Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19): Patterns, Dynamics, Prediction, and Control

SARS-CoV-2 has established itself in all parts of the world, and many countries have implemented social distancing as a measure to prevent overburdening of health care systems. Here we evaluate whether and under which conditions containment of SARS-CoV-2 is possible by isolation and contact tracing in settings with various levels of social distancing. To this end we use a branching process model in which every person generates novel infections according to a probability distribution that is affected by the incubation period distribution, distribution of the latent period, and infectivity. The model distinguishes between household and non-household contacts. Social distancing may affect the numbers of the two types of contacts differently, for example while work and school contacts are reduced, household contacts may remain unchanged. The model allows for an explicit calculation of the basic and effective reproduction numbers, and of exponential growth rates and doubling times. Our findings indicate that if the proportion of asymptomatic infections in the model is larger than 30%, contact tracing and isolation cannot achieve containment for a basic reproduction number $(ℛ_{0})$ of 2.5. Achieving containment by social distancing requires a reduction of numbers of non-household contacts by around 90%. If containment is not possible, at least a reduction of epidemic growth rate and an increase in doubling time may be possible. We show for various parameter combinations how growth rates can be reduced and doubling times increased by contact tracing. Depending on the realized level of contact reduction, tracing and isolation of only household contacts, or of household and non-household contacts are necessary to reduce the effective reproduction number to below 1. In a situation with social distancing, contact tracing can act synergistically to tip the scale toward containment. These measures can therefore be a tool for controlling COVID-19 epidemics as part of an exit strategy from lock-down measures or for preventing secondary waves of COVID-19.

10,852 views

38 citations

Perspective

01 February 2021

The Effect of An Emergency Evacuation on the Spread of COVID19

Sachit Butail

and

Maurizio Porfiri

2,659 views

0 citations

Original Research

26 January 2021

Social Heterogeneity Drives Complex Patterns of the COVID-19 Pandemic: Insights From a Novel Stochastic Heterogeneous Epidemic Model (SHEM)

Alexander V. Maltsev

and

Michael D. Stern

7,302 views

5 citations

Original Research

25 January 2021

The Connectedness of the Coronavirus Disease Pandemic in the World: A Study Based on Complex Network Analysis

Sha Zhu

, 3 more and

Guorong Du

5,215 views

23 citations

Methods

25 January 2021

Causal Analysis of Health Interventions and Environments for Influencing the Spread of COVID-19 in the United States of America

Zhouxuan Li

, 4 more and

Momiao Xiong

14,306 views

2 citations

Original Research

20 January 2021

Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions

R. Schlickeiser

and

M. Kröger

4,670 views

7 citations

Original Research

21 January 2021

Estimating Parameters of Two-Level Individual-Level Models of the COVID-19 Epidemic Using Ensemble Learning Classifiers

Zeyi Liu

, 4 more and

Qing Cheng

2,909 views

4 citations

Original Research

18 January 2021

Dynamical Analysis of a Mathematical Model of COVID-19 Spreading on Networks

Wang Li

, 2 more and

Maoxing Liu

3,057 views

0 citations

Original Research

15 January 2021

Renormalization Group Approach to Pandemics as a Time-Dependent SIR Model

Michele Della Morte

and

Francesco Sannino

We generalise the epidemic Renormalization Group framework while connecting it to a SIR model with time-dependent coefficients. We then confront the model with COVID-19 in Denmark, Germany, Italy and France and show that the approach works rather well in reproducing the data. We also show that a better understanding of the time dependence of the recovery rate would require extending the model to take into account the number of deaths whenever these are over 15% of the cumulative number of infected cases.

3,063 views

21 citations

Original Research

14 January 2021

The Suppression of Epidemic Spreading Through Minimum Dominating Set

Jie Wang

, 5 more and

Dawei Zhao

2,177 views

0 citations

The empirical distribution and Weibull distribution fitting of incubation time. The Weibull distribution has density function fW(x;A,B)=kλ(xλ)k−1e−(x/λ)k,x≥0 with λ=9.93, and k=1.79. The K–S test is 0.17, which means that Weibull distribution is proper for the data.

Original Research

11 January 2021

Characterizing COVID-19 Transmission: Incubation Period, Reproduction Rate, and Multiple-Generation Spreading

Lin Zhang

, 4 more and

Xiao-Ke Xu

Understanding the transmission process is crucial for the prevention and mitigation of COVID-19 spread. This paper contributes to the COVID-19 knowledge by analyzing the incubation period, the transmission rate from close contact to infection, and the properties of multiple-generation transmission. The data regarding these parameters are extracted from a detailed line-list database of 9,120 cases reported in mainland China from January 15 to February 29, 2020. The incubation period of COVID-19 has a mean, median, and mode of 7.83, 7, and 5 days, and, in 12.5% of cases, more than 14 days. The number of close contacts for these cases during the incubation period and a few days before hospitalization follows a log-normal distribution, which may lead to super-spreading events. The disease transmission rate from close contact roughly decreases in line with the number of close contacts with median 0.13. The average secondary cases are 2.10, 1.35, and 2.2 for the first, second, and third generations conditioned on at least one offspring. However, the ratio of no further spread in the 2nd, 3rd, and 4th generations are 26.2, 93.9, and 90.7%, respectively. Moreover, the conditioned reproduction number in the second generation is geometrically distributed. Our findings suggest that, in order to effectively control the pandemic, prevention measures, such as social distancing, wearing masks, and isolating from close contacts, would be the most important and least costly measures.

25,280 views

22 citations

Original Research

08 January 2021

The Generalized-Growth Modeling of COVID-19

Ye Wu

, 3 more and

Xin Feng

3,767 views

5 citations

Migration of population in Hunan Province and Guangdong Province [27]. (A) The immigration situation of Hunan Province before the Spring Festival. (B) The emigration situation of Guangdong Province before the Spring Festival. (C) The immigration situation of Guangdong Province after the Spring Festival. (D) The emigration situation of Hunan Province after the Spring Festival.

Original Research

23 December 2020

The Impact of Population Migration on the Spread of COVID-19: A Case Study of Guangdong Province and Hunan Province in China

Guo-Rong Xing

, 2 more and

Gui-Quan Sun

5,268 views

12 citations

Original Research

21 December 2020

Epidemiological Characteristics of COVID-19 in Mexico and the Potential Impact of Lifting Confinement Across Regions

Cristy Leonor Azanza Ricardo

and

Esteban A. Hernandez-Vargas

8,567 views

11 citations

Original Research

05 December 2020

Epidemiological Model With Anomalous Kinetics: Early Stages of the COVID-19 Pandemic

Ugur Tirnakli

and

Constantino Tsallis

Time evolution of I(t) for the q-SIR equations with Neff=108; we consider t to run virtually from zero to infinity (not necessarily during only the typical range of real epidemics, say 1,000 days). (A) Fixed β and various values of γ. For γ=0 and ∀β, I(t)/Neff precisely recovers the expression given in Eq. (6). The slope at the first inflection point for increasing time is given by max[d ln I/d ln t]=1/(1−qup), ∀ γ. (B) Fixed γ and various values of β. For β=0, the qdown-exponential function is precisely recovered. (C) Time dependence of the slope of [d ln(I/Neff)/d ln t], which appears to be bounded between 1/(1−qup) (=2 in this example) and −1/(qdown−1) (=−2.5 in this example) (dashed lines). The dotted line corresponds to the position of the peak of I(t), and the maximum (minimum) corresponds to the left (right) inflection point. (D) The maximal slope of I(t)/Neff as a function of qup. The high value at qup=1 reflects the divergence expected in the limit qup=qdown=1. Indeed, in this limit, the present q-SIR model recovers the standard SIR model, which increases exponentially (and not as a power-law) toward the corresponding peak. Notice also that this slope decreases when I0/Neff increases.

We generalize the phenomenological, law of mass action-like, SIR and SEIR epidemiological models to situations with anomalous kinetics. Specifically, the contagion and removal terms, normally linear in the fraction I of infected people, are taken to depend on $I^{q_{u p}}$ and $I^{q_{d o w n}}$ , respectively. These dependencies can be understood as highly reduced effective descriptions of contagion via anomalous diffusion of susceptible and infected people in fractal geometries and removal (i.e., recovery or death) via complex mechanisms leading to slowly decaying removal-time distributions. We obtain rather convincing fits to time series for both active cases and mortality with the same values of $(q_{u p}, q_{d o w n})$ for a given country, suggesting that such aspects may in fact be present in the early evolution of the COVID-19 pandemic. We also obtain approximate values for the effective population $N_{e f f}$ , which turns out to be a small percentage of the entire population N for each country.