Modeling time to event for epicenters of the pandemic COVID-19

Abstract

The epidemic of COVID-19 has been the most mathematically informative pandemic. The unprecedented information gives rise to some unprecedented models, problems, and discussions. One of these new matters is modeling the epicenters of a pandemic. The present paper is the first attempt to model the waiting time to introduce a new epicenter during a pandemic. This modeling is conducted in terms of time-to-event, the number of epicenters, and the normalized time. We model the waiting time data by an exponential distribution, therefore, the number of epicenters can be represented through a Poisson process. Then, the parameters are estimated by the method of moments and maximum likelihood method. All the simulations are the result of 10,000 runs conducted on MATLAB R2015b. It is expected to encounter 12 and 14 (with probability 95%, 3-24 and 7-23) epicenters from 15th May to 13th June and from June 14 to July 12, 2020, respectively. We forecast that the cumulative number of confirmed cases for coming epicenters is over 10,000 when they join the existing epicenters. The paper suggests that the time to epicenter is a suitable criterion to compare the spreading speed of an epidemic in different periods or even different epidemics.

Highlights

• The study aims to model the time to the next epicenters during the pandemic COVID-19.

• The study introduces the time to epicenter as a criterion to study of spreading speed of an epidemic in different periods or compare different epidemics.

• The study deals with the number of cumulative confirmed cases at the time that a region become epicenter.

• The study proposes the Poisson process as the model to describe the number of epicenters.

• The study suggests that exponential distribution can model the time to event for the epicenters of COVID-19.

KEYWORDS:

• COVID-19
• pandemic
• modeling
• epicenter
• time to event

Acknowledgements

Contribution of the authors: BJ: Idea, Simulation, First manuscript; MR: Final Manuscript; SJZ: Revision, Simulation; FN: Revision, Discussion.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The advantage of Figure 2(A) is that the situation of exceeding 100, 1000, and 10,000 are fixed and horizontal, and the curve illustrates the (normalized) time of becoming epicenter. Therefore, the relative situation of the time of joining epicenters is clear.

 

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes on contributors

Babak Jamshidi

Babak Jamshidi is a medical statistician with a mathematical background. His BSc and MSc were in pure mathematics and financial mathematics, respectively, and he has a PhD in statistics. He has experience in constructing novel models and introducing new methods especially in epidemiology.

Mansour Rezaei

Mansour Rezaei is a professor at Kermanshah University of Medical Sciences. His research interests cover the application of statistics in medicine, epidemiology, and public health, with a strong emphasis on clinical trials.

Shahriar Jamshidi Zargaran

Shahriar Jamshidi Zargaran is a PhD candidate in Neuroimaging. His BSc and MSc in medical engineering were earned from Sahand University of Technology, Tabriz in 2017 and Tehran University of Medical Sciences, Tehran in 2020, respectively.

Farid Najafi

Farid Najafi is a professor at Kermanshah University of Medical Sciences. His research areas are systematic review and meta-analysis, Epidemiology of chronic non-communicable disease, size estimation of hidden population, clinical trials, cancer, and cardiovascular epidemiology.