Petri Net and Probabilistic Model Checking Based Approach for the Modelling, Simulation and Verification of Internet Worm Propagation

Abstract

Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR) model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) (SEIDQR(S/I)) along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework.

A Markovian Model for the Spread of the SARS-CoV-2 Virus

“…The use of stochastic models opens for the possibility to use Stochastic Model Checking in order to study probabilistic temporal properties to evaluate the effects of a strategy on a population during the evolution of a disease. As an example, Razzaq and Ahmad [26] adapted a Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) CTMC model used to analyse the spread of internet worms using the PRISM model checker [23]. The same tool was used to validate a model and to compute the minimum number of influenza hemagglutinin trimmers required for fusion to be between one and eight [11].…”

Verifying a stochastic model for the spread of a SARS-CoV-2-like infection: opportunities and limitations

“…The use of stochastic models opens for the possibility to use Stochastic Model Checking in order to study probabilistic temporal properties to evaluate the effects of a strategy on a population during the evolution of a disease [20,8,7]. An adapted version of the Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered) continuous time Markov chain model has been used in [20] to analyze the spread of internet worms using the PRISM model checker [17]. A stochastic model to compute with the PRISM model checker the minimum number of influenza hemagglutinin trimmers required for fusion to be between one and eight has been proposed in [8].…”

“…Recently, the evolution of diseases has also been modeled with stochastic models in form of Markov Processes [6,1,19]. The use of stochastic models opens for the possibility to use Stochastic Model Checking techniques to i) validate the model using probabilistic temporal properties of the model as well as compute quantitative measures of the degree of satisfaction of a given temporal property [20]; ii) evaluate the effects of a strategy on a population during the evolution of a disease [8,7]. The work in [19] describes a stochastic compartmental model (the population has been broken down into several compartments) for the spread of COVID-19like diseases, with some preliminary results on the use of stochastic model checking techniques to analyze a simplified version of the epidemic model.…”

A content analysis-based approach to explore simulation verification and identify its current challenges

“…This increases the difficulties in determining if system level behaviors within a simulation are the result of the intricacies of these interactions or if they are due to an error in implementation. Such occurrences may be the result of non-linear actions of subgroups or local networks [118,129], changing model structures over time [28], or the scale of networked or interconnected components [132]. Therefore, techniques need to differentiate between individual-level, subgroup-level, and population-level occurrences [60,120,133] to provide traceability between occurrences and model specifications.…”