## 2 Related Work
### Malware Propagation Models  
Modeling the propagation of malware in computer networks has a history of decades. These studies have established the foundation for malware propagation modeling in WSN. The mathematical models proposed to study the malware propagation in WSN can be global or individual. In this section, the two types of models are briefly described. In addition, these models have been classified according to their compartmental model types (e.g., continuous or discrete, deterministic or stochastic) and mathematical models used (e.g., partial differential equations (PDE), ordinary differential equations (ODE), cellular automata (CA), and Markov chains). Starting with the global model, [PERSON] et al. [30] described an SIR model, which considers the discrete delay and can effectively predict the dynamic behavior and spatial distribution of malware propagation in mobile WSN. The proposal is a continuous and deterministic model. [PERSON] et al. [31] present a heterogeneous susceptible-insidious-infectious-recovered-dysfunctional (SNIRD) model on WSN. The model included the N state as the infected sensor that has not been distinguished by the intrusion detection system (IDS). The D state symbolized the node that failed due to malware demolition, power exhaustion, or physical damage. This model is discrete and stochastic. The two models are both based on PDE. [PERSON] et al. [32] proposed an improved SIRS model to describe the energy consumption during worm propagation and different node distribution density. This model is continuous and deterministic. [PERSON] et al. [33] studied the malware spreading on WANETs. Based on the classical SI epidemic propagation model, the propagation rates of two malware propagation modes and two different network modes are studied. It is a discrete and deterministic model. [PERSON] et al. [34] proposes an IoT-SIS botnet propagation model based on IoT sensor networks. The impact of IoT-specific characteristics such as limited processing power, energy restrictions, and node density on the formation of a botnet was analyzed. It is a discrete and deterministic model. The three models are based on ODE. [PERSON] et al. [35] presented a heterogeneous discrete-time SIS model. They developed a non-cooperative non-zero-sum game to describe heterogeneous WSN and malware interaction to predict malware's infection behavior. [PERSON] et al. [36] proposed a SIRD model to evaluate malware propagation on the narrowband Internet of Things (NBIOT). The nodes' availability based on the distribution of heterogeneous nodes and vulnerability was analyzed. These two models are based on Markov chains. Therefore, they are discrete, stochastic models. Subsequently, the specific network characteristics have also been taken into account in individual models. [PERSON] et al. [37] introduced a model that follows the state transition scheme of a typical SI infection model. Nevertheless, they could compute the prior probability of each sensor being infected by the worm using several iterative equations of individual security states. The Markov chains model is individual, discrete, and stochastic. [PERSON] et al. [38] proposed an improved individual-based model, which used characteristics of three types of nodes and complex topology. The states of the model were susceptible, infected, recovered, damaged, and out-of-order. [PERSON] et al. [39] presented an SEIR model to simulate the spread of computer viruses on a computer network. In this model, the parameters considered are related to the life cycle of the computer virus, the countermeasures implemented on the host, and the user's behavior. [PERSON] et al. [40] proposed a SIRD model based on two-dimensional 2D cellular automata CA. This model considered three aspects (infection, immunity, and mortality rates) in two different types of nodes (cluster-head and terminal nodes) to analyze malware propagation in WSN. In addition, a multi-player evolutionary game model was established to find the optimal evolutionary and stable strategy.