1 Infectious Probability Analysis on COVID-19 Spreading with Wireless Edge Networks

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Infectious Probability Analysis on COVID-19

Spreading with Wireless Edge Networks

Xuran Li, Shuaishuai Guo, Member, IEEE, Hong-Ning Dai, Senior Member, IEEE and Dengwang Li

Abstract—The emergence of infectious disease COVID-19 has

challenged and changed the world in an unprecedented man-

ner. The integration of wireless networks with edge computing

(namely wireless edge networks) brings opportunities to address

this crisis. In this paper, we aim to investigate the prediction of

the infectious probability and propose precautionary measures

against COVID-19 with the assistance of wireless edge networks.

Due to the availability of the recorded detention time and the

density of individuals within a wireless edge network, we propose

a stochastic geometry-based method to analyze the infectious

probability of individuals. The proposed method can well keep

the privacy of individuals in the system since it does not require to

know the location or trajectory of each individual. Moreover, we

also consider three types of mobility models and the static model

of individuals. Numerical results show that analytical results well

match with simulation results, thereby validating the accuracy

of the proposed model. Moreover, numerical results also offer

many insightful implications. Thereafter, we also offer a number

of countermeasures against the spread of COVID-19 based on

wireless edge networks. This study lays the foundation toward

predicting the infectious risk in realistic environment and points

out directions in mitigating the spread of infectious diseases with

the aid of wireless edge networks.

Index Terms—Infectious probability analysis, stochastic geom-

etry, wireless edge networks, mobility models.

I. INTRODUCTION

Recently, the rapid spread of the new coronavirus disease

(COVID-19) has brought serious challenges to the whole

world. As a high infectious disease, the virus of COVID-

19 could spread from humans to humans through respiratory

droplets, aerosols and other transmission manners [1], [2]. This

disease attacks the respiratory system of infected individuals

and results in many symptoms, such as fever, fatigue, dry

cough, muscular pain, and breathlessness. Therefore, taking

Manuscript received January 15, 2022; revised May 1, 2022; accepted June

16, 2022. The work is supported in part by the National Natural Science

Foundation of China under Grant 62171262, in part by Shandong Provincial

Natural Science Foundation under Grant ZR2021YQ47, in part by Major

Scientiﬁc and Technological Innovation Project of Shandong Province under

Grant 2020CXGC010109, in part by Tashan Young Scholar under Grant No.

tsqn201909043, in part by the National Natural Science Foundation of China

(61971271), the Jinan City-School Integration Development Strategy Project

(JNSX2021023), and the Shandong Province Major Technological Innovation

Project (2022CXGC010502). (Corresponding author: Shuaishuai Guo.)

Xuran Li and Dengwang Li are with Shandong Key Laboratory of Medical

Physics and Image Processing, School of Physics and Electronics, Shandong

Normal University, Jinan 250061, China (e-mail: sdnulxr@sdnu.edu.cn; deng-

wang@sdnu.edu.cn).

Shuaishuai Guo is with School of Control Science and Engineering,

Shandong University, Jinan 250061, China and also with Shandong Provin-

cial Key Laboratory of Wireless Communication Technologies (e-mail:

shuaishuai guo@sdu.edu.cn).

Hong-Ning Dai is with the Department of Computer Science, Hong Kong

Baptist University, Hong Kong SAR (e-mail: hndai@ieee.org).

effective countermeasures to combat the spread of the COVID-

19 becomes an important research topic for researchers in

different ﬁelds [3], [4].

A. Motivation

Research efforts from communications and computer com-

munities have been conducted to ﬁght against the spread of

COVID-19. In particular, recent studies [5]–[8] have investi-

gated to deploy the Internet of medical things (IoMT) and

establish the telemedicine platforms so as to mitigate the

bottlenecks at public healthcare institutions. Meanwhile, data

analytics and artiﬁcial intelligence (AI) techniques have been

investigated to combat COVID-19 from different perspectives,

such as diagnosis of new variants of COVID-19, spread

prediction, and transmission risk analysis [9]–[13]. Moreover,

blockchain techniques have been adopted for contact tracing

with privacy preservation [14]–[16]. However, most of the

aforementioned methods have stringent demands on the net-

work performance, such as low latency, high bitrate, and the

ability to handle requests from a large number of devices.

These proposed methods may not be feasible for off-the-shelf

network/computing infrastructures.

To fulﬁll the increasing computational/storage demands in

IoMT and telemedicine systems, a typical solution is to out-

source computational-complex tasks to remote cloud service

providers, which have stronger computational capability than

end devices. However, those cloud service providers are often

owned by untrusted third parties, who may mistakenly or

intentionally breach the data privacy [17], [18]. Meanwhile,

uploading computing tasks to remote clouds inevitably leads to

high latency. As an important complement to cloud computing,

edge computing has recently appeared as a promising solution

to IoMT [5], [19] since some computational tasks can be

ofﬂoaded to nearby edge computing nodes. Edge computing

nodes are typically deployed with existing wireless infrastruc-

tures (such as macro base stations, small base stations, access

points, and IoMT gateways) to form wireless edge networks.

In this paper, we investigate the adoption of wireless edge

networks to analyze and combat the spread of COVID-19.

The spread prediction of COVID-19 is one of the most

important countermeasures against the viral outbreaks [20].

For example, heat warning can provide a rough estimation on

possible infectious people by analyzing thermal images [21].

Moreover, the prediction system based on the conﬁrmed

infection cases [22] can predict hazard areas. Despite the

advent of these studies, most of them rely on data analysis at

cloud servers, which have privacy-leakage risks (as analyzed

arXiv:2210.02017v1 [cs.SI] 5 Oct 2022

above). In addition, the timely warning is crucial for an early

warning and disease control while cloud services inevitably

cause high latency. To address these issues, ofﬂoading the

prediction tasks at edge nodes is a promising solution. To the

best of our knowledge, there is no study on spread prediction

of COVID-19 and investigation of countermeasures based on

wireless edge networks.

B. Contributions

In this paper, we focus on establishing an analytical frame-

work to analyze the infectious probability of susceptible indi-

viduals and providing early warnings by exploiting wireless

edge networks. As indicated in previous studies [23]–[25],

the infectious probability of a susceptible individual heavily

depends on both the contact time and the distance between

the infected individual and the desired susceptible individual.

The detention time of individuals in a network is essentially

available at an edge server by service providers (i.e., we

use the detention time, which is longer than the contact

time, to calculate the infectious risk). Moreover, the distance

can be modelled by stochastic mechanism and stochastic

geometry [23], [26]–[28]. Inspired by these previous ﬁndings,

we then establish an analytical framework to evaluate the

infectious probability of susceptible individuals. Moreover, we

consider the impact of the mobility of individuals into our

analytical framework. In particular, our framework consider

three types of mobility models: the random direction (RD)

model [29], [30], random walk model (RWK) [31], [32]

and random waypoint (RWP) model [33]–[35]. Unlike other

methods requiring the location or trajectory of each individual,

our method can better protect the privacy of individuals since

only the recorded detention time1is used in our analysis.

After establishing the analytical framework of the infectious

probability and evaluating the impacts of multiple factors on

the infectious probability by extensive simulations, we also

discuss the countermeasures to combat the spread of infectious

diseases like COVID-19 and its variants. For example, edge

servers can offer early warnings to individuals within the same

network as the infected individual so that the corresponding

countermeasures (e.g., keeping social distance, wearing masks,

and improving ventilation) can be done.

The main research contributions of this paper can be sum-

marized as follows.

•In this work, we established a novel analytical frame-

work to analyze the infectious probability of susceptible

individuals within wireless edge networks. Deploying

this analytical framework at wireless edge networks can

potentially provide individuals with early warnings in

time while leaking less privacy of individuals.

•This analytical framework also investigates the effect

of individual mobility on infectious probability. Speciﬁ-

cally, the proposed framework considers the three most

commonly used mobility models: the RD model, RWK

model and RWP model. Extensive simulation results

1The detection time or access time can be obtained by mobile service

providers while less privacy is leaked in contrast to other pandemic surveil-

lance methods, which require to access more user-privacy sensitive data [36].

Base station Edge server Suspected

individual

Infected

individual

CDC

Fig. 1. System Model of Infectious Probability Analysis in Wireless Edge

Network.

agree with the analytical results, implying the accuracy

of the proposed framework.

•Analytical results suggest a number of countermeasures,

such as early warning and social distancing. The inte-

gration of these countermeasures with wireless edge net-

works can effectively mitigate the the spread of infectious

diseases.

The remainder of the paper is organized as follows. Sec-

tion II introduces the network model, the mobility models

of individuals, and the infectious model. Section III presents

the infectious probability analysis, including the analysis of

static individuals and the impact of mobility on the infectious

probability analysis. Section IV demonstrates the simulation

results. Section VI concludes this paper. Section V pointed

out the future research directions.

II. SYSTEM MODEL

This section presents the models including the net-

work model, infectious model and mobile models in Sec-

tions II-A, II-B II-C, respectively.

A. Network Model

Consider a wireless edge network as illustrated in Fig. 1,

where a number of mobile users are connected with a base

station, e.g., macro base station, Evolved Node B (eNB) in 4G

LTE or gNode in 5G networks. The base station is equipped

with an edge server, which can provide data storage and

computation services for mobile users. In this paper, we also

exploit the edge server to analyze the infectious probability

and send early warnings.

There are two types of mobile users randomly distributed in

this network. (1) The infected individuals are those individuals

who have already been infected by the virus and may transmit

the virus due to the high virus volume. (2) The susceptible

individuals are those individuals who are not infected and can

nevertheless become infected by infected individuals due to

the exposure to the infected individuals (especially in poorly

ventilated environment or enclosed environment). Section II-B

will present the infectious model. Both infected individuals

and susceptible individuals are randomly distributed according

to the uniform distribution. Moreover, those users are moving

within this network according to different mobile patterns

(they are modelled according to three types of mobility models

in Section II-C). Note that both the number of infected

individuals and the number of susceptible individuals are time-

varying since some newly infected individuals (or susceptible

individuals) may join the network while some of them may

leave in this network due to the mobility of individuals. In

addition, the susceptible individuals may become the infected

individuals after being medical diagnosed or tested (e.g.,

nucleic acid tests).

The edge server can analyze the infectious risk based on the

following available information. i) The statistical characteris-

tics of individuals’ distribution (i.e., the location distribution

of individuals) in the network area, can be obtained from

the trafﬁc management system or other related departments

(or services). ii) Infected individuals can be obtained by

Centers for Disease Control and Prevention (CDC) or other

agencies though the privacy of the infected individuals can

be properly protected by pseudonymity or other cryptographic

schemes (i.e., hiding the exact individual identiﬁcation). iii)

The detention time of each individual (both infected individual

and susceptible individual) is available by mobile services

providers. With the availability of the above information,

we aim to establish an analytical framework to analyze the

infectious probability of each susceptible individual. In our

framework, both speciﬁc location and trajectory of each indi-

vidual are not used. Therefore, the risk of privacy disclosure

for each individual is avoided. Without loss of generality,

the analysis of the infectious probability is conducted by

assuming the reference susceptible individual to be located

at the center. Based on the analytical model, the edge server

can calculate the infectious probability of each individual and

send early warning messages to the individuals (or suggest the

corresponding countermeasures in Section V).

B. Infectious Model

Although there are a number of studies on investigating the

transmission of infectious diseases [23]–[25], [37], they are

too complex to be directly adopted for the spread prediction of

infectious diseases in the scenarios of wireless edge networks.

Thus, it is a necessity to establish a simple yet effective

infectious model for estimating infectious risks in a crowded

scenario with the help of wireless edge networks.

As indicated by previous studies [23], [25], [37], [38], the

infectious risk signiﬁcantly drops with the increased distance

between the infected individual and a susceptible individual.

Inspired by these ﬁndings, we propose a simple-yet-effective

infectious model with consideration of multiple factors (such

as social distance, respiratory droplets, virus volume, time,

and transmission factor of infectious virus). In this model, we

ﬁrst deﬁne the metric of instant infectious strength denoted

by Iinf to evaluate the instantaneous spreading volume of the

virus transmitted from infected individuals to the susceptible

individual within a unit of time because previous studies

indicated the positive relation between the volume of virus and

the infectious rate [25], [37], [38]. Speciﬁcally, Iinf is given

as follows,

Iinf =

i=1

Vi·r−η

i,(1)

where Nis the number of infected individuals, Viis the virus

volume generated by the ith infected individual in the unit

time period, riis the distance from the ith infected individual

to the susceptible individual, and ηis the path loss factor of

the virus spreading that varies from 2 to 7 [25].Note that the

virus volume is a variable that varies with different infected

individuals [39]. For example, a higher virus volume may be

generated by infected individuals whose have more serious

symptoms while the infected individuals with slight symptoms

may generate fewer viral particles and have a smaller virus

volume [38], [39]. We denote the maximal virus volume and

the minimal virus volume generated by an infected individual

by VMand Vm, respectively. Therefore, the virus volume Vi

generated by the ith infected individual varies from Vmto VM.

As shown in previous studies [25], [37], a higher virus

volume leads to a higher chance of an individual being affected

and a longer detention time (or contact time) leads to a higher

risk of an individual being affected. We let Vth denote the

threshold virus volume that may lead a susceptible individual

to become an infected individual. We then deﬁne the instan-

taneous infectious probability to evaluate the probability that

a susceptible individual may become an infected individual

within a unit of time. The instantaneous infectious probability

is denoted by Pinf, which is expressed as follows,

Pinf =P(Iinf ≥Vth) = P N

i=1

Vi·r−η

i≥Vth!.(2)

We next deﬁne the total risk of a susceptible individual

becoming infected with consideration of the detention time.

The total risk of a susceptible individual becoming infected

is denoted by Rtotal. Since the detention duration Tthat a

susceptible individual is available at the edge server, we can

calculate the total risk Rtotal as follows,

Rtotal =ZT

Pinfdt =ZT

P N

i=1

Vi·r−η

i≥Vth!dt. (3)

C. Mobility Models

The mobility of an infected individual may affect the

infectious probability of the susceptible individual due to the

varied distance. Our analytical framework also considers three

conventional mobility models, which are given as follows.

1) RD Model: Each infected individual moves toward a

random direction within [0,2π), which is independent of other

infected individuals. Meanwhile, the infected individual moves

a random distance Rtoward this direction at a constant speed

v. Upon his/her arrival of a certain location, another random

direction and distance Rare chosen; this procedure repeats.

2) RWK Model: This model was originally proposed to de-

scribe the unpredictable movement of particles in nature [31].

In our framework, each infected individual moves toward a

random direction within [0,2π), independently of the other

infected individuals, and moves with a ﬁxed distance W

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1InfectiousProbabilityAnalysisonCOVID-19SpreadingwithWirelessEdgeNetworksXuranLi,ShuaishuaiGuo,Member,IEEE,Hong-NingDai,SeniorMember,IEEEandDengwangLiAbstractTheemergenceofinfectiousdiseaseCOVID-19haschallengedandchangedtheworldinanunprecedentedman-ner.Theintegrationofwirelessnetworkswithedgecomput...

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