The signature features of COVID-19 pandemic in a hybrid mathematical model - implications for optimal work-school lockdown policy
Authors: Lazebnik Teddy , Bunimovich-Mendrazitsky Svetlana 
Published: November 2020

Background

The coronavirus disease 2019 (COVID-19) first identified in China, spreads rapidly across the globe and is considered the fastest moving pandemic in history. The new disease has challenged policymakers and scientists on key issues such as the magnitude of the first-time problem, the susceptibility of the population, the severity of the disease, and its symptoms. Most countries have adopted “lockdown” policies to reduce the spatial spread of COVID-19, but they have damaged the economic and moral fabric of society. Timely action to prevent the spread of the virus is critical, and mathematical modeling in non-pharmaceutical intervention (NPI) policy management has proven to be a major weapon in this fight due to the lack of an effective COVID-19 vaccine.

Methods

We present a new hybrid model for COVID-19 dynamics using both an age-structured mathematical model and spatio-temporal model in silico, analyzing the data of COVID-19 in Israel. The age-structured mathematical model is based on SIRD two age-class model. The spatial model examines a circle of day and night (with one-hour resolution) and three main locations (work / school or home) for every individual.

Results

We determine mathematically the basic reproduction number R0 via the next-generation matrix based on Markov chain theory. Then, we analyze the stability of the equilibria and the effects of the significant differences in infection rates between children and adults. Using the hybrid model, we have introduced a method for estimating the reproduction number of an epidemic in real time from the data of daily notification of cases. The results of the proposed model are confirmed by the Israeli Lockdown experience with a mean square error of 0.205 over two weeks. The model was able to predict changes in R0 by opening schools on September 1, 2020, resulting in R0 = 2.2, which entailed a month’s quarantine of all areas of life. According to the model, by extending the school day to 9 hours, and assuming that children and adults go to school and work every day (except weekends), we get a significant reduction in R0 of 1.45. Finally, model-based analytical-numerical results are obtained and displayed in graphical profiles.

Conclusions

The use of mathematical models promises to reduce the uncertainty in the choice of “Lockdown” policies. Our unique use of contact details from 2 classes (children and adults), the interaction of populations depending on the time of day (the cycle of day and night), and several physical locations, allowed a new look at the differential dynamics of the spread and control of infection. Using knowledge about how the length of the work and school day affects the dynamics of the spread of the disease can be useful for improving control programs, mitigation, and policy.

Author summary

Everybody in the modern world understands today that the pandemics threat is not less dangerous than the wars. COVID-19 showed us that pandemics effects the economies of all the countries over the world brings to a total lockdown of social life and enormous mortality. There was no effective vaccine/treatment, to stop the spread of COVID-19 and, therefore, policymakers have taken unprecedented measures, including quarantines, public health measures, travel bans, and others, without knowing in advance the effect of these restrictions.

In this study, we develop a mathematical model of the pandemic spread taking into account the different dynamics of the disease in two age groups of children and adults. Using this model we succeeded to simulate the COVID-19 spread in Israel. The current study accurately predicts the effect of the work/school lockdown on the outbreaks. We have proven that by keeping schools open and increasing the school day to 8-9 hours, infection rates are reduced. Our results also show that if at least half of the adult population is a lockdown, the effect of children’s isolation on the infection rate is small, indicating the importance of multiple age groups of the population in the selection of restrictions.