Muthukrihnan , Senthil Kumar -

Senthil Kumar M., Dadlani A., Ardakanian O., Nikolaidis I., Harms J.J.

Myilsamy K., Kumar M.S., Kumar A.S.

Social networking platforms give people an opportunity to get in contact with each other irrespective of boundaries. Through these platforms, any individual can easily follow the ideas of other individuals like friends, relatives, politicians, actors, etc, and get in contact with them. In this paper, we examine rumor propagation with two types of infected people: highly influential people and ordinary people. Some ordinary people, blindly follow the messages shared by highly influential people. By using this concept we analyze the rumor-spreading model in networks (homogeneous and heterogeneous). We applied control strategies in homogeneous networks and observed that government policies to control rumor propagation can reduce its spread. Immunization in heterogeneous networks by giving proper information and education to people about facts can also reduce the spread and help people make the right decision when they come across a rumor.

Muthukumar S., Senthilkumar M., Veeramani C.

Nowadays, viruses and worms create the most critical problems in computer security issues. Hence, the spreading behavior of computer viruses and the investigation of their control measures are crucial since they will prevent massive economic losses and social panic. This study explores computer virus transmission with a partial immunization based on the Susceptible-Infected-Susceptible-Recovered-Susceptible model. Also, the virus spreading process is analyzed using the reproduction number $$R_0$$ and stability analysis. The developed model is justified through stochastic simulations and compared with the existing models. Furthermore, the optimal control measures are found analytically and numerically. Numerically substantiated that the spread of infected nodes and the immunity loss can efficiently be managed using an optimal control technique.

Ramamoorthi P., Muthukrishnan S., Aruchamy M.

Communicable diseases are one of the challenges to people’s health and fitness. Consuming contaminated water or food and inhaling contaminated water droplets are the main causes of water-borne pathogens spread. This paper studies the spreading dynamics of water-borne diseases with vaccination and preventive measures over a multilayer network. SVIR-process for disease spread over humans and SIS-process for disease spread over water supply mediums and UAU-process for awareness diffusion over humans via social media are taken to study the spreading dynamics. The Discrete-time Markov chain approach is used to frame and analyse the model. The optimal value corresponding to the vaccination parameter is found to control the disease spread. The impact of awareness over disease spread, basic reproduction number and vaccination are found via numerical simulation.

Myilsamy K., Senthil Kumar M., Satheesh Kumar A.

The rapid development of social networks makes the rumour, other false news disseminate to the people in a short period. Online users in social networks are dynamically changing the connectivity over time. The effect of dynamic connections results in stochastic variation which is termed as noise. In this paper, a nonlinear rumour propagation model is formulated, the basic regeneration number [Formula: see text] of the proposed model is computed and the stability for the model is discussed. Further, we extend the model to stochastic rumour propagation for online social networks incorporating noise. The existence and uniqueness of the stochastic rumour propagation for the homogeneous network are investigated. Optimal control strategy of stochastic rumour spreading model in online social network is investigated to control the parameters. A comparison between deterministic and stochastic rumour spreading model in online social network is numerically illustrated.

Kumar M.S., Dadlani A., Moradian M., Maham B., Tsiftsis T.A.

Kumar M.S., Dadlani A., Moradian M., Khonsari A., Tsiftsis T.A.

The timeliness of status message delivery in communications networks is subjective to time-varying wireless channel transmissions. In this paper, we investigate the age of information (AoI) of each source in a multi-source M/G/1 queueing update system with active server failures. In particular, we adopt the method of supplementary variables to derive a closed-form expression for the average AoI in terms of system parameters, where the server repair time follows a general distribution and the service time of packets generated by independent sources is a general random variable. Numerical results are provided to validate the effectiveness of the proposed packet serving policy under different parametric settings.

Devarajan K., Senthilkumar M.

The present research aims to study the strategic behaviour of users in an Internet of Things(IoT) system that is impeded by an unreliable server. In the system, an IoT device is equipped with an energy harvesting unit. The IoT system under study is employed as a Markovian retrial queueing system that is used in a single server, subject to active failures. The failed server is repaired immediately, while the user who was served before the system’s breakdown event waits in the server until the server is repaired. The generating function approach is used to identify important system performance metrics. Moreover, queueing theory concepts are incorporated into game theory for the analysis of the users’ strategies. The users in the IoT system, act to maximize their expected benefit without being perturbed by other users in the system and determine their equilibrium joining strategies. Furthermore, taking into account social welfare factors, the IoT device acts as a social planner, and as a consequence, socially optimal joining strategies are also analysed. Finally, the analytical findings are validated with numerical examples. • An IoT system with an unreliable server. • An IoT device with energy harvesting through renewable energy resources (green IoT). • Queueing and a game-oriented theoretical approach. • Strategic access of the IoT device. • Individual benefits and the social welfare of IoT users.

Kalimzhanov T., Khamseh'i A.H., Dadlani A., Kumar M.S., Khonsari A.

Prediction and control of spreading processes in social networks (SNs) are closely tied to the underlying connectivity patterns. Contrary to most existing efforts that exclusively focus on positive social user interactions, the impact of contagion processes on the temporal evolution of signed SNs (SSNs) with distinctive friendly (positive) and hostile (negative) relationships yet, remains largely unexplored. In this paper, we study the interplay between social link polarity and propagation of viral phenomena coupled with user alertness. In particular, we propose a novel energy model built on Heider's balance theory that relates the stochastic susceptible-alert-infected-susceptible epidemic dynamical model with the structural balance of SSNs to substantiate the trade-off between social tension and epidemic spread. Moreover, the role of hostile social links in the formation of disjoint friendly clusters of alerted and infected users is analyzed. Using three real-world SSN datasets, we further present a time-efficient algorithm to expedite the energy computation in our Monte-Carlo simulation method and show compelling insights on the effectiveness and rationality of user awareness and initial network settings in reaching structurally balanced local and global network energy states.

Kumaresan M., Kumar M.S., Muthukumar N.

<abstract><p>Aggregating a massive amount of disease-related data from heterogeneous devices, a distributed learning framework called Federated Learning(FL) is employed. But, FL suffers in distributing the global model, due to the heterogeneity of local data distributions. To overcome this issue, personalized models can be learned by using Federated multitask learning(FMTL). Due to the heterogeneous data from distributed environment, we propose a personalized model learned by federated multitask learning (FMTL) to predict the updated infection rate of COVID-19 in the USA using a mobility-based SEIR model. Furthermore, using a mobility-based SEIR model with an additional constraint we can analyze the availability of beds. We have used the real-time mobility data sets in various states of the USA during the years 2020 and 2021. We have chosen five states for the study and we observe that there exists a correlation among the number of COVID-19 infected cases even though the rate of spread in each case is different. We have considered each US state as a node in the federated learning environment and a linear regression model is built at each node. Our experimental results show that the root-mean-square percentage error for the actual and prediction of COVID-19 cases is low for Colorado state and high for Minnesota state. Using a mobility-based SEIR simulation model, we conclude that it will take at least 400 days to reach extinction when there is no proper vaccination or social distance.</p></abstract>

Myilsamy K., Satheesh Kumar A., Muthukrishnan S.K.

The transmission of infectious diseases excessively depends on the seasonality variation of the infective mediums. Infectious diseases may be contagious, vector borne, air or water borne. In this paper, we had investigated the epidemic model of a vector-borne disease (Trachoma), which is contagious as well. For this purpose, we extended the SIS model and examined the impact of seasonal variations in the dynamics of the disease spreading model. Seasonal variations are periodically occurring short-term fluctuations. Some of the causes of seasonality comprise the competence of the pathogen to survive outside the host. This relies upon several factors like temperature, sunlight, rainfall, humidity, immunity of the host and abundance of the vectors. Here we extend the mathematical model of trachoma transmission over human contact networks and studied how the disease transmission occurs in the contact networks with seasonally varying infectious medium. For this purpose, we considered mathematical SIS epidemic with homogeneous contact and heterogeneous contact networks. In both contact networks, basic reproduction number $$R_{0}$$ is derived and equilibrium analysis is also discussed. Finally, the numerical results are illustrated to corroborate the theoretical findings.

Fedorov D., Tabarak Y., Dadlani A., Kumar M.S., Kizheppatt V.

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 dynamics 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 (SI 1 I 2 SD), 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.

Devarajan K., Senthilkumar M.

This article studies the strategic access of single-server retrial queue with two types of customers, where priority is given according to their category. On the basis of this concept, a cognitive-radio network was developed as retrial queue with energy harvesting. Cognitive radio allows for a secondary user to opportunistically access the idle spectrum of a primary user (PU). Upon arrival of a primary user, the service given to the secondary user by the cognitive radio is interrupted, and the PU band is available for the primary user. After completion of service for the primary user, the PU band is again available to secondary users. Performance metrics are derived to study the equilibrium strategies of secondary users. A Stackelberg game was formulated and Nash equilibrium was derived for the noncooperative strategy of the secondary user. Game-theory concepts are incorporated with queuing theory ideas to obtain the net benefit for the noncooperative strategy and social benefit for cooperative strategy. Lastly, analytical results are verified with numerical examples, and the effects of energy-harvesting rate are discussed.

Ramamoorthi P., Muthukrishnan S.K.

This paper proposes the SISRS epidemic model to represent alcohol addiction among people. The spreading of alcohol addiction is controlled by creating awareness among the people and also by treating them to overcome it. Multiplex network is used to study the dynamics of addiction. Alcoholism spreads over the physical contact layer and follows the SISRS process whereas human awareness spreads over the virtual contact layer and follows the UAU process. Based on the Microscopic Markov Chain Approach competing dynamics of spreading of alcohol addiction and human awareness diffusion are studied. Necessary conditions for the existence of an alcohol-free population are found. An optimal control problem using a suitable cost index is formulated to reduce the alcohol addicts and the optimal control strategy using Pontryagin’s Minimum Principle is determined. Numerical results are developed to find the effect of various parameters and to analyze the effects of different control strategies. The results obtained from this model are closer to the data collected in the National Survey of Drug Use and Health (NSDUH) from 2002 to 2018.

Ramamoorthi P., Muthukrishnan S.

Social media plays a crucial role in controlling the epidemic spreading by creating awareness. Epidemic spreading processes over the multiplex network where epidemic spreading in one layer and awareness spreading in another layer, are well suitable to study the spreading of infection in a small region. Using the Microscopic Markov chain approach (MMCA), the dynamical interplay between the spreading of epidemics over the physical contact layer and human awareness diffusion over the virtual contact layer over a multiplex network framework is analyzed. SEIR process for epidemic spreading and UAU process for awareness diffusion are assumed to study the spreading process of COVID-19. The basic-reproduction number [Formula: see text] is determined using the next generation matrix approach. The stability of disease-free equilibrium (DFE) and endemic equilibrium (EE) is analyzed. Using Pontryagins Minimum Principle, optimal parametric values are determined analytically for testing and cleaning the virus-contaminated surfaces. The impact of various parameters over the epidemic spread is analyzed numerically. Through numerical illustrations, the effect of early identification of exposed people and immediate cleaning of virus-contaminated surfaces over [Formula: see text] studied. The sensitivity analysis is performed to show the importance of wearing face-mask, following social distancing, washing hands frequently and, avoiding unnecessary travel. Through numerical simulations, the results obtained coincide with real data of COVID-19 spreading in the city Chennai, India. The results obtained show that in order to control or discard the spreading of COVID-19, each people should follow the self-preventive measures without relaxation till the epidemic comes nearer to the disease free state.

Satheesh Kumar A., Bauch C.T., Anand M.

Individual attitudes vastly affect the transformations we are experiencing and are vital in mitigating or intensifying climate change. A socio-climate model by coupling a model of rumor dynamics in heterogeneous networks to a simple Earth System model is developed, in order to analyze how rumors about climate change impact individuals’ opinions when they may choose to either believe or reject the rumors they come across over time. Our model assumes that when individuals experience an increase in the global temperature, they tend to not believe the rumors they come across. The rumor rejectors limit their CO2 emissions to reduce global temperature. Our numerical analysis indicates that, over time, the temperature anomaly becomes less affected by the variations in rumor propagation parameters, and having larger groups (having more members) is more efficient in reducing temperature (by efficiently propagating rumors) than having numerous small groups. It is observed that decreasing the number of individual connections does not reduce the size of the rejector population when there are large numbers of messages sent through groups. Mitigation strategies considered by the rejectors are highly influential. The absence of mitigative behavior in rejectors can cause an increase in the global average temperature by 0.5°C. Our model indicates that rumor propagation in groups has the upper hand in controlling temperature change, compared to individual climate-denying propagation.

Ye Y., Pandey A., Bawden C., Sumsuzzman D.M., Rajput R., Shoukat A., Singer B.H., Moghadas S.M., Galvani A.P.

Integrating prior epidemiological knowledge embedded within mechanistic models with the data-mining capabilities of artificial intelligence (AI) offers transformative potential for epidemiological modeling. While the fusion of AI and traditional mechanistic approaches is rapidly advancing, efforts remain fragmented. This scoping review provides a comprehensive overview of emerging integrated models applied across the spectrum of infectious diseases. Through systematic search strategies, we identified 245 eligible studies from 15,460 records. Our review highlights the practical value of integrated models, including advances in disease forecasting, model parameterization, and calibration. However, key research gaps remain. These include the need for better incorporation of realistic decision-making considerations, expanded exploration of diverse datasets, and further investigation into biological and socio-behavioral mechanisms. Addressing these gaps will unlock the synergistic potential of AI and mechanistic modeling to enhance understanding of disease dynamics and support more effective public health planning and response. Artificial intelligence has the potential to improve epidemiological models of infectious diseases by incorporating diverse data sources and complex interactions. Here, the authors conduct a scoping review of the use of artificial intelligence in mechanistic models to summarise methodological advancements and identify research gaps.

Dhibar S., Jain M.

This research article addresses the performance analysis of Markovian retrial queueing system with two types of customers, unreliable server, and Bernoulli feedback. Both regular customers (RC) and prime customers (PC) may either join, or balk from the system based on the trade-off between service profit and delay cost. When the system is busy, the regular customers have to choose whether to join a retrial orbit and make re-attempts or leave the system. Furthermore, due to congestion among regular customers, the server may discontinue the service during breakdown. Due to the unavailability of the service process, customers may experience dissatisfaction. Therefore, our objective is to introduce a Bernoulli feedback service process to enhance service quality, ensuring that customers are successfully served with a certain probability. To analyze the proposed model mathematically, Chapman-Kolmogorov (C-K) inflow-outflow balanced equations have been framed. Then, the probability generating function (PGF) method employed to explicitly derive the queue size distribution, throughput, and other performance metrics. These performance measures provide critical insights into system behavior, which are then incorporated to determine the equilibrium strategies for two types of joining strategies: (i) non-cooperative strategies and (ii) cooperative strategies. Finally, optimization approaches are employed to determine the optimum cost and make tactical decisions regarding the quality of service (QoS) in an integrated manner. The cost optimization is done using metaheuristic optimization techniques such as PSO and GWO. The analytic results established are validated by numerical simulation. The effect of various parameters on the performance indices are examined by cost optimization and sensitivity analysis. The comparison of both algorithms, including average fitness, standard deviation, and convergence analysis, were used and combined with Wilcoxon rank-sum test.

Esfandiari S., Fakhrahmad S.M.

Jafar M.T., Yang L., Li G.

Huang D., Wu W., Bi J., Li J., Gan C., Zhou W.

Hu J., Yang X.

Distributed denial of service (DDoS) is a type of cyberattack in which multiple compromised systems flood the bandwidth or resources of a single system, making the flooded system inaccessible to legitimate users. Since large-scale botnets based on the Internet of Things (IoT) have been hotbeds for launching DDoS attacks, it is crucial to defend against DDoS-capable IoT botnets effectively. In consideration of resource constraints and frequent state changes for IoT devices, they should be equipped with repair measures that are cost-effective and adaptive to mitigate the impact of DDoS attacks. From the mitigation perspective, we refer to the collection of repair costs at all times as a repair strategy. This paper is then devoted to studying the problem of developing a cost-effective and adaptive repair strategy (ARS). First, we establish an IoT botware propagation model that fully captures the state evolution of an IoT network under attack and defense interventions. On this basis, we model the ARS problem as a data-driven optimal control problem, aiming to realize both learning and prediction of propagation parameters based on network traffic data observed at multiple discrete time slots and control of IoT botware propagation to a desired infection level. By leveraging optimal control theory, we propose an iterative algorithm to solve the problem, numerically obtaining the learned time-varying parameters and a repair strategy. Finally, the performance of the learned parameters and the resulting strategy are examined through computer experiments.

Yu K., He B., Xiong J., Kan P., Sheng H., Zhi S., Zhu D.Z., Yao Z.

Yang D., Chen K., Zhang W., Wang T., Xian J., Meng N., Wang W., Liu M., Ye J.

Jafar M.T., Yang L., Li G., Zhu Q., Gan C., Yang X.

Zhou X., Sun H., Xu W., Li W., Zhang Z.

Zwiers L.C., Grobbee D.E., Uijl A., Ong D.S.

The use of real-world data has become increasingly popular, also in the field of infectious disease (ID), particularly since the COVID-19 pandemic emerged. While much useful data for research is being collected, these data are generally stored across different sources. Privacy concerns limit the possibility to store the data centrally, thereby also limiting the possibility of fully leveraging the potential power of combined data. Federated learning (FL) has been suggested to overcome privacy issues by making it possible to perform research on data from various sources without those data leaving local servers. In this review, we discuss existing applications of FL in ID research, as well as the most relevant opportunities and challenges of this method. References for this review were identified through searches of MEDLINE/PubMed, Google Scholar, Embase and Scopus until July 2023. We searched for studies using FL in different applications related to ID. Thirty references were included and divided into four sub-topics: disease screening, prediction of clinical outcomes, infection epidemiology, and vaccine research. Most research was related to COVID-19. In all studies, FL achieved good accuracy when predicting diseases and outcomes, also in comparison to non-federated methods. However, most studies did not make use of real-world federated data, but rather showed the potential of FL by using data that was manually partitioned. FL is a promising methodology which allows using data from several sources, potentially generating stronger and more generalisable results. However, further exploration of FL application possibilities in ID research is needed.

Chandan M., Santhi S.G., Srinivasa Rao T.

Malware transmission is a significant security issue in WSN, however, the influence of the attack and defensive processes on malware propagation is rarely taken into account in traditional malware propagation prevention methods. Advanced methods are in need to stop the propagation of malware of sensor nodes. With the formulation of representing dynamics among states, a new decision-making problem as the optimal control problem via hybrid optimization algorithm. The proposing model is termed as Butterfly Updated Bald Eagle Optimization based Prevention of Malware Propagation in Wireless Sensor Network (BUBEO-PMPWSN). In the proposed controlling system, optimal system parameters are analyzed via the BUBEO for preventing malware propagation in WSN. Particularly, the sensor node states considered are Susceptible, Infectious, Infectious and sleeping, recovered, Recovered and sleeping, and finally Dead. The system parameter tuning will be under the evaluation of fitness calculation under probability of infectious sensor node becoming recovered and the probability of infectious sensor node entering sleeping state. This optimal tuning strategy ensures the preventing of malware propagation. Finally, the performance of proposed BUBEO-PMPWSN model is evaluated and validated successfully by comparing other state-of-the-art models. The BUBEO-PMPWSN achieved 250 recovered nodes for time 500, while the HGS, BOA, HBA, COOT, and HHO scored 123, 115, 236, 172, and 180, respectively, for recovered nodes.

Jafar M.T., Yang L., Li G., Yang X.

Xia Y., Jiang H., Yu S., Yu Z.

Rumor spreading occurs not only between two individuals but also among multiple individuals or influenced by groups. However, pairwise interactions in complex networks are insufficient to describe this process. In this study, we propose a rumor spreading model with higher-order interactions, in which the rumor propagation process is represented by simplicial complexes. By selecting the propagation coefficient and time delay as the threshold, the model shows richer dynamic behaviors, such as the bi-stability, discontinuous transition, forward bifurcation, backward bifurcation, Hopf bifurcation, and periodic oscillation. Besides, for exploring the collective behavior induced by rumors, the rumor synchronization model is first established by applying the adaptive feedback mechanism, which erects a theoretical bridge between rumor spreading and behavior diffusion. Moreover, an improved optimal control strategy considering system gains is performed to curb rumor diffusion. Numerical simulations suggest that rumor spreading models with higher-order interactions are more consistent with actual data than network-based ones. Our results may shed some light on comprehending higher-order interactions in rumor spreading and the coupling between rumor and behavior, and provide a promising approach to control rumors and irrational behaviors.

Badia L., Crosara L.

Xu C., Zhang X., Yang H.H., Wang X., Pappas N., Niyato D., Quek T.Q.

Sumathi M., Abilasha B., Ravikumar S., Veeramani C.

A pandemic is a disease that spreads over a broad territory. COVID-19 is the latest pandemic to be reported, following the 1918 flu pandemic. We develop a compartmental model based on the classic SEIQR model to investigate coronavirus dynamics in India, incorporating bi-modal susceptible variables and quarantine in this article. We found the reproduction number by using the next-generation matrix. The stability results were statistically validated using the reproduction number. Moreover, global stability analyses are performed analytically and illustrated through numerical simulations. In optimal control analysis, four control parameters are used to explore the increase and decrease of the infected and exposed individuals.

Myilsamy K., Senthil Kumar M., Satheesh Kumar A.

The rapid development of social networks makes the rumour, other false news disseminate to the people in a short period. Online users in social networks are dynamically changing the connectivity over time. The effect of dynamic connections results in stochastic variation which is termed as noise. In this paper, a nonlinear rumour propagation model is formulated, the basic regeneration number [Formula: see text] of the proposed model is computed and the stability for the model is discussed. Further, we extend the model to stochastic rumour propagation for online social networks incorporating noise. The existence and uniqueness of the stochastic rumour propagation for the homogeneous network are investigated. Optimal control strategy of stochastic rumour spreading model in online social network is investigated to control the parameters. A comparison between deterministic and stochastic rumour spreading model in online social network is numerically illustrated.

Frąszczak D.

AbstractSocial media platforms are broadly used to exchange information by milliards of people worldwide. Each day people share a lot of their updates and opinions on various types of topics. Moreover, politicians also use it to share their postulates and programs, shops to advertise their products, etc. Social media are so popular nowadays because of critical factors, including quick and accessible Internet communication, always available. These conditions make it easy to spread information from one user to another in close neighborhoods and around the whole social network located on the given platform. Unfortunately, it has recently been increasingly used for malicious purposes, e.g., rumor propagation. In most cases, the process starts from multiple nodes (users). There are numerous papers about detecting the real source with only one initiator. There is a lack of solutions dedicated to problems with multiple sources. Most solutions that meet those criteria need an accurate number of origins to detect them correctly, which is impossible to obtain in real-life usage. This paper analyzes the methods to detect rumor outbreaks in online social networks that can be used as an initial guess for the number of real propagation initiators.

Muthukumar S., Myilsamy K., Balakumar A., Chinnadurai V.

AbstractEfficacy of the healthcare system and illumination (awareness) activities control COVID‐19. To defend public health, the spreading pandemic of COVID‐19 disease necessitates social distancing, wearing masks, personal cleanliness, and precautions. Due to inadequate awareness programs, COVID‐19 rapidly increases in India. The primary goal of this research is to investigate the spreading behavior of the COVID‐19 virus in India when people are aware of the disease. We find the optimum value of disease transmission rate and detection of the unidentified asymptomatic and symptomatic populations. An optimal control problem is designed with limited resource allocation to improve the recovered individuals. A stability analysis presents for emphasizes the relevance of disease awareness in preventing the spread of the disease. The control parameters are used to explore the increase and decrease of the infected individual with and without control in optimal control analysis. The model is simulated using the Hattaf‐fractional derivative to study the memory effect in the epidemic. To adapt the model to the total number of reported COVID‐19 cases in India, we collected data from March 20, 2021 to September 30, 2021. According to the simulation results, the pandemic would spread faster if awareness campaigns were improperly carried out.

Hussain S., Tunç O., Rahman G.U., Khan H., Nadia E.

The” Middle East Respiratory” (MERS-Cov) is among the world’s dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration.

Khan H., Alzabut J., Gulzar H.

In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for modified ABC-fractional differential equations (mAB-FDEs) with p-Laplacian operator. We also study the uniqueness and Hyers-Ulam stability (HU-stability) for the solutions of the presumed mABC-FDEs system. For the recently developed mABC-operator, such a problem has not yet studied also our problem is more general than those in the available literature.

Khan H., Alzabut J., Shah A., He Z., Etemad S., Rezapour S., Zada A.

Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution’s existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional integral form and study its qualitative analysis using an iterative convergent sequence and fixed-point technique to see whether there is a solution. We use Lagrange’s interpolation to construct numerical algorithms for the fractal-fractional waterborne disease model in terms of computations. The approach is then put to the test in a case study, yielding some interesting outcomes.

Khan H., Alzabut J., Gulzar H., Tunç O., Pinelas S.

The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations.

Ojha R.P., Srivastava P.K., Awasthi S., Srivastava V., Pandey P.S., Dwivedi R.S., Singh R., Galletta A.

Kumar M.S., Dadlani A., Moradian M., Khonsari A., Tsiftsis T.A.

The timeliness of status message delivery in communications networks is subjective to time-varying wireless channel transmissions. In this paper, we investigate the age of information (AoI) of each source in a multi-source M/G/1 queueing update system with active server failures. In particular, we adopt the method of supplementary variables to derive a closed-form expression for the average AoI in terms of system parameters, where the server repair time follows a general distribution and the service time of packets generated by independent sources is a general random variable. Numerical results are provided to validate the effectiveness of the proposed packet serving policy under different parametric settings.

Tong J., Fu L., Han Z.

Age-of-information (AoI) based minimization problems have been widely considered in Internet-of-Things (IoT) networks with the settings of multi-source single-channel systems and multi-source multi-channel systems. Most existing works are limited to either the case of identical multi-channel or independent sources. In this paper, we study this problem under the identical and non-identical multi-channel, as well as the correlated sources setting. This correlation defines the case when updating a source’s AoI; others correlated to this one will also reveal partial information. To tackle this AoI-based minimization problem, we formulate it as a correlated restless multi-armed bandit (CRMAB) problem. By decoupling the CRMAB problem into $N$ independent single-armed bandit problems, we derive the closed-form expressions of the generalized Whittle index (GWI) and the generalized partial Whittle index (GPWI) under the identical channel and the non-identical channel settings, respectively. Then, we put forth the GWI-based and GPWI-based scheduling policies to solve this AoI-based minimization problem. In addition, we provide two lower numerical performance bounds for the proposed policies by solving the relaxed Lagrange problem of the decoupled CRMAB. Numerical results show that the proposed policies can achieve these lower bounds and outperform the state-of-the-art scheduling policies. Compared with the case of independent sources, the performance of the proposed policies in the case of correlated sources improves significantly, especially in high-density networks.

Tripathi V., Modiano E.

We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss how to find optimal stationary randomized policies and show that they are at-most a factor of two away from optimal policies in general. Then, we develop a Lyapunov drift-based max-weight policy that performs better than randomized policies in practice and show that it is also at-most a factor of two away from optimal. Next, we derive scaling results that show how AoI improves in large networks in the presence of correlation. We also show that for stationary randomized policies, the expression for average AoI is robust to the way in which the correlation structure is modeled. Finally, for the setting where correlation parameters are unknown and time-varying, we develop a heuristic policy that adapts its scheduling decisions by learning the correlation parameters in an online manner. We also provide numerical simulations to support our theoretical results.

Sun R., Chen C., Wang X., Zhang Y., Wang X.

Community detection is one of the most fundamental problems in social network analysis, while most existing research focuses on unsigned graphs. In real applications, social networks involve not only positive relationships but also negative ones. It is important to exploit the signed information to identify more stable communities. In this paper, we propose a novel model, named stable $k$ -core, to measure the stability of a community in signed graphs. The stable $k$ -core model not only emphasizes user engagement, but also eliminates unstable structures. We show that the problem of finding the maximum stable $k$ -core is NP-hard. To scale for large graphs, novel pruning strategies and searching methods are proposed. We conduct extensive experiments on 6 real-world signed networks to verify the efficiency and effectiveness of proposed model and techniques.