidirectional methods is determined. This research could be useful for organisations working against COVID-19 and determining their long-term plans.

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Section: Uncited Referencesunclassified

Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods

et al. 2021

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“…In general, different stochastic computations [7,8] and numerical methods [9][10][11][12][13][14] are exploited to assess the various aspects of the COVID-19 outbreak. In this sense, Katoch et al used the autoregressive integrated moving average (ARIMA) model to forecast the COVID-19 dynamics in India [15].…”

Section: Sars-cov-2 (Covid-19mentioning

confidence: 99%

Network Autoregressive Model for the Prediction of COVID-19 Considering the Disease Interaction in Neighboring Countries

Khoojine

Shadabfar

Hosseini

et al. 2021

Entropy

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Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of total currently infected cases with coronavirus disease 2019 (COVID-19) in Iran until the end of December 2021 in view of the disease interactions within the neighboring countries in the region. For this purpose, the COVID-19 data were initially collected for seven regional nations, including Iran, Turkey, Iraq, Azerbaijan, Armenia, Afghanistan, and Pakistan. Thenceforth, a network was established over these countries, and the correlation of the disease data was calculated. Upon introducing the main structure of the NAR model, a mathematical platform was subsequently provided to further incorporate the correlation matrix into the prediction process. In addition, the maximum likelihood estimation (MLE) was utilized to determine the model parameters and optimize the forecasting accuracy. Thereafter, the number of infected cases up to December 2021 in Iran was predicted by importing the correlation matrix into the NAR model formed to observe the impact of the disease interactions in the neighboring countries. In addition, the autoregressive integrated moving average (ARIMA) was used as a benchmark to compare and validate the NAR model outcomes. The results reveal that COVID-19 data in Iran have passed the fifth peak and continue on a downward trend to bring the number of total currently infected cases below 480,000 by the end of 2021. Additionally, 20%, 50%, 80% and 95% quantiles are provided along with the point estimation to model the uncertainty in the forecast.

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“…However, while checking with great care predictions done while using this analysis, one will easily see that this analysis cannot help humans predict waves in spread. For example, several mathematical models have been suggested to predict the spread of Covid-19, unwillingly no analysis help to predict the numbers of waves that humans will faced by Covid-19 spread [5][6][7][8][9][10][11][12]. In fact, some researchers showed that, the reproductive number was not su¢ cient to provide a clear behavior of the spread, although no attention was paid to such analysis, one will agree that suggested mathematical models and analysis done in the last decades have not really help to predict waves.…”

Section: Introductionmentioning

confidence: 99%

Advanced analysis in epidemiological modeling: Detection of wave

Atangana

Araz

2021

Preprint

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Some mathematical concepts have been used in the last decades to predict the behavior of spread of infectious diseases. Among them, the reproductive number concept has been used in several published papers for study the stability of the spread. Some conditions were suggested to predict there would be either stability or instability. An analysis was also suggested to determine conditions under which infectious classes will increase or die out. Some authors pointed out limitations of the reproductive number, as they presented its inability to fairly help understand the spread patterns. The concept of strength number and analysis of second derivatives of the mathematical models were suggested as additional tools to help detect waves. In this paper, we aim at applying these additional analyses in a simple model to predict the future. Keywords: Strength number, second derivative analysis, waves, piecewise modeling.

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Mathematical analysis of a stochastic model for spread of Coronavirus

Cited by 43 publications

References 24 publications

Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods

Time series forecasting of new cases and new deaths rate for COVID-19 using deep learning methods

Network Autoregressive Model for the Prediction of COVID-19 Considering the Disease Interaction in Neighboring Countries

Advanced analysis in epidemiological modeling: Detection of wave

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