Collective effect of personal behavior induced preventive measures and differential rate of transmission on spread of epidemics

Abstract

In the present work, the effect of personal behavior induced preventive measures is studied on the spread of epidemics over scale free networks that are characterized by the differential rate of disease transmission. The role of personal behavior induced preventive measures is parameterized in terms of variable λ, which modulates the number of concurrent contacts a node makes with the fraction of its neighboring nodes. The dynamics of the disease is described by a non-linear Susceptible Infected Susceptible model based upon the discrete time Markov Chain method. The network mean field approach is generalized to account for the effect of non-linear coupling between the aforementioned factors on the collective dynamics of nodes. The upper bound estimates of the disease outbreak threshold obtained from the mean field theory are found to be in good agreement with the corresponding non-linear stochastic model. From the results of parametric study, it is shown that the epidemic size has inverse dependence on the preventive measures (λ). It has also been shown that the increase in the average degree of the nodes lowers the time of spread and enhances the size of epidemics.

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

“…They provide a detailed insight into the co-evolving dynamics of the disease along with its corresponding information over the infection (L 1 ) and awareness (L 2 ) layers by taking into account the selfconsistent temporal modulations of the respective transmission rates. It is well known, that in the absence of such temporal variations, the outbreak and progression of these dynamical processes depend on the critical value of the respective transmission rates [25,28,36]. The focus of the present work is twofold: firstly, to understand the mechanism of temporal modulation of these rates and to subsequently examine their effect on the critical properties of the aforementioned processes.…”

“…. It is known from previous studies [25,28,36], that for both homogeneous and heterogeneous rates of transmission the disease free state is asymptotically stable if the largest eigenvalue of M given by ζ M satisfies the condition ζ M < 1. Thus for ζ M < 1, the infection or awareness will die out exponentially fast with the rate determined by ζ M .…”

“…disease, information etc. over complex network with fixed number of nodes upon the number of links [35,36]. Thus in order to avoid the additional effects arising due to difference in layer density, the ratio of total number of nodes to total number of links has been kept the same and each of the layers differ only in their linking patterns.…”

“…In the above mentioned studies, the transmission rates for the spread of epidemics (β I ) along with its corresponding awareness rate (β A ) have been assumed to be stationary in time. The criticality of the outbreak and the subsequent evolution of these processes have been associated with the largest eigenvalue of the network adjacency matrix [25][26][27]36].…”

Dynamics of Epidemic Spreading in the Group-Based Multilayer Networks

“…Along this line, other studies extend the co-evolution model by considering more influencing factors [21,22]. Moreover, more effects are further investigated, such as nonlinear coupled multiplex networks [23], resource control [24], global awareness [25], awareness cascade [26], time varying transmission rates [27,28], epidemic suppression [29,30] and coupled spreading process based on SIR model [31,32].…”