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Dynamics of Multi-Strain Malware Epidemics over

Duty-Cycled Wireless Sensor Networks

Dmitriy Fedorov∗, Yrys Tabarak∗, Aresh Dadlani∗, Muthukrishnan Senthil Kumar†, and Vipin Kizheppatt‡

∗Department of Electrical and Computer Engineering, Nazarbayev University, Nur-Sultan, Kazakhstan

†Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore, India

‡Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science Pilani, Goa, India

Emails: {dmitriy.fedorov, yrys.tabarak, aresh.dadlani}@nu.edu.kz, msk@amc.psgtech.ac.in, kizheppattv@goa.bits-pilani.ac.in

Abstract—Insights on the salient features of malicious software

spreading over large-scale wireless sensor networks (WSNs) in

low-power Internet of Things (IoT) are not only essential to

project, but also mitigate the persistent rise in cyber threats.

While the analytical ﬁndings on single malware spreading dynam-

ics are well-established, the interplay among multiple malware

strains with heterogeneous infection rates in power-limited WSNs

yet remain unexplored. Inspired by compartmental modeling

in epidemiology, we present the mean-ﬁeld approximation for

a novel stochastic epidemic model of two mutually exclusive

malware strains spreading over WSNs with sleep/awake modes

of energy consumption. Referred as the susceptible-infected by

strain 1 or by strain 2-susceptible with duty cycles (SI1I2SD),

we then derive the basic reproduction number to characterize

the sufﬁcient conditions for the existence and stability of the

infection-free and endemic equilibrium states. Simulation results

show the predictive capability of the proposed model for energy-

efﬁcient WSNs evolving as random geometric graphs against

uniformly connected networks.

Index Terms—Wireless sensor networks, malware epidemic

modeling, duty cycle, mean-ﬁeld theory, stability analysis.

I. INTRODUCTION

Empowered by wireless sensor networks (WSNs), the op-

portunities created by diverse Internet of Things (IoT) appli-

cations have proliferated in recent years [1]. Unlike typical

networks, IoT-enabled WSNs comprise mainly of low-powered

components with limited storage and processing capabilities

that communicate via unreliable wireless channels. Inevitable

loopholes arising due to such shortcomings have been exploited

by adversaries to intrude WSNs and launch versatile large-scale

malicious attacks such as the renown Mirai botnet [2], [3]. Thus,

predicting the key factors in potential viral outbreaks can serve

beneﬁcial in devising effective defense mechanisms [4].

Given the behavioralsimilarities between malware and biolog-

ical pathogens, epidemic modeling approaches have been vastly

applied to analyze spreading processes in networks. Depending

on the virulence state of each constituent node, the network is

partitioned into compartments with possible transitions governed

by the underlying connectivity pattern. Such models are instru-

mental in determining not only the existence and stability of

the system equilibria, but also the convergence conditions in

terms of the network spectral radius [5]. While the population-

level dynamics of WSN malware have been widely explored, the

advantage of individual-level epidemic models is that they allow

for microscopic analysis of inter-nodal interactions. The latter

however, are challenging to analyze as they suffer from the curse

of dimensionality which grows exponentially with the size of the

network [4]. Consequently, different approximation techniques

have been used to make individual-based models tractable at

the expense of prediction accuracy [6]. Nonetheless, reported

efforts on the development of non-deterministic WSN epidemic

models that capture the sporadic behavior of malware are scarce

[7]. In particular, assessing the impact of sensors with built-in

sleep/wake mechanisms on the nodal infection and recovery rates

is core to determining the critical epidemic outbreak threshold.

More recently, research on multi-virus propagation dynamics

has received much attention. As a simple extension of the

classical susceptible-infected-susceptible (SIS) model for single

virus spread, the authors in [8] investigated the interplay between

two viruses, each competing over distinct contact networks. The

mean-ﬁeld SI1I2Sframework in [8] was further extended to

incorporate inter-switching between the spreading processes,

where closed-form expressions for the steady-state thresholds

dictating the transitions between extinction, co-existence, and

absolute dominance of the viruses were derived [9]. Criteria for

the co-extinction and survival of each virus in a continuous-time

composite bi-virus spreading model with generic infection rates

was investigated in [10]. Moreover, the authors in [11] presented

the equilibrium analysis for a network-dependent coupled bi-

virus model that allows interpolation between the de-coupled two

virus model to the completely competitive model. The non-trivial

equilibria of the bi-virus SI1I2Smodel over directed graphs and

their stability for both homogeneous and heterogeneous viruses

were analyzed in [12]. In an attempt to scrutinize the impacts of

patch distribution on restraining virus propagation, a competing

spreading dynamical process was developed in [13] to study the

interplay between virus spread and patch dissemination. In spite

of the above notable efforts ([8]–[13]), all the models fail to

account for the profound impact of duty-cycled strategies for

energy conservation, that are unique to WSNs, on the spreading

behavior of multiple mutually exclusive virus strains.

Motivated by the large-scale Mirai botnet attacks that made

headline in 2016 and the several active spin-offs such as Persirai,

BrickerBot, HideNSeek, and LiquorBot [14] that prevail in IoT-

based WSNs, we propose in this paper the ﬁrst agent-based

stochastic epidemic model for two competing virus strains in

WSNs composed of sensors equipped with active/sleep mech-

anisms. We then employ the next-generation matrix method to

quantify the basic reproduction number, denoted by R0, for the

asymptotic stability analysis of the infection-free and the unique

infection-chronic equilibria of the mean-ﬁeld network model.

Considering heterogeneity in infection rates of sensors with duty-

cycles, simulation results compare the prediction accuracy of our

propagation model over random geometric and uniform grid net-

works. Such ﬁndings are insightful to network administrators and

managers in ensuring optimal countermeasures that maximize

the operational efﬁciency of the WSNs.

The remainder of this paper is organized as follows. Section II

presents the multi-strain epidemic model for malware propa-

gation in duty-cycled WSNs. Section III details the derivation

of R0, which is followed by the equilibria stability analysis in

Section IV. Simulation results are discussed in Section V. Finally,

Section VI concludes the paper along with future research works.

II. SY ST EM MO DE L DESCRIPTION

In this section, we ﬁrst introduce the underlying WSN structure

as the basis for further analysis in this study and then mathemat-

ically formulate the multi-strain spreading model.

A. WSN Topology

Consider a single layer network of Nsensors with sleep cycles,

where communication among sensor nodes is bounded by their

transmission ranges. Let G= (V,E)represent the WSN, where

V={1,2, . . . , N }is the set of sensor nodes and E={(i, j)}

denotes the set of edges between any two arbitrary nodes i, j ∈ V,

such that (i, j)=1if and only if iand jlie within the transmission

range of each other, and (i, j)=0if otherwise. Assuming that

the graph Gis connected and unvaried, we use A≜[ai,j]N×N

to denote the irreducible adjacency matrix of G. We also assume

that the number of nodes are ﬁxed and the lifetime of the WSN

is longer than duration of the epidemic.

B. Proposed Multi-Strain Epidemic Model

Given two mutually exclusive virus strains, every sensor node

is in one of six possible states at any time: susceptible-awake

(Sa), susceptible-sleeping (Ss), infected by strain-1virus-awake

(Ia

1), infected by strain-2virus-awake (Ia

2), infected by strain-1

virus-sleeping (Is

1), or infected by strain-2virus-sleeping (Is

2).

For all i∈ V at any time t, the state of the entire WSN can thus,

be characterized by the N-tuple continuous-time Markov chain

(CTMC) X(t)={(Xi(t)) ; t≥0}with states deﬁned as:

Xi(t) =

0,if node iis susceptible and awake,

1,if node iis susceptible and sleeping,

2,if node iis infected by strain-1and awake,

3,if node iis infected by strain-1and sleeping,

4,if node iis infected by strain-2and awake,

5,if node iis infected by strain-2and sleeping,

(1)

where Sa

i(t)≜Pr(Xi(t) = 0),Ss

i(t)≜Pr(Xi(t) = 1),Ia

1,i(t)≜

Pr(Xi(t)=2),Is

1,i(t)≜Pr(Xi(t) = 3),Ia

2,i(t)≜Pr(Xi(t) = 4),

and Is

2,i(t)≜Pr(Xi(t) =5) are the state probabilities of node i,

and Sa

i(t)+Ss

i(t)+Ia

1,i(t)+Is

1,i(t)+Ia

2,i(t)+Is

2,i(t)=1.

The infection of an awake (active) susceptible node iby strains

1 and 2 are Poisson processes occurring at rates α1Yi(t)and

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IଵୟIଵୱIଶୟIଶୱߢୱߢୟߤୱSୱߤୟߣୱߣୟWSN

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Fig. 1. Schematic of the SI1I2SD epidemic model for IoT-enabled WSNs.

α2Zi(t), respectively. Here, α1(α2)is the infection rate and

Yi(t)(Zi(t)) denotes the number of neighboring nodes infected

by the stain-1 (strain-2) virus. The curing processes of strains 1

and 2 are speciﬁed by γ1>0and γ2>0, respectively, only when

the infected nodes are awake. Each active susceptible node duty-

cycles to its sleep-mode with rate µs>0. The sleeping time for

a susceptible node has an exponential distribution characterized

by the rate µa>0. Similarly, λs(κs)and λa(κa)are the rates at

which strain-1 (strain-2) infected nodes toggle between the two

energy modes. Fig. 1 depicts the proposed epidemic model.

1) The Original SI1I2SD Epidemic Model: The state space

of the SI1I2SD model, which basically is a coupled Markov

process, contains 6Nelements and is given as follows:

Ω={X(t)|Xi(t)∈ {0,1,2,3,4,5},where i= 1,2, . . . , N }.

(2)

According to the transition diagram in Fig. 1, the inﬁnitesimal

generator matrix Q≜[qi,j ]6N×6Nfor the N-node graph is:

qi,j =

−PN−1

k=0,k=iqi,k ,if i=j,

α1PN

k=1 ai,k1{xk=2},if i=j−2(6m−1);xm= 0,

α2PN

k=1 ai,k1{xk=4},if i=j−4(6m−1);xm= 0,

γ1,if i=j+2(6m−1);xm= 2,

γ2,if i=j+4(6m−1);xm= 4,

µs,if i=j−6m−1;xm=0,

µa,if i=j+6m−1;xm= 1,

λs,if i=j−6m−1;xm=2,

λa,if i=j+6m−1;xm= 3,

κs,if i=j−6m−1;xm=4,

κa,if i=j+6m−1;xm= 5,

(3)

where m= 1,2, . . . , N and 1{·} is the identity operator. Now,

let pi(t)≜Pr(X1(t)=x1, X2(t) = x2, . . . , XN(t) = xN)be the

probability of being in network state i=PN

k=1 xk6k−1at any

time t. Then, we have p(t)=[p1(t), p2(t), . . . , p6N−1(t)]Tthat

obeys the following linear differential system:

dp(t)

dt =pT(t)Q.(4)

Since ﬁnding the solution of (4) is mathematically intractable, we

approximate the model using mean-ﬁeld theory in what follows.

2) The Mean-Field SI1I2SD Epidemic Model: The theorem

of total probability allows us to express the state probabilities

deﬁned in Section II-B as follows:

Sa

i(t+∆t) = γ1Ia

1,i(t)∆t+γ2Ia

2,i(t)∆t+µaSs

i(t)∆t

+[1−α1Yi(t)−α2Zi(t)−µs]Sa

i(t)∆t+o(∆t),

(5)

Ss

i(t+∆t) = µsSa

i(t)∆t−µaSs

i(t)∆t+o(∆t),(6)

Ia

1,i(t+∆t) = α1Sa

i(t)Yi(t)∆t+ (1−λs−γ1)Ia

1,i(t)∆t

+λaIs

1,i(t)∆t+o(∆t),(7)

Ia

2,i(t+∆t) = α2Sa

i(t)Zi(t)∆t+ (1−κs−γ2)Ia

2,i(t)∆t

+κaIs

2,i(t)∆t+o(∆t),(8)

Is

1,i(t+∆t) = λsIa

1,i(t)∆t−λaIs

1,i(t)∆t+o(∆t),(9)

Is

2,i(t+∆t) = κsIa

2,i(t)∆t−κaIs

2,i(t)∆t+o(∆t),(10)

where Yi(t)and Zi(t)are deﬁned as PN

j=1 ai,j 1{Xj(t)=2}and

PN

j=1 ai,j 1{Xj(t)=4}, respectively. By rearranging the terms in

(5)-(10) and letting ∆t→0, we obtain the following mean-ﬁeld

approximated model with a reduced dimensionality of 6N:

Sa

i

′(t) = γ1Ia

1,i(t)+γ2Ia

2,i(t)+µaSs

i(t)−Sa

i(t)hµs

+α1

N

X

j=1

ai,j Ia

1,j (t)+α2

N

X

j=1

ai,j Ia

2,j (t)i,(11)

Ss

i

′(t) = µsSa

i(t)−µaSs

i(t),(12)

Ia

1,i

′(t) = α1Sa

i(t)

N

X

j=1

ai,j Ia

1,j (t)−(λs+γ1)Ia

1,i(t)+λaIs

1,i(t),

(13)

Ia

2,i

′(t) = α2Sa

i(t)

N

X

j=1

ai,j Ia

2,j (t)−(κs+γ2)Ia

2,i(t)+κaIs

2,i(t),

(14)

Is

1,i

′(t) = λsIa

1,i(t)−λaIs

1,i(t),(15)

Is

2,i

′(t) = κsIa

2,i(t)−κaIs

2,i(t).(16)

III. DERIVATION OF R0

The evolution of the dynamical model given in (11)-(16)

can be analyzed in terms of R0, which relates to the average

number of secondary infections caused by a single infected node

introduced into a susceptible network. To obtain the infection-

free equilibrium (IFE), E0, each node i∈ V should be in either

one of the two susceptible states, i.e., Sa

i+Ss

i= 1 in steady-state.

Thus, E0is given as:

E0=µa

µa+µs

eN,µs

µa+µs

eN,0,0,0,0,(17)

where eNand 0are unit and zero row vectors of order 1×N,

respectively. Using the next generation matrix method detailed

in [15], the new infection vector,Fi, and the recovery vector,

Vi, are obtained from (13) and (14) for node i∈ V as follows:

Fi="α1Sa

iPN

j=1 ai,j Ia

1,j +λaIs

1,i

α2Sa

iPN

j=1 ai,j Ia

2,j +κaIs

2,i#,Vi="(γ1+λs)Ia

1,i

(γ2+κs)Ia

2,i#.

(18)

With ˆ

F≜[F1,F2,...,FN]Tand ˆ

V=[V1,V2,...,VN]T, all N

sensory nodes can be represented in the following matrix form,

where Sa= [Sa

1, Sa

2, . . . , Sa

N]T,Ia

1= [Ia

1,1, Ia

1,2, . . . , Ia

1,N ]T,

Is

1= [Is

1,1, Is

1,2, . . . , Is

1,N ]T,Ia

2= [Ia

2,1, Ia

2,2, . . . , Ia

2,N ]T, and

Is

2=[Is

2,1, Is

2,2, . . . , Is

2,N ]T:

ˆ

F=α1(Sa)T·A·Ia

1+λaIs

1

α2(Sa)T·A·Ia

2+κaIs

2,ˆ

V=(γ1+λs)Ia

1

(γ2+κs)Ia

2.(19)

For k∈ {1,2}, let ˆ

Fkand ˆ

Vkbe the k-th elements of ˆ

Fand ˆ

V,

respectively. Using (19), we now deﬁne matrices Fand Vas:

F=

∂ˆ

F1

∂Ia

1

∂ˆ

F1

∂Ia

2

∂ˆ

F2

∂Ia

1

∂ˆ

F2

∂Ia

2

2N×2N

,V=

∂ˆ

V1

∂Ia

1

∂ˆ

V1

∂Ia

2

∂ˆ

V2

∂Ia

1

∂ˆ

V2

∂Ia

2

2N×2N

.(20)

Evaluating matrices Fand Vat equilibrium E0yields:

F|E0=

α1µa

µa+µsA0

0α2µa

µa+µsA

,V|E0=(γ1+λs)I0

0 (γ2+κs)I,

(21)

where IN×Nis the identity matrix. The R0value is identiﬁed

by the maximum eigenvalue of FV−1, i.e., R0=ρ(FV−1) =

max (R1, R2), where thresholds R1and R2are obtained to be:

R1=ρα1µaA

(µa+µs)(γ1+λs), R2=ρα2µaA

(µa+µs)(γ2+κs).

(22)

IV. EQUILIBRIUM STABILITY ANALYS IS

In this section, we investigate the asymptotic stability of

the IFE and the non-trivial infection-chronic equilibrium (ICE)

points in terms of R0. An equilibrium is asymptotically stable

if any orbit of the system starting near to it remains within

close proximity [16]. Following directly from [15], E0is locally

asymptotically stable if R0<1and unstable if R0>1. Theorem 1

proves the global stability of the IFE, E0.

Theorem 1. If R0<1, then the IFE E0is globally asymp-

totically stable in Ω1={(Sa,Ss,Ia

1,Is

1,Ia

2,Is

2)|Sa

i+Ss

i+Ia

1,i +

Is

1,i +Ia

2,i +Is

1,i ≤1for all i∈N}.

Proof. Let Li(t)= I1,i(t)+I2,i (t). Taking the derivative of Li(t)

with respect to time and substituting (13) and (14) results in:

L′

i(t)≤α1Sa

i(t)

N

X

j=1

ai,j Ia

1,j (t)−(λs+γ1)Ia

1,i(t)

+α2Sa

i(t)

N

X

j=1

ai,j Ia

2,j (t)−(κs+γ2)Ia

2,i(t).(23)

At E0, (23) can be expressed in the long-run as follows:

L′

i≤

N

X

j=1 α1µaai,j

(µa+µs)(γ1+λs)−IIa

1,j

+

N

X

j=1 α2µaai,j

(µa+µs)(γ2+κs)−IIa

2,j .(24)

Thus, L′

i≤0when R1<1and R2<1, and L′

i= 0 when Ia

1,i =

Ia

2,i = 0. As a result, ∀i∈ V,Liis a Lyapunov function on Ω1.

Using Lasalle’s invariant principle, the largest compact invariant

set for model (11)-(16) is E0which completes the proof. ■

==

Fig. 2. Random geometric (left) and uniform grid (right) network formations

for transmission range of radius r= 2.

There exist two possible endemic equilibria namely, E∗

1and

E∗

2, for the model when R0>1. In other words, the system has

ICE E∗

1when R1>1and R2< R1, and exhibits ICE E∗

2when

R2>1and R1<R2. Theorem 2 proves the global stability.

Theorem 2. If R0>1, then the endemic equilibrium of the

model is globally asymptotically stable in Ω1.

Proof. Let R1>1and R2< R1and Di(t) = Ia

1,i −Ia∗

1,i(1 +

ln(Ia

1,i/I a∗

1,i)), where Ia∗

1,i ∈E∗

1. Taking the derivative of Di(t)

with respect to tand substituting (13) yields:

D′

i(t)≤Ia

1,i −Ia∗

1,i

Ia

1,i α1Sa

i

N

X

j=1

ai,j Ia

1,j +λaIs

1,i

=

N

X

j=1

Ia

1,j

Ia

1,i

ai,j α1(Sa

i−Sa∗

i)Ia

1,i −Ia∗

1,i

+α1Sa∗

i

N

X

j=1

ai,j Ia∗

1,j 1−Ia

1,i

Ia∗

1,i

+Ia

1,j

Ia∗

1,j

−Ia∗

1,iIa

1,j

Ia

1,iIa∗

1,j !

≤

N

X

j=1"α1Sa∗

iai,j Ia∗

1,j Ia

1,j

Ia∗

1,j

−Ia

1,i

Ia∗

1,j

−lnIa

1,j

Ia∗

1,j+lnIa

1,i

Ia∗

1,j!#

=

n

X

j=1

mi,j ϕi,j ,(25)

where mi,j =α1Sa∗

iai,j Ia∗

1,j and ϕi,j =Ia

1,j

Ia∗

1,j −Ia

1,i

Ia∗

1,j −lnIa

1,j

Ia∗

1,j +

+ lnIa

1,i

Ia∗

1,j . Now, let ˆ

Gbe a weighted graph associated with the

matrix M= [mi,j ]N×N. Given the recursive structure of ϕi,j,

we have P(i,j)∈C ϕi,j = 0 for every closed cycle Cin ˆ

G. From

Theorem 3.5 of [17], there exist constants nisuch that PiniDi

admits a Lyapunov function for the model. By Lasalle’s invariant

principle, E∗

1is the largest compact invariant set for the system.

A similar argument holds for E∗

2. This completes the proof. ■

V. SIMULATION RESU LTS AND DISCUSSIONS

We now analyze the transmission dynamics of our model by

numerical (ODE) and Monte Carlo (MC) simulations for random

geometric (rnd) and uniform grid (uni) networks shown in Fig. 2.

A. Simulation Setup

We spatially distribute N=900nodes with connectivity radius

of r= 3 in a 30×30 grid area using the GEMF simulator [18].

Infected nodes are assumed to undergo prolonged sleep periods

as compared to susceptible nodes in order to reﬂect the adverse

Fig. 3. Time evolution of the SI1I2SD model over random geometric (rnd)

and uniform grid (uni) WSNs (α1= 0.2,α2= 0.15,µa=µs= 0.04,

γ1= 0.08,γ2= 0.05,λa= 0.1,λs= 0.12,κa= 0.09,κs= 0.11).

effect of the virus on the normal functionality of duty cycles. At

t=0,10 nodes are initially set to be infected by each virus strain.

All Monte Carlo results are averaged over 50 simulation runs.

B. Comparative Analysis

Fig. 3 shows the proportion of infected nodes in active and

sleep modes. Apart from the Monte Carlo validation, the impact

of the underlying topology on the propagation of both strains is

compared with the homogeneously mixing baseline, where every

susceptible node is equi-probable to get infected. We observe that

the prediction accuracy of our model over the uni network with

(R1, R2) = (13.66,12.81) is close to that of the baseline. This

implies that the rnd network with (R1, R2) = (17.91,16.79),

evolving as the result of rvalues subjective to the nodes, reveals

a more realistic projection of the spreading dynamics of the

competing virus strains. That is to say, the estimated fraction

of compromised nodes in a uni network would converge to that

of homogeneous mixing with increase in r. Moreover, in spite

of the higher recovery rate of active nodes affected by strain-

1, Ia

1and Is

1continue to increase with time. This is because of

the relatively higher infection and sleeping rates experienced by

nodes infected by strain-1 as compared to (α2, κs). It can also

be seen that both Ia

2and Is

2gradually decrease and reach zero

in steady-state. Such behavior can be justiﬁed by the higher R1

threshold value of both network structures.

Fig. 4 plots the infection trajectories over rnd for four potential

cases that may occur depending on the different values of R1

and R2deﬁned in (22). In Case I shown in Figs. 4(a)-(b), where

(R1, R2) = (0.46,0.68) (and thus R0<1), the system tends

towards IFE E0with non-zero Saand Ssvalues as the number

of compromised nodes in both energy modes reaches zero in

steady-state. When R0>1, Figs. 4(c)-(d) portray Case II where

R1= 0.75 and R2= 1.23. It is evident that strain-2 of the virus

completely dominates the network in these ﬁgures, while Ia

1and

Is

1eventually drop to zero. This case demonstrates the system

convergence towards ICE E∗

2. A similar, but opposite, trend is

seen in Figs. 4(e)-(f) of Case III, wherein (R1, R2)=(1.27,0.66)

and the fraction of nodes infected by strain-1 clearly overshadows

Fig. 4. Comparison of equilibrium convergence of random geometric WSNs with different R0values.

the dying-out fraction of strain-2 infected nodes. The system

convergence towards ICE E∗

1is apparent in this case. Finally,

Case IV is shown in Figs. 4(g)-(h) where (R1, R2)=(1.69,1.48).

Like Case III, Ia

1and Is

1dominate the network, but unlike Case III

where nodes compromised by strain-1 die-out almost instantly,

this decay occurs gradually in Case IV. Therefore, the dominant

strain (and the ICE point) is determined by the greater of the two

threshold values. Irrespective of the initially infected population

size and the four cases discussed above, both competing strains

cannot prevail in a single-layered network simultaneously.

VI. CONCLUSION

In this paper, we developed a novel individual-level mean-ﬁeld

epidemic model to describe the dynamics of mutually exclusive

virus strains propagating over IoT-enabled WSNs equipped with

sleep/awake mechanism. We then derived the expression for

the basic reproduction number, R0, to characterize the stability

of the infection-free and infection-chronic equilibrium points.

Monte Carlo simulations were conducted to corroborate the

theoretical ﬁndings and compare the prediction accuracy of the

proposed model under several parametric settings for the random

geometric and uniform connectivity patterns emerging due to the

spatial distribution and coverage radius of the sensory nodes. In

future, we aim to investigate the impact of mobility and control

strategies on the predictive accuracy of the model.

ACKNOWLEDGMENT

This research was supported by the FDCRG Program (No.

240919FD3918), Nazarbayev University.

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