key: cord-169428-g6k0vqrm
authors: Schurwanz, Max; Hoeher, Peter Adam; Bhattacharjee, Sunasheer; Damrath, Martin; Stratmann, Lukas; Dressler, Falko
title: Infectious Disease Transmission via Aerosol Propagation from a Molecular Communication Perspective: Shannon Meets Coronavirus
date: 2020-10-31
journal: nan
DOI: nan
sha: 
doc_id: 169428
cord_uid: g6k0vqrm

Molecular communication is not just able to mimic biological and chemical communication mechanisms, but also provides a theoretical framework regarding viral infection processes. In this tutorial, aerosol and droplet transmission is modeled as a multiuser scenario with mobile nodes, related to broadcasting and relaying. In contrast to data communication systems, in the application of pathogen-laden aerosol transmission, mutual information between nodes should be minimized. Towards this goal, several countermeasures are reasoned. The findings are supported by experimental results and by an advanced particle simulation tool. This work is inspired by the recent outbreak of the coronavirus (COVID-19) pandemic, but also applicable to other air-borne infectious diseases like influenza.

and innovative solutions to urgent problems. The need for novel solutions has already created rapid infection control solutions during the pandemic. These include "social distancing" rules [5] , mouth and nose protection in public spaces, and large-scale disinfection measures as suggested by the various institutes of health care and virology around the world. Just as MC combines biological/chemical and communication/information theoretical approaches to provide systematic solutions, a bridge can be built between MC and infectiology to apply known techniques from information engineering to the field of health care and infection prevention. Findings from health research dealing with the spread of aerosols and the viruses they may contain, can be joined with insights from MC in order to predict infection processes and to identify more sophisticated and safer protective measures.

Recent research in combining these areas has dealt with possible use cases for aerosol communications [6] , and with channel modeling considering infectious aerosols in a point-topoint scenario [7] , [8] . An infected person acts as a transmitter of pathogen-laden aerosols and a device or another person acts as a receiver of the infectious particles. The close relation to the domain of macroscopic MC, where a transmitter emits molecules into a fluid environment with an absorbing receiver to recover the information, was exploited. In [9] , the concept has been expanded to include several features:

• The transmission of infectious aerosols is suggested to be a multiuser MC scenario. • In each MC transmitter, the modulator is modeled by respiratory-event-driven higher order molecular variableconcentration shift keying [10] . • Channel modeling is aided by air-based experiments using a fluorescence dye in conjunction with optical detection, motivated by the macroscopic testbed for airbased MC published in [11] . • An advanced computer simulation tool has also been designed based on the work in [12] . Parameters feeding this tool were obtained by own experiments, among other established sources.

A large variety of safety measures can be rethought from a communication and information theory perspective to optimize the goal of infection prevention. Building on the novel contributions revealed in [9] , this tutorial presents the following communication aspects in greater depth:

• The transmission of infectious particles is modeled as a multiuser MC scenario with mobile nodes in a timevarying environment. Infected users are transmitters that broadcast pathogen particles, whereas the remaining users are potential receivers. After a certain delay, some of the receivers may become active transmitters, like in relaying. • The reception of the particles is represented by effective apertures, which map specific body regions of the user responsible for the infection, similar to antennas in wireless communications. • Infection is considered to be a generalized threshold detection problem: if the density of infectious particles received exceeds a user-dependent threshold, an infection is likely to occur. Furthermore, the viral load may also affect the course of the disease if it is above the infection threshold. In the field of MC, the corresponding analogy is reliability information. • The viral infection rate is modeled by the concept of mutual information [13] . Contrary to data transmission, the aim is to minimize the mutual information between an infected user and the healthy ones. The remainder of this tutorial paper is structured as follows: Section II describes the duality between communication and information theory on the one hand and the field of airborne aerosol infection on the other. In Section III, the concept of mutual information is introduced to the area of infectious disease transmission. Prevention techniques from different areas are discussed to minimize the mutual information in order to reduce the risk of infection. Section IV presents a particle simulation tool suitable for the problem under investigation, and corresponding simulation results for a multiuser scenario. Section V discusses the challenges that arise from the duality concept, before finally drawing the conclusions in Section VI.

In the area of wireless communications, a general multiuser scenario consists of multiple participants distributed in a three dimensional (3D) environment, acting as transmitters and/or receivers. The communication links between all users are distorted channels, influenced by various environmental parameters and the emitted signal powers. In the scenario under investigation, the signal powers are modeled in terms of the parameters of the emitted aerosols and the contained viral load coming from the infected user(s). Analogous to infectiology, in this multiuser scenario one assumes at least one infected person who, unlike the other participants, emits infectious aerosols and droplets. This situation can be understood as a point-to-multipoint communication scenario at the physical layer, related to broadcasting and relaying. In case of a successful transmission -a necessary condition is that the ingested amount of infectious aerosols exceeds the infection threshold -the receiver itself becomes an active transmitter after a certain incubation period. The relays act as virus spreaders or even superspreaders, i.e., they boost the viral load. Table I features some duality aspects between air-based MC on the one hand and infectious particle transmission on the other. Details will be presented next.

The emission of aerosols and droplets is triggered by respiratory events such as breathing, speaking, singing, coughing or sneezing. These actions can be divided into three categories according to their type of occurrence, cf. Fig. 1 :

1) Breathing can be modeled as continuous emission, following a breathing pattern, mainly influenced by the physical stress on the human body. Other factors like size of the body or age may also be considered. 2) Speaking/singing can be described as a two-state Markov process with the two states being either silence or singing/speaking. The model is defined by the transition probabilities between the two states and retention probabilities for staying in the current state. 3) Coughing/sneezing can be emulated as a Poisson random process. The density parameters are influenced by the infection state of the user, resulting in a higher probability for an infected user to cough or sneeze than for a healthy user. Based on these actions, the users emit aerosols into the environment. The different respiratory actions are responsible for the main parameters of the emission of aerosols, namely the • number of emitted aerosols, • diameter distribution, • initial velocity distribution, • temperature distribution, and • viral load or viral distribution. Each respiratory event causes a time-varying particle cloud, even in the absence of air movement. Due to a counteraction between air drag, buoyancy, and gravity, aerosols survive for a longer period than droplets [7] , [8] . The particle clouds of different respiratory events superimpose. All parameters are of stochastic nature where the actual emitted aerosol distribution changes between users and with each emission. The infection state of the human ultimately decides if an emission contains pathogens or not, so every healthy user emits aerosols, but these have no influence on the infection status of the other users when received.

As an alternative to the experiments conducted in [9] , the mentioned respiratory events can be emulated in the macroscopic-scale air-based testbed introduced in [11] . Mouth and nose are replaced by transmitter-side sprayers. In order to visualize particles, a fluorescent dye solution is emitted. Intensity and duty cycle are software-controlled. The angle of departure is adjustable. All mentioned actions can be emulated by respiratory-event-driven higher order molecular variableconcentration shift keying (MoVCSK) modulation [9] . In this context, an MoVCSK modulator is capable to release infected and non-infected particles. This can be further refined by distinguishing between particles of different sizes. The intensities of the respiratory events are mapped to the different concentration levels. The random occurrence of the events over time can be represented by a sequence of MoVCSK symbols.

Several parts of the human body are actively or passively involved in the absorption of aerosols, as depicted in Fig. 2 . The facial region with the mouth, the nose and the eyes is the most sensitive receiving area [8] , implying that a small amount of received aerosols can lead to an infection of the user. Other parts of the body like hands and feet or shoes are passively involved by receiving infected aerosols and either transferring them to more sensitive parts of the user by smear infection or contaminating other surfaces, which in turn can cause infection.

The reception-sensitive body areas can be interpreted as effective apertures, similar to spatially distributed antennas, with individual antenna gains and sensitivity levels. Starting with the highly sensitive body regions in the face, which can trigger an infection even with a low viral load, to the feet or shoes, which are only infectious to humans in certain cases and with a very high viral load. The sensitivity levels of the individual sensors contribute to the user-dependent infection threshold, which depends on other criteria as well including the health conditions.

The amount of viral molecules that the receiver absorbs per time unit, i.e. the viral load, has an impact on the probability of infection. According to the state-of-the-art, the human-dependent infection threshold is checked by hypothesis testing [7] , [8] : the probability of infection corresponds to the situation where the viral load exceeds the threshold. However, the viral load additionally is likely to have an influence on the severity of the course of the disease. This situation is related to reliability information. In communication and information theory, receiver-side reliability information describes the quality of information transmission in terms of the error rate.

From the perspective of our testbed, the water-based dye solution from the sprayer can be monitored and recorded by a digital camera at the receiver side under the influence of an ultraviolet (UV-A) light source. The intensity recorded by the camera can be interpreted as the viral load carried by the transmitted droplets over a certain distance through active transmission. The region between the sprayer and the camera also contains those droplets which settle down under the influence of gravity. The intensities from these droplets can be recorded to formulate a model for passive transmission of pathogens.

The spatially-distributed time-varying aerosol clouds that are emitted into the environment from the various users, are subject to a dynamic channel with turbulences and changing parameters. Various effects change the channel and cause the aerosols to propagate through the space with different velocities and ranges. The turbulences in the air are caused by the movement of the users, ventilation devices, air streams introduced through windows and doors, temperature gradients, and/or weather phenomena. Turbulence can either increase the range of the aerosols by constructively influencing the propagation vector, or reduce it when the particles are forced to the ground. In the testbed environment, turbulence can be modeled by introducing an external fan into the setup to cause an artificial air movement.

The turbulent channel can be described by Shannon's "mother of all models" [14] . This analogy is exploited subsequently.

The scenario under investigation comprises multiple users in a predefined environment, see Fig. 3 .

Initially, at the physical layer level, the multiuser scenario can be described by a point-to-multipoint network, the nodes of which comprise of the entire set of users. The infectious user broadcasts pathogens. Some of these can be absorbed by one or more healthy users. Those users can be modeled as store and forward relays, which after some delay may broadcast even more pathogens. When the number of infectious users increases on average, the reproduction factor is said to be greater than one.

In the case of a testbed, a point-to-multipoint scenario can be emulated by having multiple cameras placed at various locations acting as receivers. The intensities are recorded by the cameras and if the measurements breach a certain threshold level, the receivers may be termed as "infected" which may further trigger new sprayers to activate and start spraying the water-based dye solutions, mimicking a relay mechanism.

The users are able to dynamically move and change their absolute and relative positions. The absolute position change results in a random emission pattern, where the infectious aerosols are emitted at multiple locations throughout the environment. Depending on the channel characteristics, the aerosols are able to stay suspended in the air for some time, resulting in a risk of infection for other users that move with their apertures through the aerosol clouds or that are hit by moving clouds.

Infection prevention by means of "social distancing" is focused on the relative positions among the users. Keeping appropriate relative distances may lead to a reduction of mutual information transfer, but ignores the possibility of the presence of suspended aerosols in the environment from previous respiratory events from other users at the same absolute position.

In addition, the movement of the users create movement and turbulences of the surrounding air, which in itself results in a change of aerosol movement.

In this section, the concept of mutual information is introduced to the area of infectious disease transmission. Contrary to a maximization of mutual information in data communication systems, the aim of infection prevention is to minimize the mutual information between nodes. This can be accomplished by employing several methods that are discussed afterwards.

Infection is strongly related to the probability that a certain density of pathogen-laden particles successfully come into contact with the effective aperture area of the receiver. If the receiver-side density exceeds the user-dependent infection threshold, after a certain incubation time, the receiver will become infected with a certain probability. In terms of Shannon information theory, this situation can be modeled mathematically by means of mutual information. Starting off with a point-to-point channel [14] , let x denote the channel input symbol and y the corresponding observation. The mutual information is a function of the channel input distribution, p(x), and the joint probability p(x, y). In our case, the channel input distribution depends on the respiratory events and the joint distribution on the nature of the turbulent atmospheric channel. This concept can be generalized to multiuser channel models. Details, however, are beyond the tutorial style of this article. The analogy between aerosol-based infection and mutual information demonstrates three important facts: the risk of infection depends on the channel input distribution, the turbulent channel, and the infection threshold. Although a minimization of mutual information is counterproductive in classical communication scenarios, it is a common design objective in cryptosystems. Fig. 4 summarises several techniques/approaches that reduce the risk of infection. These are described next in connection with mutual information.

Spatial actions: Maximization of Euclidean distances between the users in the multiuser scenario under investigation, i.e., "social distancing", aims to reduce the probability of direct infection caused by respiratory events. Other techniques like pruning/thinning the user density in a certain space as well as route optimizations to reduce the interference of users trajectories with infectious aerosol clouds have a similar impact on the propagation conditions. Despite these spatial actions, sometimes it is desirable that the users are still able to communicate with each other. Hence, Another physical approach is air humidification. If the relative humidity of the room air is below 40 percent, the emitted particles absorb less water, stay lighter and move around the room for a longer period. In addition, the nasal mucous membranes in our noses become drier and more permeable to viruses when the air is dry. This has an impact on the infection threshold. Additional precautions like indoor fans, air ventilation, and air purification devices are also useful, as well as fresh air through open windows to prevent an accumulation of infectious aerosols in the ambient air.

Temporal actions: The allocation of individual time slots on user or group level leads to a more orderly procedure and this results in a lower probability of infection. This technique is known as time-division multiple access and is widely used in communication engineering.

Chemical actions: Reducing the viral load on surfaces is a key factor in infection prevention. This can be accomplished by cleaning of shoes or disinfection of the hands, as they are part of the effective aperture of the receiver. Household bleach solution containing 5.25 to 8.25 percent sodium hypochlorite could be used to disinfect surfaces while at least a 70 percent ethyl/isopropyl alcohol solution proves to be effective when it comes to proper disinfection of hands.

Optical actions: The viral load in airborne aerosols that were expelled into the air can be reduced by ultraviolet germicidal irradiation. This technique can be used in air purifiers to filter stale air, to clean handles, and other surfaces. It is essential to ensure that the skin and eyes are protected from radiation. Furthermore, UV-C irradiation can be employed for cleaning protection masks, even online when integrated into exhalation valves embedded in medical masks. Biological actions: Medical methods with a direct effect on the receiver's detection mechanism provide the best protection against transmission of infection. At the same time, a biological solution is also the most difficult to apply to a wide range of users. An example of a biological action would be vaccination. At the same time, this is also the least broadly based mechanism, as vaccination usually only protects against a specific pathogen. Ongoing research on biochemical nose sprays and mouthrinses is aimed at improving the infection threshold as well.

Note that all these techniques/approaches have an influence on the mutual information. Some target the propagation conditions while others affect either the particle emission or the infection threshold, respectively.

The propagation of aerosols can be simulated with high accuracy with the help of existing computational fluid dynamics (CFD) tools [15] . This approach, however, is very demanding on computational resources. If the goal is to simulate the spreading of disease in a multiuser scenario with mobility and over longer periods of simulated time, MC simulation tools optimized for the simulation of pathogen-laden particle transfer may become useful.

In previous work [9] , we have extended the MC simulator presented in [12] aiming to replicate a coughing event. In the current contribution, this scenario is extended further towards a multiuser network. An emitter as presented in [9] is an object which can be freely moved or duplicated in the simulation space. At a specified time, the emitter releases 20 particles in intervals of 0.25 ms simulation time for a fixed duration of 100 ms. The angle and velocity of emission are determined randomly based on the configured random distributions. After emission, the trajectory of each particle is guided by its inertia and the forces acting on it, namely air drag, buoyancy, and gravity. When a particle eventually collides with an absorbing receiver such as the ground or a spherical shape, it will be removed from the simulation and the position and speed of collision can be logged.

As an example, let us consider a scenario with three people. Each of the three people is modeled as having one point emitter at mouth height (1.65 m), one absorbing spherical receiver with a radius of 5 cm immediately behind the point of emission, as well as two additional spherical receivers of the same size to model the hands at a height of 70 cm with a lateral offset of 30 cm. Initially, person A represents an emitter and coughs with the parameters we determined experimentally in [9] . As one alteration to these parameters, the emission opening angle is now sampled randomly for each ejected particle based on the empirical cumulative distribution function of observed emission angles. Previously, the emission opening angle was approximated with a normal distribution. At a distance of 2 m opposite of person A, person B is a passive receiver. 75 cm to the left of person B is person C, who acts as both a receiver as well as a second transmitter with a delay of 3 s. In our previous work, the trajectory of simulated particles was only determined by their initial velocity vector at the time of emission and the forces acting on them, assuming a completely stationary volume of air for computing the drag force. In order to emulate the initial ejection of air in a coughing event in a simplified fashion, we can emit the simulated particles inside a volume of constant air speed. For this demonstration, we chose a 3 m long and 1 m wide cylindrical volume aligned with the vector of emission at the mouth, and an air speed of 5 m s −1 .

As shown in Fig. 5 , the receiving person B standing 2 m in front of the emitter A is surrounded by the bulk of particles that have been emitted. This receiver's facial region has received 112 simulated particles and the hands have received 14 particles, out of a total of 8000 emitted particles per cough. The second receiver, offset by 75 cm to the left of the first receiving person, did not receive any particles from the cough. When this receiver C becomes the second emitter, the situation is mirrored and the first emitter A, now a receiver, is only reached by two particles at the closest hand.

In future work, this simulation concept can be extended further to account for both the aspect of mobility and the remaining types of aerosol emissions outlined in Section II. Mobility can be realized, for example, by letting simulated persons follow predetermined paths collected from real-world mobility traces, or paths hand-drawn using 3D animation software. Alternatively, such paths may be generated randomly. When incorporating other emission types, like with the airbased testbed as also outlined in Section II, MoVCSK can be used as a modulation scheme to control the emission of particles.

This article extends recent advancements with respect to the symbiosis of MC and infectiology [6]- [9] . Emphasis is on a conceptual level by pointing out dualities and similarities between these fields. A key aspect is to treat the transmission of pathogen-laden particles as a dynamic multiuser communication scenario. Nevertheless, especially when combining different disciplines like engineering and health care, it should be checked whether the proposed approaches also lead to comparable results and are therefore fundamentally correct.

New findings from existing and refined MC techniques can be applied in infectiology and evaluated from a health care point of view. Furthermore, a reverse check of established infection prevention techniques can be accomplished by means of tools established in communication and information theory. These reviews will show whether the dualities and similarities described above can lead to new prevention approaches being useful in the real world and thus reducing the incidence of infection. The fact that both research areas are mature, opens up the possibility for a reciprocal examination of the respective other side.

Air-based MC with fluorescent particles offers new possibilities with regard to the investigation of the propagation of aerosols. The testbeds and measurement tools can be used to verify precautions like face masks and gain further insights into infectious ranges.

Due to the continuing spread of SARS-CoV-2, it is assumed that the social objective is now to "live with the virus" and to control viral spreading or at least its impact on individuals, on the society, and on economical aspects. Other diseases such as influenza show a similar behavior. Warning apps, already used in many countries in the context of the SARS-CoV-2 virus to track contacts between infected and non-infected people, are already laying the foundations for this objective. They can perhaps be extended with an online functionality to warn users in real time of a possible infection with the virus. It is also conceivable that MC-based contributions including channel modeling can be exploited to place future virus detectors at the best possible positions.

We studied infectious disease transmission via aerosol propagation as viewed from a communication and information theory perspective. Towards this goal, dualities and similarities between macroscopic air-based MC and infected particle transmission are worked out. In the concept, for the first time, users are modeled as mobile nodes in a multiuser scenario. Infected users emit aerosol clouds in the sense of broadcasting, whereas healthy users may become infected with a certain probability if they absorb a sufficient viral load by viral-sensitive aperture areas, like spatially distributed antennas in the area of wireless communications. In turn, after some incubation time, these users may become pathogen-laden spreaders or superspreaders as well, related to store and forward relaying. Apart from being a pure binary problem of getting infected or not, the viral load frequently has an impact on the course of the disease, similar to reliability information in MC. In the sense of Shannon information theory, the goal is to minimize the mutual information between infected and non-infected users, where the information corresponds to infected and non-infected particles. In this stochastic approach of infection prevention, numerous actions are discussed regarding channel input distribution, channel propagation, and channel output characteristic. For example, protective masks affect the channel input distribution. Spatial and temporal actions mainly have an impact on the channel propagation. Biochemical actions as well as health conditions affect the infection threshold at the channel output. Additionally, challenges regarding "living with the virus" are discussed. The conceptual approach is supported by an experimental macroscopic-scale molecular communication testbed and by an advanced simulation tool. As an example, simulation results are presented for a 3D environment with three users who emit aerosols that are subject to air movement due to the ejection action.

Molecular Communication. Cambrigde

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Channel modeling for diffusive molecular communication -A tutorial review

Targeted social distancing designs for pandemic influenza

Communication through breath: Aerosol transmission

Modeling of viral aerosol transmission and detection

A molecular communication perspective on airborne pathogen transmission and reception via droplets generated by coughing and sneezing

Duality between coronavirus transmission and air-based macroscopic molecular communication

EXIT chart analysis of higher order modulation schemes in molecular communications

A testbed and simulation framework for air-based molecular communication testbed using fluorescein

Efficient simulation of macroscopic molecular communication: The Pogona simulator

Mutual information and maximum achievable rate for mobile molecular communication systems

A mathematical theory of communication

Numerical investigation of aerosol transport in a classroom with relevance to COVID-19

Since 2020, he is a Research Assistant at the Chair of Information and Coding Theory, Kiel University. His current research interests include air-based macroscopic molecular communication and radar signal processing

Since 1998 he is a Full Professor of electrical and information engineering at

where he is currently pursuing the Dr.-Ing. (Ph.D.) degree at the Faculty of Engineering. Since 2019, he has been a Research and Teaching Assistant at the Chair of Information and Coding Theory, Kiel University. His current research interests include physical layer issues of