COVID19: Confinement Control based on a New Discrete

Localization Algorithm (DLA)

Yves Frederic Ebobisse Djene

1,2

, Rafiqa Zerououl

, Amine Berrazzouk

, Youness Chaabi

Fatima-Zahra Belouadha

4,5

, Younes Bekali Karfa

5,6

, Brahim El Bhiri

LARIT- IBN Tofail University, Kenitra, Morocco

SMARTiLab EMSI, Rabat, Morocco

CEISIC, IRCAM, Rabat, Morocco

EMI, Rabat, Morocco

Faculté des Sciences de Rabat

Mohammed V University in Rabat, Morocco

,bra.elbhiri}@gmail.com, y.bekali@um5r.ac.ma

Keywords: COVID-19, mobile Applications, Graph theory, Code QR, Confinement/Deconfinement.

Abstract: Mobile apps have potential to reinforce contact- tracing policies to cover and reverse the spread of COVID-

19. However, the majority of applications are based on the use of GPS, which have limitations linked to the

violation of data privacy. This finding is strongly refused by human rights NGOs. In this context, we propose

a concrete and operational digital solution related to epidemics including Covid-19, which is today the highest

international priority. This solution based on Discrete Localization Algorithm (DLA) is a complete and legal

intelligent solution to automate containment control and the deconfinement processes.

1 INTRODUCTION

The first case of the Corona virus epidemic (COVID-

19) procured in China (Wu, 2020), started at the end

of 2019 and quickly dispersed to the whole word.

Indeed, the mortality rate of Covid-19 is not as

high as that of MERS or SARS. However, it is a novel

virus with no effective cures or vaccines, which can

disrupt the public health systems. Moreover, most

Covid-19 patients in modest parts of the population

have to battle with severe pneumonia without crucial

life support, and thus leading to much higher fatality

rates (Ferguson, 2020).

Over the world, to curb the outbreak and stop the

spread of COVID-19, national governments

particularly implemented two approaches. The first

approach included rigorous social distancing

measures, such as the national lockdown (closing

down of schools, public places, closure of non-

essential commercial and industrial activities and a

ban on non-essential traveling). The main goal of this

strategy was to reduce contact between all types of

persons and subsequently control the reproduction

number R0, which is the average number of persons

affected by an infectious person. This methodology

was thoroughly implemented by China, effectively

conquering the epidemic in a couple of months, and

the method was thereafter adopted by most Western

countries. However, there has been no reports on the

strategies to implement after the Pandemic is tamed,

which leaves most of the population still vulnerable

to the virus and thus prone to a second wave of virus

propagation.

The second approach is mitigation: The idea is to

focus on slowing rather than stopping the spread of

the epidemic, leading to herd immunity, while

controlling it by protecting those at most risk of

serious illness from infection, in a way that ensures

the continuity of the public health system. This

approach initially spearheaded by (Hunter, 2020), has

been adopted by the UK government, which later

changed the strategy to transmission suppression after

the public release of the 9th related report from

Imperial College London (Ferguson, 2020).

Truly, other measures and procedures can be used

to control the mentioned index R0. For instance, the

use of digital and special mobile applications in

combating COVID-19 has been largely discussed and

suggested. These apps are designed to help contact

tracing and identifying persons in response to the

COVID-19 pandemic. In this perspective, several

applications were suggested, with official

government support in some countries. Several states

recognize that the value of such apps needs to be

considered within the context of wider public health

measures and the stage of the spread of the infection.

These mobile applications seem to be very interesting

as they can help in identifying the infected persons,

contact tracing and averting, symptoms checking and

contact notification contacts etc.

Since the beginning of the COVID-19 pandemic,

many smartphone apps have been developed, some of

them by public authorities. Moreover, the World

Health Organization (WHO) is working on an

application that can provide medically- approved

information and inform the users based on their

symptoms (WHO, 2020). This standalone application

comes besides the WhatsApp-based messaging

(WHO, August 2020).

However, the Covid-19 mobile apps must have

full compliance and ensure privacy legislation and

data protection. These Privacy worries have been

raised, especially about systems that are established

on tracking the geographical location of application

users. A of lot of measurements are taken to deal with

such problems, like the use of the anonymized data,

which does not consist of storing data in centralized

databases...

In the case of Morocco, the police have been using

a mobile application to follow on individuals that do

not respect the travel restrictions imposed to fight

Covid-19. With the same objective, we propose in

this study a new efficient system for controlling the

COVID-19 pandemic. This digital system is based on

a mathematical formalism to ensure confinement

control while respecting privacy data protection. This

solution can widely control the R0 parameter by

controlling the citizens mobility.

As presented in the following sections of this

paper, the proposed system uses a new concept called

the Discrete Localization Algorithm (DLA) and can

help to widely control R0 index with data protection.

The main objective of our system is twofold. On

one hand, it targets the authorization strategy control

and congestion suppression by automatically

generating authorizations to go out of the house or

those delivered by the job office with respect of the

data privacy. On the other hand, the system targets

data census by collecting information on people’s

mobility and compliance to confinement rules. Our

system therefore solves problems related to the time

delays in the measurements and control of the R0

parameter.

This study presents Graph theory and Minimum

Spanning Tree algorithm as well as details on the

Discrete Localization Algorithm (DLA), including

simulations.

2 GRAPH THEORY AND

MINIMUM SPANNING TREE

Our approach is based on graph theory and minimum

spanning tree. Thus, each city (region or country) can

be rep- resented by its corresponding undirected and

connected graph G(B; E) where B is the set of vertices

(nodes) representing different police control point,

and E is the set of links between nodes (itineraries).

Each vertex of B is indicated by an index i € 1, ..., N.

identifies the edge between the nodes B

and B

represented in figure 1.

For the connected graph G (B; E), the minimum

spanning tree (MST) problem is focused on finding a

spanning tree with minimum total edge weight. This

problem has been widely considered and is a sub-

problem of many known network problems. Its

applicable in wireless networks and VLSI design

(AFP, 2020), (Tseng, 1998), (Zheng, 1996) and many

graph problems such as connectivity checking (Maon,

1986), (Tarjan, 1985). It is also used on ovarian and

bronchial cancer detection and various other medical

analyses (Brinkhuis, 1997), and network evolvement

(Matos, 2002).

Boruvka, Kruskal, and Prim algorithms provide a

large number of the known algorithms. Since

Kruskals algorithm works on arranged edges and

MST edges are likely to be among the θ(nlog(n))

smallest weight edges, partial sorting of edges work

greatly to find out lighter edges (Brennan, 1982),

(Paredes, 2006).

Filtering of edges connecting nodes makes the

algorithm very faster (Kershenbaum ,1972).

Figure 1: An example illustrating an undirected graph

In addition, Bucket sorting on edges is employed

in Kruskal’s algorithm which performs greatly for

uniformly distributed random edge weights

(Katajainen, 1983).

A recently devised Filter-Kruskal algorithm has a

higher performance over a wide range of input types

(Osipov, 2009). Edge Pruned Minimum Spanning

Tree (EPMST) algorithm uses the benefits of

Kruskal’s and Prims algorithms. As Kruskal’s

algorithm performs better on sparse graphs and

produces a minimum spanning forest, EPMST filters

out a large number of edges before running the

Kruskal’s algorithm. Then it runs Prims algorithm on

a compact dense graph. Selection of pivot value is a

major concern on the EPMST (Mamun, 2016).

3 GRAPH THEORY AND

MINIMUM SPANNING TREE

The objective of this part is to define the relation

between controlled geographic space by the local

authorities and graph theory. In addition, we present

the DLA algorithm to control the confinement. Using

the graph theory and the Minimum spanning Tree we

can define:

 Identification of the authorized area As: For

each displacement, an authorized area As is

generated. It’s based on the source and

destination positions and on the tolerated space

by the authorities. This area is computed using

Edge Pruned Minimum Spanning Tree

(EPMST) algorithm, which has a superior

performance relative to the best-known

algorithms especially when the graph is not

very sparse (Mamun, 2016). Moreover,

EPMST algorithm (Mamun, 2016) is also used

to select the shortest path and the tolerated

space by the authorities. Any control by the

agents of authorities inside the authorized zone

will be accepted and validated, except if there

the estimated duration for the displacement is

not exceeded. In addition, if the check is carried

outside this zone, the application automatically

generates police fine. The figure 2 shows a

simulated graph highlighting the departure and

the arrival points demanded by the user. The

city is a 50km2 square with 50 control stations

represented as a network. Figure 3 represents

the shortest path between the source and

destination. This path is used to compute the

time duration authorised for the displacement if

the control stations are identified by a number

or a specific value. Figure 4 presents in addition

to the shortest path, the control station

identifications. Figure 6 resumes the ADL

solution based on the EPMST. It shows the

connected graph, the minimum weight

spanning tree and the shortest path. The Figure

5 illustrates a simulated graph highlighting the

shortest path between the departure and the

arrival points and the control stations identified

by values (codes). Besides, Figure 6 shows in

addition to the shortest path, the authorized

space for the concerned displacement. This

space is indicated by the nodes and paths in

pink color. Indeed, each control by authorities

in this region gives an accepted permission.

Figure 2: Simulated graph highlighting the departure and

arrival points

 Computation of the duration of the

displacement: Our system also computes the

displacement duration based on the shortest

path. In this study and to simplify the process,

we used the mean duration of all paths from

source to destination.

The equation 1 represents this duration as:

𝑇𝑑





𝑗

𝑡







(1)

Where t

represents the source and destination. The

parameter j represents the total number of possible

paths without loops.

Figure 3: A Simulated graph with the shortest path between

source and destination points, 50 control station and 50x50

square region

Figure 4: Simulated graph the node identifiers and the

shortest path

4 SALAMATI APPLICATION

BASED ON THE DLA,

SIMULATION AND RESULTS

All citizens must download and correctly install the

SALAMATI Application (Figure 7) from the

internet space reserved for this operation. A person

going out for different reasons (to work, shop, or

buy medicine) must authenticate and identify the

destination. The authentication is based on the

National Identity Code (NIC) (CIN in the case of

Morocco) which is largely sufficient to identify all

persons. The application generates a QR code for

each service request.

Figure 5: Simulated graph highlighting the short paths and

the authorized area

Figure 6: Simulated graph highlighting the minimum

weight spanning tree and the shortest path

This code will be used for each control by the police

or authorities. The user can switch-off their internet

connection and only use the QR code generated by

the SALAMATI Application. This code contains

three types of data:

 User Identification

 The authorized area

 Duration of the displacement.

For the control, while respecting social and

physical distance, the person presents the QR code to

the agent and the latter can then validate the real

position or not. The reader displays the NIC and two

different colors; green for approbation and red for no

authorization. The figures 8 and 9 show QR codes

generated by the SALAMATI Application and two

different responses for two different controls. The

first is rejected whereas the second is validated. The

agent must install the application SALAMATI for

lecture and control. In principle, internet connection

is not necessary, but can be used for centralizing data

and giving information about people’s mobility

compliance to confinement. In addition, this

parameter will be used for different uses, especially

in finding the relation between mobility and the R0

parameter.

Figure 7: SALAMATI Application

Figure 8: A non-authorized scanned localization

Figure 9: An authorized scanned localization

5 CONCLUSION

In this paper we propose a new approach to deal with

data privacy in the case of the confinement control.

This solution overcomes the limitations linked to the

violation of data privacy. We proposed a concrete and

operational digital solution to fight epidemics

including Covid-19, which is today the highest

international priority, based on a theoretical and

practical solution. Indeed, the SALAMATI mobile

application is based on the Discrete Localization

Algorithm (DLA) which is a complete and legal

intelligent solution to automate confinement control

processes and the progressive easing of lockdown by

controlling the displacement of citizens and the area

for which the authorization was delivered. The

SALAMATI mobile application is based on the QR

code solution identifying three parameters: a) User

Identification, b) The authorized area and c) Duration

of the displacement.

In the perspective works, we will measure time

computation and solve the congestion problem using

the SALAMATI mobile Application.

ACKNOWLEDGEMENTS

The authors would like to thank SMARTiLAB/EMSI

the High School of engineering group. This paper was

written within the scope of a COVID-19 project

supported by the supervisory ministry MENFPESRS

and the CNRST of Morocco with the aim of

prevention and forecast the spread of the COVID-19

pandemic (GRANT Number: COV/2020/87)

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