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We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the…
The contact model for the spread of disease may be viewed as a directed percolation model on $\ZZ \times \RR$ in which the continuum axis is oriented in the direction of increasing time. Techniques from percolation have enabled a fairly…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
We explore a rigorous formulation of agent-based SIR epidemic dynamics as a discrete-state Markov process, capturing the stochastic propagation of infection or an invading agent on networks. Using indicator functions and corresponding…
Among the consequences of the disordered interaction topology underlying many social, techno- logical and biological systems, a particularly important one is that some nodes, just because of their position in the network, may have a…
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on dynamical networks that involve local and global contacts among…
Networked SIR models have become essential workhorses in the modeling of epidemics, their inception, propagation and control. Here, and building on this venerable tradition, we report on the emergence of a remarkable self-organization of…
In this paper we are concerned with the SIR (Susceptible-Infective-Removed) epidemic on open clusters of bond percolation on the squared lattice. For the SIR model, a susceptible vertex is infected at rate proportional to the number of…
We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let $p$ be the site occupation probability of the square lattice. For $p$ greater than a critical value $p_c$, the steady state consists of…
Epidemics in large complete networks is well established. In contrast, we consider epidemics in non-complete networks. We establish the fluid limit macroscopic dynamics of a multi-virus spread over a multipartite network as the number of…
We obtain tight thresholds for bond percolation on one-dimensional small-world graphs, and apply such results to obtain tight thresholds for the \emph{Independent Cascade} process and the \emph{Reed-Frost} process in such graphs. These are…
The metapopulation network model is effectively used to study the spatial spread of epidemics with individuals mobility. Considering the time-varying nature of individual activity and the preferences for attractive destinations in…
Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine…
It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of…
In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are…
In the absence of other tools, monitoring the effects of protective measures, including social distancing and forecasting the outcome of outbreaks is of immense interest. Real-time data is noisy and very often hampered by systematic errors…
Discontinuous percolation transitions and the associated tricritical points are manifest in a wide range of both equilibrium and non-equilibrium cooperative phenomena. To demonstrate this, we present and relate the continuous and first…
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…
We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…
During the COVID pandemic, periods of exponential growth of the disease have been mitigated by containment measures that in different occasions have resulted in a power-law growth of the number of cases. The first observation of such…