# Reliability Evaluation for Clustered WSNs under Malware Propagation
## 2 Related Work  
Based on classical epidemic models, many extended studies have been performed to describe the characteristics of malware propagation in WSNs. In a good survey, [PERSON] _et al._[13] presented current works on modeling malware propagation. Generally, sensor nodes periodically enter sleep mode to save energy. Typical models reflecting nodes sleeping during malware propagation include EiSIRS [14], a modified SI model [15], a modified SIS model [16], and [PERSON]'s model [17]. Moreover, sensor nodes \"die\" due to energy exhaustion or intentional destruction by malware. Thus, a dead state was introduced in iSIRS [18] based on the SIR model and [PERSON]'s model [17]. Furthermore, a reaction-diffusion-theoretic model [19], a pulse-differential-equation-based SIR model [20], and a susceptible-exposed-infected-recovered-susceptible model [21] were proposed in order to foresee spatial distribution and the temporal dynamics characteristic of malware propagation. In addition, [PERSON] _et al._[22] proposed a two-layer malware propagation model that better represents malware propagation in large-scale networks compared with existing single-layer epidemic models. [PERSON] and [PERSON] [23] presented a susceptible-exposed-infectious-recovered model with two time delays for charactering the transmission dynamics of malware propagation. [PERSON] and [PERSON] [24] explored a SIR-based nonlinear malware propagation model in WSNs. [PERSON] _et al._[25] presented a survey on modeling malware propagation in networks including WSNs. Other typical models [26; 27; 28; 29] address the problem of malware propagation in multi-hop networks, which can help illustrate malware propagation in WSNs. Several authors have considered decision-making dilemmas arising during malware propagation. [PERSON] _et al._[30] established a zero-sum dynamic game between the network system and the malware, given that malware can dynamically alter infection parameters based on the network system's dynamics. [PERSON] _et al._[31] used an evolutionary game to construct a malware propagation model under bounded rationality, where the game is to predict the trend of malware's evolutionary infection. [PERSON] _et al._[32] employed a complete information game to obtain the defender's optimal strategy that minimizes the security cost as well as the malware effect. In addition, [PERSON] _et al._[33] found decentralized optimal protection strategies for the network system by proposing a game-theoretic framework and seeking its Nash equilibria and the Price of Anarchy. Several methods have been proposed using various techniques to cope with the challenge of evaluating WSNs' reliability. In a pioneering work [34], the authors employed a probabilistic graph to represent WSNs given a failure probability estimation of sensor nodes. [PERSON] _et al._[35] modeledWSNs' energy reliability assuming Markovian sensor discharge/recharge periods. [PERSON] [36] used dynamic reliability block diagrams to represent static structural interactions between sensor nodes, where sleep/wake-up standby policies and interference are considered dynamically. Based on [36], he further gave a reliability evaluation model integrating Petri nets [37]. [PERSON] _et al._[38] proposed an evaluation methodology supporting arbitrary failure conditions based on automatically generated fault trees. [PERSON] _et al._[39] proposed reliability analysis of wireless communications systems in the smart grid, which is also suitable for WSNs. [PERSON] _et al._[40] developed a novel framework called Packet-Level Attestation for sensor data reliability evaluation using the spatial relationship among data sensed by nearby sensor nodes. In [41] [PERSON] _et al._ proposed a reliability evaluation model based on routing algorithms in WSNs and sensor nodes' various battery levels.