Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network

Abstract

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a SIS (Susceptible Infected Susceptible) process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an UAU (Unaware Aware Unaware) process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes is studied in terms of a network topology dependent parameter (α). Using a second order linear theory it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter(α), the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Further, for the case of an endemic state it is shown that inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The endemic state infection probability of a given node corresponding to the damped dynamics is found to have a dependence upon both the transmission rates as well as on the absolute intra-layer and relative inter-layer degrees of the individual nodes.

Coevolution spreading in complex networks

“…Because the transmission probability of epidemic may be time-varying [276,277], Sagar et al [278] proposed a generalized UAU+SIS model, in which the transmission probabilities of the awareness and epidemic vary with time. The system can be in one of the sustained oscillatory and damped dynamics.…”

Interacting Spreading Processes in Multilayer Networks: A Systematic Review

“…Other framework designed for modelling co-evolution of epidemics and awareness spreading uses as a key parameters time variation of transmission rates [111]. Differential rate of transmission within epidemic layer is dependent on spread- VOLUME 8, 2016 ing probabilities of related nodes within information layer and the same for information layer in relation to epidemic layer.…”

Asymmetrically interacting dynamics with mutual confirmation from multi-source on multiplex networks

“…The time scale of information propagation doesn't affect the outbreak threshold, but an optimal relative timescale of information and disease spreading may reduce the epidemics incidence [25,26]. Some works define heterogenous disease or information transmission rate for nodes by taking the local or global infection or awareness density into consideration, where the awareness density is obtained from the communication layer and the infection density is obtained from the physical contact layer [27][28][29]. In all the studies, the individuals receive information on one layer and transmit disease on the other layer.…”