Correcting pandemic data analysis through environmental fluid dynamics.

It is well established that the data reported for the daily number of infected cases during the first wave of the COVID-19 pandemic were inaccurate, primarily due to insufficient tracing across the populations. Due to the uncertainty of the first wave data mixed with the second wave data, the general conclusions drawn could be misleading. We present an uncertainty quantification model for the infected cases of the pandemic's first wave based on fluid dynamics simulations of the weather effects. The model is physics-based and can rectify a first wave data's inadequacy from a second wave data's adequacy in a pandemic curve. The proposed approach combines environmental seasonality-driven virus transmission rate with pandemic multiwave phenomena to improve statistical predictions' data accuracy. For illustration purposes, we apply the new physics-based model to New York City data.

INTRODUCTION

Modeling and analysis of global epidemiology are very challenging. The COVID-19 pandemic has been widely spreading due to airborne virus transmission. The coronavirus pandemic has impacted the economics and the environment at a global worldwide scale since March 2020.

The daily number of infected cases, reported during the first wave of the pandemic, was inaccurate due to several factors:

Insufficient tracing across the population.

Inaccuracy of testing equipment.

Lack of reproducible confirmation tests.

Inaccuracy of management by public and private health institutions.

Many online digital libraries, platforms, and institutions continue to utilize inaccurate data from the first wave. However, statistical comparisons between the first and second wave could lead to misleading conclusions for the reasons mentioned above.

The number of deaths is a more reliable source of information than the number of infected cases. This has been a topic of recent debate. Ioannidis et al. investigated the second vs the first wave of COVID-19 deaths. From available data on the age vs the number of deaths, they correlated the second vs the first wave of COVID-19 deaths to the shifts in age distribution and nursing home fatalities. Graichen investigated the difference between the first and the second (and third wave) of COVID-19 to form a German and European perspective. Other research works emerge along similar lines. Yue et al. tried to estimate the actual size of a pandemic from surveillance systems. Stamatakis et al. and Huang investigated pandemic data reported in the United Kingdom to examine associations between lifestyle risk factors and mortality outcomes. The above is due to an unknown lack of representativeness that can affect the magnitude and direction of effect estimates.

We recently showed that two pandemic outbreaks would be inevitable due to environmental weather seasonality. Our findings were based on high-fidelity, multiphase fluid dynamics, and heat and mass transfer simulations of airborne virus transmission. We combined the simulation results with epidemiological modeling enhanced by a new airborne infection rate index (AIR) and meteorological data. It is generally believed that the high-temperature and high-humidity environment is conducive to reducing the transmission rate of the new coronavirus. In our previous research, we showed a complex mechanism associated with the effects of weather conditions on virus transmission. It incorporates combinations of three major parameters: relative humidity, temperature, and wind speed.

The daily infected cases' published data during the first wave is inaccurate and thus can be misleading. We develop a new uncertainty quantification model using environmental-climate data that corrects the daily number of infected cases during the first wave, thus improving the second and first waves' comparative analysis. For illustration purposes, we apply the new model to correct the first wave data reported for NYC between March 2020 and March 2021 for the daily number of infections.

MATHEMATICAL MODEL DEVELOPMENT

The pandemic's second wave data constitute a more reliable source of information than the pandemic's first wave's data recorded starting from early March 2020.

In March 2021, thus after one year's period of the COVID-19 pandemic, we know the following:

The order of magnitude of the total number of deaths from COVID-19 did not change significantly between the first and the second wave periods.

The order of magnitude of the number of patients in intensive care units (ICUs) did not change importantly between the first and the second wave periods.

Given the above, one can define an accurate mortality rate, , in an infected population as the following:

Moreover, could be considered as an inaccurate representation of which is per unit time and depends on the wavenumber (n) of the pandemic such that

Note that the inaccuracy of is placed only in . n = 1 and n = 2 denote the first and second wave of the pandemic; I and D are the stationary cumulative number of infected cases and deaths due to the infection; β is the transmission rate of infection per unit time inside a general population N. In other words, β represents the probability per unit time that a susceptible individual becomes infected.

Liu et al. shed light on the role of seasonality in the spread of the COVID-19 pandemic. Dbouk and Drikakis quantified the relationship between the weather seasonality and the transmission rate β through extensive fluid mechanics simulations for crucial weather parameters such as temperature, relative humidity and wind. They quantitatively showed how a weather-dependent β could produce two pandemic waves during one year. Our analysis and modeling approaches are based on the following premises:

The weather seasonality is a major driving force behind two pandemic waves occurred annually.

The virus fatal strength level did not change importantly between two similar seasons between the first and second wave of the pandemic, i.e., winter 2020 vs winter 2021.

The social behaviors and global restriction strategies did not change significantly between the two waves' periods (i.e., masks, social distance, lockdowns, etc.).

The age-pyramid of a country did not change significantly between the two pandemic waves.

Using the above, the mortality rate among the stationary cumulative number of infected individuals should be approximately the same in two consecutive waves of the pandemic, i.e., where denotes the nth-wave period of a pandemic. The final time is determined by where ε is a positive infinitesimal value. It is worth noting that .

It is well established that the non-cumulative number of infected cases reported during the first pandemic wave is inaccurate, primarily due to the insufficient tracing across the population. Therefore, we aim to correct the inaccurate (old) data, , to obtain the more accurate (new) data, I(1),

Substituting n = 1 in Eq. (3) and using Eqs. (1) and (5) yield

NYC CASE

Figure 1 shows the weather-dependent transmission rate (β) in NYC between March 2020 and March 2021. A maximum transmission rate of 0.5 per , related to the coronavirus airborne concentration rate, means that the probability is P = 1 (100%) for a susceptible individual infected in two days due to the weather conditions (wind speed, temperature, and relative humidity). Figure 1(a) shows the NYC weather history data with the hat symbol denoting daily weather data averaged per month. Figure 1(b) illustrates the weather-dependent transmission rate (airborne infection rate index ( )), showing three trends labeled as high, medium, and low separated by the respective threshold values of 0.4 and 0.3; see Dbouk and Drikakis.

FIG. 1.

Weather-dependent transmission rate (β) in NYC between March 2020 and March 2021 (one-year period). A maximum transmission rate of 0.5 per means that the probability is P = 1 (100%) for a susceptible individual to be infected in two days ( ) due to the weather conditions (wind speed, temperature, and relative humidity) in a region. (a) NYC weather history data with the hat symbol denoting daily weather data averaged per month. (b) Weather dependent transmission rate (airborne infection rate index ( )) showing three trends denoted high, medium, and low separated by the respective threshold values 0.4 and 0.3.

The reported pandemic curves data for NYC are shown in Fig. 2 as cumulative number of infections [Fig. 2(a)] and cumulative number of deaths [Fig. 2(b)]. The maximum stationary values for the cumulative infected cases are and for the first and second waves. Similarly, the cumulative number of deaths is denoted by and (corresponding to null slopes approximately). Figure 2(c) shows the weather-dependent transmission rate (β) as obtained by Dbouk and Drikakis with and representing the transmission rate during the first and the second wave of the pandemic, respectively. This pandemic data can be downloaded free of charge from. It can be observed from Fig. 2(c) that the symmetry line is well aligned with the maximum stationary values of the cumulative number of deaths ( ) and with the maximum cumulative number of infections ( ). This sheds light on the physics-based behavior of the computed transmission rate [β of Fig. 2(c)] driven by the force of weather seasonality in NYC.

FIG. 2.

The first (n = 1) and second (n = 2) waves of the COVID-19 pandemic in NYC between March 2020 and March 2021. (a) The cumulative number of infections (I); (b) the cumulative number of deaths (D); (c) the weather-dependent transmission rate (β) as obtained by Dbouk and Drikakis. and are the transmission rate during the first and the second wave of the pandemic, respectively. The pandemic data can be downloaded free of charge from.

Figure 3 shows the mortality rate in the infected population of NYC between 03 March 2020 and 03 March 2021, computed using Eq. (1) with n = 1, and Eq. (2) with n = 2. If both waves data were accurate, we should have . is, however, different from . Thus, any asymmetry between and is a measure of uncertainty quantification associated with the first wave. The above prompt to correct the inaccurate daily number of infected cases reported during the first pandemic wave.

FIG. 3.

The mortality rate , per unit time, in the infected population of NYC between March 2020 and March 2021 showing the two waves of the pandemic. An inaccurate is observed different from an accurate . This asymmetry between and is a measure of uncertainty quantification of the first wave data's inadequacy concerning the second wave data's adequacy. The daily number of infected cases reported during the first pandemic wave also needs to be corrected according to .

The corrected first wave data for the daily number of infected cases in NYC are shown in Fig. 4. One can see that the correction results in increasing the infected cases fourfold.

FIG. 4.

The daily number of COVID-19-infected persons reported for NYC between 03 March 2020 and 03 March 2021 showing the two waves of the pandemic. Squares-line curve: inaccurate reported first wave data ; circles-line curve: corrected first wave data using Eq. (6) for accurate daily number of infected cases I(1). The reported pandemic data can be downloaded free of charge from.

CONCLUSIONS AND PERSPECTIVES

The coronavirus pandemic data for the daily number of infections vs the number of deaths during the first wave were incomplete. They lead to misleading conclusions if considered as a data reference. The data inaccuracy for the first wave was primarily due to insufficient tracing across the population. Unfortunately, various online digital libraries and platforms continue to adopt, host, and diffuse these inaccurate data from the first wave, followed by more accurate data of the daily number of infections from the second and subsequent waves.

We proposed a new fluid dynamics, physics-based uncertainty quantification, and correction model that rectifies the first wave data's inadequacy. As an illustration example, we applied the new model to correct the pandemic's first wave data for the daily number of infected cases reported in NYC, USA. The proposed model is limited to regions that witnessed more than one pandemic wave. It can be used to correct their first wave data reported for the daily number of infected cases.

Environmental temperature and humidity affect the ability of the virus to infect, but they are not themselves the decisive factor in preventing the spread of the virus. We cannot rely on seasonal temperature rises to suppress the epidemic. Instead, we should focus more on the formulation and implementation of active epidemic prevention control policies. Social protective measures such as social distancing and face masks will remain important during a pandemic.