Mathematical and Statistical Analysis of Doubling Times to Investigate the Early Spread of Epidemics: Application to the COVID-19 Pandemic

Abstract

Simple mathematical tools are needed to quantify the threat posed by emerging and re-emerging infectious disease outbreaks using minimal data capturing the outbreak trajectory. Here we use mathematical analysis, simulation and COVID-19 epidemic data to demonstrate a novel approach to numerically and mathematically characterize the rate at which the doubling time of an epidemic is changing over time. For this purpose, we analyze the dynamics of epidemic doubling times during the initial epidemic stage, defined as the sequence of times at which the cumulative incidence doubles. We introduce new methodology to characterize epidemic threats by analyzing the evolution of epidemics as a function of (1) the number of times the epidemic doubles until the epidemic peak is reached and (2) the rate at which the doubling times increase. In our doubling-time approach, the most dangerous epidemic threats double in size many times and the doubling times change at a relatively low rate (e.g., doubling times remain nearly invariant) whereas the least transmissible threats double in size only a few times and the doubling times rapidly increases in the period of emergence. We derive analytical formulas and test and illustrate our methodology using synthetic and COVID-19 epidemic data. Our mathematical analysis demonstrates that the series of epidemic doubling times increase approximately according to an exponential function with a rate that quantifies the rate of change of the doubling times. Our analytic results are in excellent agreement with numerical results. Our methodology offers a simple and intuitive approach that relies on minimal outbreak trajectory data to characterize the threat posed by emerging and re-emerging infectious diseases.

The doubling effect of COVID-19 cases on key health indicators

“…The decrease in risk can also be caused by other factors that play an important role such as the varying stringency measures implemented by all countries and their time-varying nature. Indeed, a disease outbreak is influenced by multiple factors such as severity that shapes the transmission network structure [31] as well as the fraction of the susceptible population and the effects of behavioral changes and non-pharmaceutical interventions [5,[31][32][33].…”

“…The doubling time has been well studied and applied to, for example, infectious disease epidemics, population size, tumor growth, and in vitro cell growth [2]. The dynamics of infectious disease outbreaks are commonly measured by the doubling time, especially during the initial epidemic stage, and used to quantify the threat posed by infectious disease outbreaks [3][4][5][6]. In this paper, a relatively straightforward but useful measure is proposed to quantify the public health threat of an epidemic, denoted as the "doubling effect", which mathematically takes the form of a relative risk.…”

Nonlinear Combinational Dynamic Transmission Rate Model and Its Application in Global COVID-19 Epidemic Prediction and Analysis

“…. ,α * N ) be the optimal solution of the optimization problem (9). Then the decision function can be expressed as follows: ] andα 0 is a scalar in d(x) called bias term.…”

“…Tang et al [6] proposed that the risk of secondary outbreaks can be effectively reduced by intermittent population mobility and effective isolation of infected people in the floating population based on a novel stochastic discrete transmission model. In the meantime, the data-driven statistical models were also widely used in the prediction and analysis of COVID-19 epidemics, including function fitting models [7][8][9], machine learning [10,11], deep learning [12,13], and time series models [14,15].…”

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans

“…Most mathematical modelling of infectious disease occurs at the population scale and throughout the COVID-19 pandemic there have been many such studies (cf. Tang et al (2020); Moyles et al (2021); Yuan et al (2022a); Fair et al (2022); Childs et al (2022); Vignals et al (2021); Betti et al (2021); Dick et al (2021); Moore et al (2021); Moss et al (2020); Smirnova et al (2021); Wells et al (2021); Li et al (2020); Yuan et al (2022b); Hogan et al (2021)). While the impacts of vaccine efficacy and waning are important at these scales, the actual process of immune development occurs within-host.…”