Predicting the Stagnation Time of Covid-19 Pandemic Using Bass Diffusion and Mini-Batch Gradient Descent Models

The coronavirus (SARS-CoV-2), which first appeared in Wuhan, China, in December of 2019, spread quickly around the world, eventually categorizing it as a global "Epidemic". In early 2020, the SARS-CoV-2 emerging virus had devastating effects on all aspects of daily life, public health, and even the global economy. During that epidemic, much effort had been made to predict the number of confirmed and deaths, and when the epidemic would subside. However, the prediction of epidemic indications (COVID-19) was highly uncertain and different from what happened next. Multiple and rapid virus mutations, and late detection of infection in many cases of people, have made the prediction process complicated and difficult, with some of the proposed models appearing to be largely misleading. In this research paper, we reviewed the analytical and statistical methods to extrapolate the most important data and indicators about the infection (COVID-19) and the rate of confirmed, recovery, and deaths during the past few months in some countries of the world, especially in the Kingdom of Saudi Arabia. On the other hand, we proposed the time for the infection to subside in the Kingdom of Saudi Arabia and some other countries. In the proposed prediction model, the Bass diffusion model was adopted by combining with the mini-batch Gradient descent algorithm to obtain the optimum values for the Bass algorithm parameters. The model was trained on about 85% of the available historical data and tested on the rest of the data. The proposed model indicated that the Kingdom of Saudi Arabia will face an increase in the coming days in terms of the high number of confirmed cases. Moreover, the rate of increase in injuries will decrease over time until it reaches its lowest levels in January of the next year. The model also showed that the curved flattening point for confirmed figures will be at the mentioned month, which is the expected date for the epidemic to recede in Saudi Arabia in the absence of other aftershocks.

[1] "Update and Interim Guidance on Outbreak of 2019 Novel Coronavirus (2019-nCoV) in Wuhan, China CDC Health Update". New Jersey Department of Health. 18 January 2020

[2] Institute of Health Metrics and Evaluation (IHME) at University of Washington https://covid19.healthdata.org/united-states-of-america

[3] MRC Centre for Global Infectious Disease Analysis at the Imperial College. https://mrc-ide.github.io/covid19-short-term-forecasts/index.html

[4] IHME COVID-19 Health Service Utilization Forecasting Team and Christopher JL Murray. “Forecasting COVID-19 impact on hospital bed-days, ICU-days, ventilator-days and deaths by US state in the next 4 months,” 2020. MedRxiv https://doi.org/10.1101/2020.03.27.20043752

[5] IHME COVID-19 health service utilization forecasting team and Christopher JL Murray. “Forecasting the impact of the first wave of the COVID-19 pandemic on hospital demand and deaths for the USA and European Economic Area countries,” 2020. MedRxiv https://doi.org/10.1101/2020.04.21.20074732

[6] Woody S., et al. “Projections for first-wave COVID-19 deaths across the US using social-distancing measures derived from mobile phones,” 2020. MedRxiv https://doi.org/10.1101/2020.04.16.20068163

[7] Yang Z., et al. “Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions.” J Thorac Dis, 12(3): 165-174, 2020. DOI: 10.21037/jtd.2020.02.64

[8] Ferguson N.M., et al. “Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College London.” 16 March 2020. Accessed at www.imperial.ac.uk/media/imperial-college/medicine/mrc-gida/2020-03-16-COVID19-Report-9.pdf.

[9] Petropoulos F., Makridakis S. “Forecasting the novel coronavirus COVID-19,” PLoS ONE, 15(3): e0231236, 2020. https://doi.org/10.1371/ journal.pone.0231236

[10] Kissler S,M. et al. “Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period.” Science, 14 April 2020. DOI: 10.1126/science.abb5793

[11] Chinazzi M., et al. “The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak.” Science, 24 April 2020, 395-400

[12] Jewell N.P., et al. “Caution Warranted: Using the Institute for Health Metrics and Evaluation Model for Predicting the Course of the COVID-19 Pandemic.” Ann Intern Med, 14 April 2020. DOI: https://doi.org/10.7326/M20-1565

[13] Marchant R., et al. “Learning as we go: An examination of the statistical accuracy of covid19 daily death count predictions,” 2020. DOI: https://doi.org/10.1101/2020.04.11.20062257

[14] Grey S. and MacAskill A. “Special Report: Johnson listened to his scientists about coronavirus - but they were slow to sound the alarm.” Reuters, April 7, 2020. https://reut.rs/2Rk3sa7

[15] Resnick B. “The White House projects 100,000 to 200,000 Covid-19 deaths.” Vox, March 31, 2020. https://www.vox.com/science-and-health/2020/3/31/21202188/us-deaths-coronavirus-trump-white-house-presser-modeling-100000

[16] Rittel H.W.J. and Webber M.M. "Dilemmas in a General Theory of Planning." Policy Sciences, 4 (2): 155–169, (1973). doi:10.1007/bf01405730

[17] Kermack W. O. and McKendrick A. G. (1927) “A Contribution to the Mathematical Theory of Epidemics,” Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, Vol. 115, 772, pp. 700-721.

[18] Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159-175.

[19] Du, X. F., Leung, S. C., Zhang, J. L., & Lai, K. K. (2013). Demand forecasting of perishable farm products using support vector machine. International journal of systems Science, 44(3), 556-567.

[20] Kuo, R. J. (2001). A sales forecasting system based on fuzzy neural network with initial weights generated by genetic algorithm. European Journal of Operational Research, 129(3), 496-517.

[21] Mahajan, Vijay, Muller E, and Wind,Yoram. (2000) New-Product Diffusion Models, vol. 11, New York: Springer Science & Business Media.

[22] Bass, Frank M. (1969) “A New Product Growth for Model Consumer Durables” Management Science, Vol. 15, 5, pp. 215–227.

[23] Bass, Frank M., Krishnan, Trichy V. and Jain, Dipak C. (1994) "Why the Bass Model Fits without Decision Variables" Marketing Science Vol. 13, 3, pp. 203-223.

[24] Bass, Frank M. (2004) “Comments on ‘A New Product Growth for Model Consumer Durables the Bass Model’” Management Science Vol. 50, 12, pp. 1833–1840.

[25] Ruder, S. (2016). An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747.

[26] Alzahrani, S. I., Aljamaan, I. A., & Al-Fakih, E. A. (2020). Forecasting the spread of the COVID-19 pandemic in Saudi Arabia using ARIMA prediction model under current public health interventions. Journal of infection and public health, 13(7), 914-919.

[27] Gurumurthy, K., & Mukherjee, A. (2020). The Bass Model: a parsimonious and accurate approach to forecasting mortality caused by COVID-19. International Journal of Pharmaceutical and Healthcare Marketing.

[28] Zeny L. Maureal, Jovelin M. Lapate, Madelaine S. Dumandan, Vanda Kay B. Bicar, Derren N. Gaylo (2020). Adapted Bass Diffusion Model for the Spread of COVID-19 in the Philippines: Implications to Interventions and Flattening the Curve. International Journal of Innovation, Creativity and Change. www.ijicc.net Volume 14, Issue 3, 2020.