Indoor Risk Estimation Model for Health Protection from COVID-19

Abstract

In this chapter, a conceptual framework for assessing the probability of COVID-19 transmission is presented and discussed. The Wells-Riley probabilistic methodology for indoor environments is adopted, by integrating updated clinical data, thereby ensuring a reliable estimation of the probability of infection, through the model implementation on a specific Android platform. Notifications are sent to the user when detecting a high probability of infection and high carbon dioxide concentration levels. In addition, the Bluetooth signal is exploited to accurately determine the proximity between devices, thus facilitating the efficient enforcement of social distancing protocols among individuals. The effectiveness of the proposed model is validated through the application on different test scenarios.

1. Introduction

The Coronavirus disease (COVID-19) pandemic has highlighted the critical need for comprehensive public health protection measures, particularly when considering indoor environments with a high risk of viral transmission. The cause of COVID-19 is attributed to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus [1]. The transmission of the virus occurs through the dissemination of tiny liquid droplets from the oral or nasal cavities of an infected individual. These droplets are typically released during coughing, sneezing, speaking, singing, or breathing. These particles exhibit a spectrum of sizes, ranging from relatively sizable respiratory droplets to diminutive aerosols [2]. The SARS-CoV-2 viral load in the oral cavity has been observed to exhibit a wide range of values, as reported in Refs. [3, 4], lasting from 10² to 10¹1 copies per mL of respiratory fluid. The viral loads exhibit fluctuations throughout the illness progression, with a tendency to reach their highest levels near the symptoms manifestation [5]. Factors such as indoor gatherings and inadequate ventilation may facilitate the spread of COVID-19. A comprehensive analysis of over 300 COVID-19 outbreaks, each one involving three or more individuals, has revealed that all instances of transmission are associated with specific indoor settings [6]. According to a research study adopting contact tracing [7], the probability of COVID-19 transmission from a primary case is 18.7 times higher in an enclosed environment as compared to an outdoor environment. In order to estimate the potential for COVID-19 transmission within indoor areas and to execute practical mitigation efforts, it is crucial to develop reliable risk estimation models. These should be founded on theories and mathematical equations that are biologically plausible or consistent with clinical or laboratory evidence. In general, assessing the risk of infection involves two primary components: first, estimating the amount of the infectious agent that has been ingested, and second, estimating the probability of infection based on this amount. Deterministic and stochastic models can be used to classify infection risk. Each individual has a certain tolerance level for the infectious agent, and if they are exposed to a dose that exceeds their tolerance level, they will become infected. By this hypothesis, the deterministic models can predict whether or not an individual will be infected after a given dose of ingestion. Instead, stochastic models estimate the probability of contracting the infection at the ingested dose [8]. The Wells-Riley model is extensively applied to estimate the risk of airborne infectious disease transmission. It provides a framework for computing the risk of infection based on essential variables in a particular environment. Recently, it has been widely utilized to determine the COVID-19 transmission rate [9]. This model, originally developed by William F. Wells and Richard L. Riley [10, 11], was initially used to investigate tuberculosis and measles. In 1995, Well expressed the viral load emitted in terms of the quantum emission rate (E, quanta/h). Quantum refers to the number of infectious airborne particles needed to infect a person. On the other hand, in 1978, Riley proposed a modification of the Reed-Frost equation to estimate the probability of averting infection based on the amount (in quanta) of airborne pathogen particles a person intakes. In order to mitigate the transmission of COVID-19, it is essential to consider some factors [12], including social distancing, interpersonal contact, mask adherence, and ventilation. Adhering to the recommended guidelines of health authorities to maintain a safe physical distance from others is paramount in mitigating transmission risks. Reducing social gatherings and/or adopting the preference for virtual alternatives, may mitigate potential exposure. Properly donning masks to cover both the nose and mouth can offer an extra level of safeguarding. Adequate ventilation, especially in enclosed environments, may facilitate the dispersion and the elimination of suspended particulate matter in the air.

The initial focus of this chapter relates to the theoretical aspect of the Wells-Riley model, which is adapted to determine the risk of infection by COVID-19. The methodology to acquire each employed parameter is also discussed. Section 3 includes the modeling and the analysis of the outcomes derived from the model. Section 4 exposes the architecture of an experimental setup, which aims to estimate the probability of infection and the degree of distancing between individuals within indoor environments. Section 5 displays the outcomes of the experimental configuration for different scenarios. Finally, in Section 5, the conclusions are outlined.

2. Theory and formulation

The Wells-Riley [10, 11] equation is formulated by combining the Poisson probability distribution, where the probability of infection p is dependent on the total inhaled infectious quanta n. Inhaled quanta are determined by multiplying the quanta concentration of the air $\left(C_{\mathit{avg}},\mathit{\text{quanta}}/m^3\right)$ by the pulmonary ventilation volumetric flow rate of the exposed person $\left(Q_b,m^3/h\right)$ and the duration of exposure in hours $\left(D,h\right)$, as follows:

$$p=1-e^{-n}=1-e^{-C_{\mathit{avg}}\cdot Q_b\cdot D}$$E1

Assuming equilibrium and well-mixed conditions, Eq. (2) describes the quantum concentration C in a room with a ventilation rate Q, housing I infected individuals who emit infectious pathogens at a constant rate of q infectious quanta per person per unit time.

$$C_{\mathit{avg}}=\frac{l\cdot q}{Q}$$E2

Therefore, the probability of infection for a person in this room is calculated with Eq. (3), which can be also represented as the relationship between the number of cases of developing infection $N_{\mathit{ca}}$ and the number of susceptible people $N_{\mathit{sus}}$.

$$p=1-e^{\frac{-l\cdot q\cdot Q_b\cdot D}{Q}}=\frac{N_{\mathit{ca}}}{N_{\mathit{sus}}}$$E3

2.1 Quanta emission rates for SARS-COV-2

The emission rate of quanta is highly variable, ranging from 3 to 300 quanta per hour, as reported in [13], whereas in [14], based on the work of [15], it is recommended a range of $\sim$ 2–14 quanta per hour for oral breathing and 61–408 quanta per hour for loud speaking. This variation is influenced by the intensity of activities, such as shouting, chanting, speaking aloud, and metabolic rates. The values relative to four different activity levels (resting, light intensity, moderate intensity, and high intensity) are shown in Table 1, based on reference [14]. The quanta emission rate is calculated by assuming the droplets of an infected person contain the same viral load as the sputum [15]. Using a mass balance, the expelled viral load can be determined from the virus concentration in the sputum and the number of tiny droplets smaller than 10 μm in size. The emitted viral load is expressed as the quantum emission rate (ERq, quanta h1) and evaluated as follows:

Activity	Oral breathing	Speaking	Aloud speaking or singing
Sedentary/passive resting	2	9.4	60.5
Light intensity/standing	2.3	11.4	65.1
Moderate intensity	5.6	26.3	170
High intensity	13.5	63.1	408

Table 1.

Quanta emission rates for SARS-CoV-2 (quanta/hour) [14].

$${\mathit{ER}}_q=c_v\cdot c_i\cdot V_{\mathit{br}}\cdot N_{\mathit{br}}\cdot {\int }_0^{10\mathit{\mu m}}{N}_d\left(D\right)\cdot {\mathit{dV}}_d\left(D\right)$$E4

where $c_v$ is the viral load in the sputum (measured as RNA copies per ${\mathit{mL}}^{-1}$), $c_i$ is a conversion factor that relates an infectious quantum to the infectious dose expressed in viral RNA copies, $V_{\mathit{br}}$ is the volume of exhaled air per breath measured in ${\mathit{cm}}^3$, $N_{\mathit{br}}$ is the breathing rate in breaths per hour breath $h^{-1}$, $N_d$ is the droplet number concentration in (part. ${\mathit{cm}}^3$) and $V_d$ is the volume of a single droplet in $\mathit{mL}$, which is determined by the diameter D of the droplet. The volume of the drop $V_d$ is calculated using experimental data obtained by the authors of [16].

2.2 Volumetric breathing rates

Estimating the volume of air exchanged during breathing is crucial for understanding the factors that contribute to the spread of respiratory droplets and aerosols. Airborne respiratory droplets containing germs are released whenever an infected person breathes, coughs, or speaks. This study employs the Exposure Factors Manual (Chapter 6 of the United States Environmental Protection Agency [14]) factors. Table 2 displays information on average daily inhalation rates for short exposures as a function of age and activity level.

Activity level	Age group	Mean	95th Percentile
	[years]	m^3/minute	m^3/minute
Sedentary/passive	16 to <21	5.3E–03	7.2E–03
	21 to <31	4.2E–03	6.5E–03
	31 to <41	4.3E–03	6.6E–03
Light intensity	16 to <21	1.2E–02	1.6E–02
	21 to <31	1.2E–02	1.6E–02
	31 to <41	1.2E–02	1.6E–02
Moderate intensity	16 to <21	2.6E–02	3.7E–02
	21 to <31	2.6E–02	3.8E–02
	31 to <41	2.7E–02	3.7E–02
High intensity	16 to <21	4.9E–02	7.3E–02
	21 to <31	5.0E–02	7.6E–02
	31 to <41	4.9E–02	7.2E–02

Table 2.

Short-term exposure values average daily volumetric breathing rates [14].

2.3 Mask efficiencies in reducing virus emission

The investigation also focuses on the adoption of respiratory protective equipment, such as masks, by both infected and susceptible individuals. Masks provide a physical barrier that can capture respiratory droplets harboring viruses, restricting their escape into the environment. The effectiveness of various masks in reducing virus emission is compared in Table 3.

Mask	Exhalation mask efficiency	Inhalation mask efficiency
Type	Infected person	Susceptible person
N95 masks (KN95, FF2)	90%	90%
N95 with exhalation valve	0%	0%
Cloth, surgical	50%	30%
Face shields worn without a mask	23%	23%

Table 3.

Mask efficiency in preventing virus inhalation by a susceptible individual [14].

2.4 Ventilation rates

The estimation of the infection rate caused by aerosols in an indoor environment depends on a crucial parameter, namely the ventilation rate. This uniquely refers to the substitution of indoor air with outdoor air. As indicated in Ref. [14], a ventilation rate of one hour does not necessarily imply a complete air replacement within the same period. The mixing process prevents the displacement of indoor air by fresh air. Ventilation variations across diverse settings are of significant importance.

ASHRAE Standard 62 [17] outlines the minimum ventilation rates required for conditioned spaces to ensure satisfactory indoor air quality (IAQ), taking into account the use and occupancy of the building. These rates are detailed in Table 4.

					Default values
	People outdoor		Area outdoor		Occupant	Combined outdoor air
	Air rate (Rp)		Air rate (Ra)		Density	Rate
Occupancy	cmf/	L/s.	cmf/ft^2	L/s.m^2	#/1000 ft^2	cmf/	L/s.	Air
Category	Person	Person			or #/100 m^2	Person	Person	Class
Domestic	5	2.5	0.06	0.3	15	9	4.5	1
Schools	10	5	0.12	0.6	35	13	6.7	1
Food service	7.5	3.8	0.18	0.9	70	10	5.1	2
Hotels resorts/dormitories	5	2.5	0.06	0.3	10	11	5.5	1
Office buildings	5	2.5	0.06	0.3	10	11	5.5	1
Public assembly spaces	5	2.5	0.06	0.3	150	5	2.7	1
Sports and Entertainment	20	10	0.18	0.9	7	45	23	2

Table 4.

Minimum ventilation rates in breathing zone.

2.5 Decay rate of virus infectivity in aerosol

Environmental circumstances may influence the infectiousness of SARS-CoV-2 in natural aerosols, and the virus may be able to survive for extended periods in some conditions. Important factors that affect the persistence of infectious SARS-CoV-2 in aerosols include temperature, sunlight, and humidity. On the other hand, sunshine and temperature have a much more significant impact on the decomposition rate than humidity. According to research in [18], the time needed to reduce infectious virus by 90% ranged from 4.8 minutes at 40°C, 20% relative humidity, and high-intensity sunlight. In contrast, the time required indoors or at night is over two hours. The decay rate of aerosol virus infectivity is computed using the following equation:

$$\begin{array}{c}{K}_{\mathit{\text{infectivity}}}=0.16030+0.04018\left(\frac{T-20.615}{10.585}\right)+0.02176\left(\frac{\mathit{RH}-45.235}{28.665}\right)\\ +0.14369\left(\frac{S-0.95}{0.95}\right)+0.02636\left(\frac{T-20.615}{10.585}\right)\left(\frac{S-0.95}{0.95}\right)\end{array}$$E5

where $K_{\mathit{\text{infectivity}}}$ is the decay constant for viral infectivity; T is the temperature measured in degrees Celsius (°C); RH is the relative humidity (%) and S is the UV irradiance (W/m²), ranging from 0 (indoors) up to 10 (full sun noon).

2.6 Virus removal rate using controlled systems

A useful indicator of ventilation quality is the rate of air change in the room. This measurement is known as air changes per hour (ACH). Ventilation with clean outdoor air removes viruses, particulates, and gasses, making it healthier. However, most heating and ventilation systems use recirculated air, which does not reduce the risk of COVID-19 unless the recirculated air is filtered to remove minute particles. An air filter’s Minimum Efficiency Reporting Values (MERV) rating indicates how effectively it extracts airborne particles. MERV is expressed on a 16-point scale based on three ranges of Average Particle Size Efficiency (PSE) [19]. Refer to Table 5 for MERV Parameters. For instance, if the filter has a MERV value of 12 or higher, it suggests that it can remove at least 90% of the aerosol-sized virus-containing particles. High-efficiency particulate air (HEPA) filters [20] are a type of air filter that can remove up to 99.97% of dust, pollen, mildew, and other airborne particles up to 0.3 microns in size, making them effective at reducing the risk of covid. Table 6 illustrates an example of ACH calculation for a HEPA filter.

Standard 52.2	Composite average particle size efficiency, size range, (μ m)
Minimum	Range 1	Range 2	Range 3	Average arrestance,
Efficiency value	(0.3–1.0)	(1.0–3.0)	(3.0–10.0)	(%)
(MERV)
1	n/a	n/a	E3 < 20	Aavg <65
2	n/a	n/a	E3 <20	65≤Aavg < 70
3	n/a	n/a	E3 <20	70≤Aavg <75
4	n/a	n/a	E3 <20	75≤Aavg
5	n/a	n/a	20 ≤E3	n/a
6	n/a	n/a	35 ≤E3	n/a
7	n/a	n/a	50 ≤E3	n/a
8	n/a	20 ≤E2	70 ≤E3	n/a
9	n/a	35 ≤E2	75 ≤E3	n/a
10	n/a	50 ≤E2	80 ≤E3	n/a
11	20 ≤E1	65 ≤E2	85 ≤E3	n/a
12	35 ≤E1	80≤E2	90 ≤E3	n/a
13	50 ≤E1	85≤E2	90 ≤E3	n/a
14	75 ≤E1	90≤E2	95 ≤E3	n/a
15	85 ≤E1	90≤E2	95 ≤E3	n/a
16	95 ≤E1	95≤E2	95 ≤E3	n/a

Table 5.

MERV (Minimum Efficiency Reporting Value) parameters.

Parameters	Values	Units	Description
Recirculated flow rate (Rfr)	300	m^3/h
Volume of room (V)	100	m^3
Filter efficiency (Feff)	90	%	MERV 13 – Enter from Table 5
Removal in ducts, Air handler (Rd)	10	%	Assuming
Other removal	0	%	Germicidal UV
Measures (Rot)
ACH for additional control measures	3	h^−1	$\mathit{ACH}=\frac{\mathit{Rfr}}{V}\cdot \mathit{MIN}\left(F_{\mathit{eff}}+\mathit{Rd}+\mathit{Rot}\right)$

Table 6.

ACH (Air Changes Per Hour) for a HEPA filter.

2.7 Fraction of immune people

Vaccination and spontaneous infection are the two main ways to gain immunity [21]. This is most commonly acquired through vaccination, which delivers antigens or attenuated forms of diseases into the body and stimulates an immune response. However, acquiring natural immunity through getting sick and recovering from disease is also possible. Multiple online resources offer accurate information that can be used to calculate the vaccination rate in a given community. Information on vaccination rates can be gathered from various places, including the New York Times’ vaccine tracker. Additional country-specific resources, such as the https://lab24.ilsole24ore.com/coronavirus/website, are available. The efficiency of COVID-19 immunizations depends on the vaccine, the period between doses, and the prevalent variants in a given population. The Ref. [22] provides comprehensive information on the percentages of the efficiency of the most effective vaccines for COVID-19, including Pfizer, Moderna, AstraZeneca, and Johnson & Johnson, with an efficiency value of 95.0%, 94.1%, 80.7%, and 66.9% respectively.

As shown in Eq. (6), the number of immune individuals is equal to the product of the number of vaccinated individuals and the efficiency of the vaccine.

$$N_{\mathit{\text{in}}}=N_{\mathit{vac}}\ast V_{\mathit{eff}}$$E6

where $N_{\mathit{\text{in}}}$ is the number of immune people, $N_{\mathit{vac}}$ is the number of people vaccinated and $V_{\mathit{eff}}$ is the percentage of vaccine efficiency.

2.8 CO₂ emission rate

Metabolic production of carbon dioxide (CO₂) by humans is adopted as an indicator to measure ventilation rates in occupied rooms [23]. In this context, individual CO₂ emission rates are determined by analyzing human metabolism, energy-consuming physical activity, and factors such as ventilation and IAQ. Furthermore, the anthropometric variables of body mass, gender, and age are considered when analyzing the individuals in question.

• Initially, determine the metabolic rate (met) for the activity of interest presented in Table 7.

• Subsequently, determine the rate of CO₂ production by taking into account the age, sex, and metabolic activity of the individual.

• If the value of met exceeds 4, as indicated in Table 7, it is admitted to use the maximum value in Table 8 to satisfy the requirement of 4.

Activity	M (met)	Range
Dancing aerobic, general	7.3
Health club exercise classes general	5.0
Kitchen activity moderate effort	3.3
Lying or sitting quietly		1.0 to 1.3
Sitting reading, writing, typing	1.3
Sitting tasks, light effort (e.g., office work)	1.5
Sitting quietly in religious service	1.3
Sleeping	0.95
Standing quietly	1.3
Standing tasks, light effort (e.g., store clerk, filing)	3.0
Walking, less than 2 mph, level surface, very slow	2.0
Walking, 2.8 mph to 3.2 mph, level surface, moderate pace	3.5

Table 7.

Values of physical activity levels (met).

CO2 generation rate (L/s)
	Mean	Basal	Level of physical activity (met)
Age	Body	Metabolic
	Mass	Rate (BMR)
[years]	[Kg]	[MJ/day]	1.0	1.2	1.4	1.6	2.0	3.0	4.0
Males
to < 21	77.3	7.77	0.0037	0.0045	0.0053	0.0060	0.0059	0.0113	0.0150
to < 30	84.9	8.24	0.0039	0.0048	0.0056	0.0064	0.0063	0.0120	0.0160
to < 40	87.0	7.83	0.0037	0.0046	0.0053	0,0061	0.0059	0.0114	0.0152
to < 50	90.5	8.00	0.0038	0.0046	0.0054	0.0062	0.0060	0.0116	0.0155
Females
to < 21	65.9	6.12	0.0029	0.0036	0.0042	0.0047	0.0059	0.0089	0.0119
to < 30	71.9	6.49	0.0031	0.0038	0.0044	0.0050	0.0063	0.0094	0.0126
to < 40	74.8	6.08	0.0029	0.0035	0.0041	0,0047	0.0059	0.0088	0.0118
to < 50	77.1	6.16	0.0029	0.0036	0.0042	0.0048	0.0060	0.0090	0.0119

Table 8.

CO₂ generation rates for ranges of ages and physical activity, at 273°K and 101 KPa.

Suppose an individual exceeds the threshold of 4. In this case, it is essential to recognize that maintaining such levels of physical activity for extended periods is typically unfeasible for the general population, except for professional athletes.

Based on the outlined rules and tabulated data, the CO₂ emission rate can be computed as follows:

$${\mathit{CO}}_2=\left(\mathit{met}\ast N\right)\ast \frac{1}{\mathit{Pr}}\ast \frac{273.15+T}{273.15}$$E7

where CO₂ is the emission rate (for all people) and is expressed in $L/s$; $\mathit{Pr}$ is the Pressure and is expressed in $\mathit{atm}$; $\mathit{met}$ is the generation rate; $N$ is the number of people present; T is the Temperature, measured in °C.

In addition, CO₂ mixing ratio is given by the following formula:

$${\mathit{CO}}_{2{\mathit{AVG}}_m}=\frac{\left(\mathit{CO}2\ast 3.6\right)}{\mathit{\lambda v}V}\ast \left(1-\left(\frac{1}{\mathit{\lambda v}D}\right)\ast \left(1-e^{-\mathit{\lambda v}D}\right)\right)\ast 1000000+B_{{\mathit{CO}}_2}$$E8

where ${\mathit{CO}}_{2{\mathit{AVG}}_m}$ is the avg. mixing ratio $\left(\mathit{ppm}\right)$; CO₂ is the emission rate (for all people) $\left(L/s\right)$; $\lambda$v is the added effects of ventilation $\left(1/\mathit{\text{hours}}\right)$; D is the duration of exposure $\left(\mathit{\text{hours}}\right)$; $B_{{\mathit{CO}}_2}$ is the Background CO₂ Outdoors $\left(\mathit{ppm}\right)$ measured in the range between 350 and 450 ppm.

3. Modeling infection risk

3.1 Infection probability

The quantum emission rates exhibit a wide range of variation, depending mainly on the nature of the activities to be performed. Activities with low intensity correspond to lower emission rates. In contrast, loud talking, shouting, and singing correspond to higher emission rates, as highlighted by data reported in Table 1. The volumetric breathing rates vary depending on the specific activity being performed, as highlighted by data presented in Table 2. Despite the presence of uncertainties in the emission values of SARS-CoV-2 quanta/h, it is feasible to compute estimates of infection risk and draw comparisons regarding the impact of factors such as ventilation, room characteristics, duration of exposure, and the adoption or non-adoption of masks. The estimation of the probability of infection as a function of the duration of exposure time for a set of commonly used environments is depicted in Figure 1. People between the ages of 21 and 31 are considered. It is also assumed that at least one person is infected. The study evaluates different quantum emission rates for various settings. For instance, a quantum emission rate of 11.4 quanta/h is assumed to be appropriate for school and office environments, while a rate of 26.3 quanta/h is considered to be suitable for restaurants. Similarly, a quantum emission rate equal to 5.6 quanta/h is considered to be appropriate for libraries, and a rate of 63.1 quanta/h is suitable for gyms. The results depicted in Figure 1 indicate a positive correlation between the duration of exposure and the probability of contracting an infection. Based on a two-hour exposure time, the probability of infection is relatively low, specifically below 5%, for a library accommodating 20 individuals, a school classroom with 21 students, and a restaurant with 78 people. In contrast, in high-intensity activity settings, such as a GYM, the probability of contagion increases more rapidly, due to the increase in the emission of quanta by individuals. There is also a higher probability of infection in office rooms due to their relatively small dimensions and typical occupancy ranging from one to two people.

Figure 1.

Relationship between occupancy time and probability of infection in various common environments.

3.2 The impact of mask-wearing

Figure 2(a) displays the projected correlation between the probability of contracting an infection, the duration of residency, and the number of ACH for individuals wearing a mask. Conversely, Figure 2(b) illustrates the same association for individuals not wearing masks. The results suggest that using masks is a significant factor in mitigating the probability of contracting an infection. In the case of an infected individual being present in a given space, the adoption of masks by both the infected and susceptible individuals may reduce the probability of infection to less than 1%, thereby requiring a specific ACH. The results depicted in Figure 2 indicate that a higher ACH value corresponds to a relatively low probability of infection, with a rate below 5%. Conversely, a decrease in the ACH value is associated with an increase in the probability of infection.

Figure 2.

Probability of infection vs. permanence time, for different ACH values: (a) without a mask (b) with a mask.

3.3 CO₂ generation rate

The rate of CO₂ generation is evaluated for different environments featuring activities of varying intensities, and the results are illustrated in Figure 3. The correlation between the CO₂ concentration and the number of quanta required by an individual in an enclosed space is observed. Similarly, CO₂ concentrations tend to considerably increase over time, depending on the nature of the task and the number of individuals present.

Figure 3.

Relationship between carbon dioxide (CO₂) concentration and permanence time across various indoor environments.

The reference values for the concentration of CO₂, as defined in the literature [24], are considered as threshold values. A CO₂ concentration of less than 450 ppm is typically recommended for outdoor air, while indoor environments during pandemic situations are advised to maintain a reference value of 800 ppm for CO₂. However, it is also acceptable for indoor environments that CO₂ levels reach up to 1000 ppm. For levels greater than 1000 ppm, it is recommended that the duration of exposure should not surpass 8 hours. The sustained elevation of CO₂ levels over time can indicate insufficient ventilation relative to the number of occupants and the activities to be conducted.

3.4 Social distance to prevent COVID-19

Implementing social distancing measures is a crucial consideration to mitigate the transmission of viral infections within enclosed environments. The distance index can be derived through theoretical analysis of droplet dispersion and transmission resulting from human respiratory activities. According to the research conducted in [25], it is suggested that a distance of 1.6–3.0 m (5.2–9.8 ft) may be assumed as a safe criterion in terms of aerosol transmission from large exhaled droplets during speech. However, when accounting for all droplets in still air, the safe social distance can be extended up to 8.2 m (26 ft). The adoption of Bluetooth technology is suggested to measure social distancing using the received signal intensity indicator (RSSI). The current approach exploits the functionalities of Bluetooth-enabled devices to determine proximity among individuals and mitigate the transmission of infectious diseases. Observing RSSI values of packets received from proximate devices makes it feasible to approximate the distance between individuals. As the distance between devices increases, RSSI values tend to decrease, thereby establishing a negative correlation between signal strength and proximity, as seen in Figure 4(a). In Figure 4(b), the application of curve fitting to experimental data is considered, wherein distances ranging from 0 to 7 meters between devices are assumed. This approach is applied to accurately correlate the distance and the RSSI-measured values. Eq. (9) represents the approximation model that depicts the correlation between the distance y measured in meters and the RSSI (dBm) value, namely:

Figure 4.

Distance measurements: (a) Relationship between RSSI and Distance; (b) Curve fitting to experimental data.

$$y=a1\ast \mathit{sin}\left(b1\ast x+c1\right)+a2\ast \mathit{sin}\left(b2\ast x+c2\right)+a3\ast \mathit{sin}\left(b3\ast x+c3\right)$$E9

where: a1 = 23.57; b1 = 0.005066; c1 = −2.92; a2 = 1.168; b2 = 0.09591; c2 = −1.643; a3 = 0.42; b3 = 0.2547; c3 = −3.135.

4. Experimental setup

The previously outlined model applied in this section to assess the probability of COVID-19 transmission is depicted in Figure 5, which incorporates all relevant parameters and equations. An application with specific functionalities is developed using Android Studio. An extensive representation of the architecture for the proposed system is illustrated in Figure 6. In particular, the system allows to choose between two distinct user categories: Regular User and Healthcare User. Three distinct blocks exist, namely the user input parameters, the risk analyzer, and the measurement of interpersonal distance. They are described in detail as follows.

1. Users enter data: in this block, the application requests the user to submit specific parameters related to the prediction of COVID-19, on the basis of the specific indoor environment. In the case of a regular user, an interface is presented that allows him to input known parameters and easily comprehend and navigate the application. In this instance, specific parameters are omitted, including the dimensions of the location (standard dimensions are considered for each environment), the number of infected individuals, the number of vaccinated individuals, the number of individuals who are already infected, and the type of vaccine. In contrast, healthcare users must input these more specific parameters to obtain more precise results. The information gathered by this block is sent to the Covid Risk Analyzer block.

2. Covid Risk Analyzer block: this block receives input from the first block; it processes data and computes the probability of contracting COVID-19, the maximum occupancy of a given space, the concentration of CO₂, and the necessary ACH required for the environment. Furthermore, this block enables the application to display alert notifications to the user under certain circumstances, namely:

   • when the probability of contagion is high;

   • once the maximum admitted capacity of individuals is overcome;

   • when the air quality is suboptimal, specifically when the concentration of CO₂ exceeds 1000 ppm.

3. Distance between individuals: the distance monitoring functionality is devised to collect Bluetooth data, including the approximated RSSI metric, and assess the proximity between close devices. In order to make use of this functionality, users must enable their Bluetooth connectivity. Upon activation, the system consistently monitors the distances among its users. If the proximity between individuals is measured under two meters, a notification alert is promptly generated to inform the user. Figure 7 depicts the visual representation of the block and its functionality. The above feature is essential to promote social distancing and ensure user’s safety.

Figure 5.

Flowchart for estimating the COVID-19 contagion risk.

Figure 6.

Application architecture.

Figure 7.

Schematic representation of social distancing.

5. Results and discussion

This section illustrates some relevant assessment cases of the application outlined in Ref. [26], by emphasizing critical scenarios essential for evaluating the probability of infection and quantifying distance between individuals. The study is limited to participants aged from 21 to 31 years, as this age group is the most prominent demographic for the selected scenarios in our analysis. However, users are not limited to this age range, and they can confidently choose any other age group.

5.1 Scenario 1-classroom

Scenario 1 involves a parameter analysis in a classroom with 61.2 m² in the area and 4.9 meters in height. A total number of 22 individuals are considered, with ages ranging from 21 to 31 years. It is important to note that in this scenario all individuals present wear facial masks, and the lesson time is scheduled to last two hours. The involved activity is characterized by light intensity and speaking. Significantly, this particular scenario considers the existence of ventilation with filters. Under these conditions, it is observed from Figure 8 that the probability of contracting an infection stands at 1.19%. Additionally, the concentration of CO₂ is measured at 927, indicating a tolerable level of indoor air quality.

Figure 8.

Evaluation of Scenario 2-Classroom.

5.2 Scenario 2-restaurant

In scenario 2, the case of a restaurant with an area of 111.48 m² and a height of 7.31 m is considered. The number of present people is equal to 78, with ages ranging from 21 to 31 years. They spent a total of 2 hours in the designated location. In this scenario, individuals do not wear masks, while filters facilitate ventilation. Moderate intensity and speaking are assumed for this activity. Figure 9 illustrates that the probability of infection under these conditions equals 2.08%, and the maximum allowed occupancy limit is not exceeded. However, by examining a significant population, the CO₂ concentration during this period assumes the high value of 1997, indicating poor indoor air quality. So, it is advisable to reduce the permanence duration.

Figure 9.

Evaluation of scenario 3-restaurant.

5.3 Scenario 3-sports and entertainment

The present scenario involves the analysis of a GYM, which encompasses an area of 371.61 m² and a height of 3.66 meters. There are 20 individuals in attendance, ranging in age from 21 to 31 years, and anyone wearing masks. The activity lasts two hours, characterized by high-intensity and loud speaking activity. Furthermore, the consideration of filter ventilation is included in this particular scenario. The analysis depicted in Figure 10 indicates a significant infection probability of 13.16%. Although the maximum occupancy limit has not been surpassed and the concentration of CO₂ is within acceptable levels, limiting the duration of stay is recommended due to the high intensity of the activity being conducted in this environment.

Figure 10.

Evaluation of scenario 6-sports and entertainment.

5.4 Distance between individuals

Figure 11 illustrates the operational capabilities of the application, demonstrating its capacity to exhibit a complete list of nearby devices, accompanied by their respective IP addresses, Indicator RSSI measurements, and approximated distances. If the distance of two meters between individuals is exceeded, a notification is sent to the user’s smartphone. This alert reminds individuals to modify their physical proximity and comply with the recommended social distancing protocols.

Figure 11.

Evaluation of distance between individuals.

6. Conclusions

An accurate model based on the Wells-Riley probabilistic methodology has been presented and discussed in this chapter to predict COVID-19 transmission in indoor environments. The basic theory of the proposed model has been deeply illustrated, by emphasizing its accuracy in assessing the transmission probability. In order to facilitate continuous monitoring of COVID-19 infection risk in indoor environments, the model has been incorporated into an innovative Android application that also computes the distance between individuals. The results obtained during the assessment stage of the model indicate that a combination of factors should be adopted accurately to manage the transmission of COVID-19 in indoor environments effectively. A proper approach should in fact include factors such as optimal ventilation, adherence to mask-wearing protocols, respect for occupancy limits, the minimization of time spent in closed spaces, and the maintenance of a minimum physical distance of two meters between individuals.

Acknowledgments

This research was funded by PNRR project Age-IT (Ageing well in an ageing society) - Conseguenze e sfide dell’invecchiamento, and by Progetto POS (Piano Operativo Salute) 2021 dal titolo “Radioamica – Open Network per la RADIOmica/rAdiogenoMIca Cooperativa basata su intelligenza artificiale” - Traiettoria 2 “E-Health, diagnostica avanzata, medical devices e mini invasività”, Azione 2.1 “Creazione di una rete nazionale per le malattie ad alto impatto” del Piano Sviluppo e Coesione Salute - FSC 2014-2020.

Abbreviations

IAQ	Indoor Air Quality
ACH	Air Changes per Hour
MERV	Minimum Efficiency Reporting Values
PSE	Particle Size Efficiency
HEPA	High-Efficiency Particulate Air
atm	Standard Atmosphere
RSSI	Received Signal Intensity Indicator
ppm	Parts per Million
IP	Internet Protocol