Online social networks (OSNs) have become an integral mode of communication among people and even nonhuman scenarios can also be integrated into OSNs. The ever-growing rise in the popularity of OSNs can be attributed to the rapid growth of Internet technology. OSN becomes the easiest way to broadcast media (news/content) over the Internet. In the wake of emerging technologies, there is dire need to develop methodologies, which can minimize the spread of fake messages or rumors that can harm society in any manner. In this article, a model is proposed to investigate the propagation of such messages currently coined as fake news. The proposed model describes how misinformation gets disseminated among groups with the influence of different misinformation refuting measures. With the onset of the novel coronavirus-19 pandemic, dubbed COVID-19, the propagation of fake news related to the pandemic is higher than ever. In this article, we aim to develop a model that will be able to detect and eliminate fake news from OSNs and help ease some OSN users stress regarding the pandemic. A system of differential equations is used to formulate the model. Its stability and equilibrium are also thoroughly analyzed. The basic reproduction number (R₀) is obtained which is a significant parameter for the analysis of message spreading in the OSNs. If the value of R₀ is less than one (R₀ 1 the rumor will persist in the OSN. Real-world trends of misinformation spreading in OSNs are discussed. In addition, the model discusses the controlling mechanism for untrusted message propagation. The proposed model has also been validated through extensive simulation and experimentation.

Due to the fast advancement of Internet technology, the popularity of Online Social Networks (OSN) over the Internet is increasing day by day. In the modern world, people are using OSN to communicate with others around the world who may or may not know each other. OSN has become the most convenient means to transmit media (news/content) and gather or spread information in the world. The posts (contents) on OSN affect and impact people, and minds at least for some time. These contents are important because they play a crucial role in taking the decision. The posts which are available on the OSN may be information or just misinformation. The misinformation may be a type of fake news or rumour. This is very difficult for people to differentiate whether the posts are information or rumour. Therefore, the development of techniques that can prevent the transmission of false information or rumours that might harm society in any way is critical. In this paper, a model is developed based on the epidemic approach, for examining and controlling fake information dissemination in OSN. The proposed model illustrates how different misinformation debunking measures impact and how misinformation spreads among different groups. In this article, we explain that the proposed model will be able to recognize and eradicate fake news from OSN. The model is written as a system of differential equations. Its equilibrium and stability are also carefully examined. The basic reproduction number ( R ₀ ) is calculated, which is an important parameter in the study of message propagation in OSN. If R ₀ < 1, the propagation of rumor in the OSN will be minimal; nevertheless, if R ₀ > 1, the fake information/rumor will continue in OSN. The effects of disinformation of rumours in OSN in the real world are explored. In addition, the model covers the fake information/rumour dissemination control mechanism. The comparative study shows that the proposed model provides a better mechanism to prevent the dissemination of fake information in OSN in comparison to other previous models. Extensive theoretical study and computation analysis have also been used to validate the proposed model.

Wireless sensor network (WSN) comprises thousand sensor nodes, which exchange data from each other. Sensor network faces different types of problem such as energy constraint as well as malware attacks. The malware (virus, malicious codes, Trajan horse, worm, etc.) targets sensor node of WSN straightforwardly owing to constraint of resources. The spreading behavior of the malware is similar to the virus spreading in susceptible population. Therefore, prevention method is needed against malware attack in WSN. In this paper, we proposed an epidemic based model which describes the propagation dynamics of malware and depletion of sensor nodes’ energy due to malware attack. Security issue along with energy depletion of sensor node is addressed. The method of low energy sensor nodes charging is considered. The proposed model with consideration of low energy is SILRD (Susceptible-Infectious–Low Energy–Recovered–Dead) model. The charging method of sensor nodes with low energy is incorporated. To describe the dynamics of malware spreading and effect of charging constructed a set of differential equations. The deterrence technique of malware dissemination in WSN is explained. And the effect of charging on WSN is also discussed. The basic reproduction number of the model is also calculated which is used in the analysis of prominence of malware spreading. The points of equilibrium of the system have obtained for malware-free and endemic. And stability condition of WSN and related theorems are discussed in details. The proposed model has been substantiated by simulation results.

The malware spreading in Wireless Sensor Network (WSN) has lately attracted the attention of many researchers as a hot problem in nonlinear systems. WSN is a collection of sensor nodes that communicate with each other wirelessly. These nodes are linked in a decentralised and distributed structure, allowing for efficient data collection and communication. Due to their decentralised architecture and limited resources, WSN is vulnerable to security risks, including malware attacks. Malware can attack sensor nodes, causing them to malfunction and consume more energy. These attacks can spread from one infected node to others in the network, making it essential to protect WSN against malware attacks. In this paper, we focus on the analysis of a novel fractional epidemiology model, specifically the fractional order SEIVR epidemic model in the sense of Caputo’s fractional derivative of order 0<α≤1 with the goal of examining the efficacy of vaccination strategies and the heterogeneity of a scale-free network on epidemic spreading. First, using the next-generation technique and obtain the basic reproduction number of the proposed epidemic model, which is essential for determining both the locally asymptotically stable equilibrium point of the worm-free system and the unique existence of the endemic equilibrium point. To numerically solve the model, the Adam-Bashforth-Moulton predictor-corrector (ABM) method is applied. The fractional calculus enables us to deal directly with the "memory effect" of numerous phenomena, taking into account the system’s dependence on previous stages. This method provides the results of a complex system. Additionally, research demonstrates that vaccine treatments are quite effective at preventing the spread of malware. The outcome of the study reveals that the applied ABM predictor-corrector method is computationally strong and effective to analyse fractional order dynamical systems in the SEIVR epidemic model for malware propagation in WSN. The results show that the order of the fractional derivative has a significant effect on the dynamic process. Also, from the result, it is obvious that the memory effect is zero for α=1. When the fractional order α is decreased from 1, the memory effect appears, and its dynamics vary according to the time. This memory effect points out the difference between derivatives of fractional and integer orders. The theorems and their proofs are presented to validate the validity of the proposed model. To validate the proposed model, extensive theoretical study and computational analysis have also been applied.