In this paper, we set up a double-layer multiplex network to elucidate the interaction of social contagion and epidemic spreading. The two types of transmission occur at layer 1 and layer 2 respectively, which are correspondingly described by the threshold model and classical SIR model. The assumption that the transmission and recovery probabilities are constants in unit time implies that the time intervals of transmission and recovery follow the exponential distribution. However, the time interval distributions are not only limited to be exponential in most practical cases. To address the general scenario, we take arbitrary distributions of transmission and recovery intervals into consideration. We formulate the interactional transmission in a finite multiplex network and large scale random multiplex networks via the message passing approach. Finally, concrete numerical examples demonstrate the consistency of the theoretical results with Monte Carlo simulations, and specifically, we investigate the effects of parameters (the threshold and inhibiting factor) on the two types of transmission.
Connected vehicle (CV) technology offers the ability, through cooperative driving, to a potential improve of the heterogeneous traffic efficiency and safety. In this paper, an extended cellular automaton model is proposed to study the effect of connected vehicles (CVs) on the dynamics of cooperative overtaking along a two-lane bidirectional system under mixed traffic conditions composed of CVs and human-driven vehicles (HDVs). The proposed model incorporates vehicle-to-vehicle communication within a finite communication range D, allowing CVs to perform cooperative anticipation, speed harmonization, overtaking maneuvers coordination and an adaptive speed limit (ASL) strategy. Traffic performance is characterized using fundamental diagrams, overtaking frequency, and inter-lane velocity correlation. In addition, microscopic traffic conflict-risk indicators are introduced to quantify potentially dangerous rear-end (P RE ) and head-on (P HO ) configurations associated with longitudinal interactions and overtaking maneuvers, respectively. The results show that the communication range D emerges as an important control parameter governing the collective dynamics of the system. Short communication ranges favor efficient local coordination, leading to higher traffic flow and stronger inter-lane synchronization, whereas larger communication ranges improve longitudinal safety by reducing the rear-end conflict-risk indicator. However, extended communication ranges may simultaneously increase the head-on conflict-risk indicator during cooperative overtaking, revealing a trade-off between longitudinal and lateral safety. Within the investigated communication ranges, intermediate values provide a favorable compromise between traffic efficiency and the two conflict-risk indicators. Furthermore, the ASL strategy improves overall traffic performance by increasing throughput and reducing both rear-end and head-on conflict risks. These findings highlight the coupled roles of communication range and adaptive speed control in shaping the collective dynamics, efficiency, and safety of mixed connected traffic on bidirectional roads.
During an epidemic outbreak, individuals decrease the number of their social contacts. We consider the time evolution of an epidemic coupled with the time evolution of such an adaptive network and formulate the degree-based approximation of the SIR dynamics. The paper presents an analytical theory and numerical results both for evolving node degree distribution of the network and for the time dependence of subpopulations of susceptible and infected individuals.
In connected vehicle environments, drivers no longer rely solely on their own perception of the vehicle ahead, Vehicle-to-Everything (V2X) communication now allows them to access real-time weighted speed information from surrounding traffic, while their car-following decisions are still influenced by recollection of past driving states, referred to here as driver memory. This study explores how these two factors, cognitive memory and V2X-based weighted speed awareness, jointly govern car-following dynamics by extending the classical Full Velocity Difference (FVD) model to include both effects explicitly. Through linear stability analysis, the stability criterion of the proposed model is derived and the results show that the combined inclusion of memory and weighted speed information enlarges the stable traffic flow region well beyond what is achieved by the conventional FVD model. Near the neutral stability boundary, a nonlinear analysis based on the reductive perturbation approach is used to derive the modified Korteweg–de Vries (mKdV) equation, whose kink–antikink soliton solution captures the density wave behavior that develops close to this critical threshold. The energy consumption is calculated to check how much memory and V2X information affect traffic disturbances. The simulation results agree with the analytical results, confirming that the proposed model exhibits markedly reduced stop-and-go oscillations and lower energy dissipation than earlier models.
This work investigates the use of time-varying parameters in SEIR epidemic models to describe the temporal evolution of COVID-19 incidence data. Three models are considered: the classical SEIR model with constant parameters, a SEIR model incorporating a quasi-periodic effective progression rate, and an extended SEIR model that additionally includes a periodic vaccination function. The proposed approach is motivated by the observation that epidemic dynamics are influenced by multiple temporal factors acting at different scales, including behavioral changes, public health interventions, environmental variability, and vaccination campaigns. Model parameters were estimated from COVID-19 incidence data corresponding to the third epidemic wave in Jalisco, Mexico, using a differential evolution optimization algorithm. The results show that introducing temporal variability in the effective progression rate improves the agreement between the model and the reported data. Furthermore, the inclusion of a vaccination mechanism yields a substantial reduction in the fitting error. The proposed framework demonstrates that quasi-periodic and periodic parameterizations provide a flexible and effective approach for capturing complex epidemic dynamics and improving the description of observed incidence patterns.
