Related papers: A model for anomalous directed percolation
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
We study the phase transition phenomena for long-range oriented percolation and contact process. We studied a contact process in which the range of each vertex are independent, updated dynamically and given by some distribution $N$. We also…
Edge-based percolation methods can be used to analyze disease transmission on complex social networks. This allows us to include complex social heterogeneity in our models while maintaining tractability. Here we review the seminal works on…
We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed…
Metapopulation models provide the theoretical framework for describing disease spread between different populations connected by a network. In particular, these models are at the basis of most simulations of pandemic spread. They are…
We study the continuum percolation model, which is defined on $\mathbb{Z}^d\times \mathbb{R}$ so that the connections in the continuous directions are not oriented in time, with quasiperiodically disordered fields. The oriented version of…
In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the…
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of…
The directed bond percolation is a paradigmatic model in nonequilibrium statistical physics. It captures essential physical information on the nature of continuous phase transition between active and absorbing states. In this paper, we…
We study a model for the spread of an infectious disease which incorporates spatial and temporal effects. The model is a delayed multi-type branching process in which types represent geographic regions while infected individuals reproduce…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…
We discuss attacks and infections at propagating fronts of percolation processes based on the extended general epidemic process. The scaling behavior of the number of the attacked and infected sites in the long time limit at the ordinary…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
Physical contact or proximity is often a necessary condition for the spread of infectious diseases. Common destinations, typically referred to as hubs or points of interest, are arguably the most effective spots for the type of disease…
We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear,…
The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies…
We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-\alpha} for some \alpha>0.…
We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework…
In the past few decades, the frequency of pandemics has been increased due to the growth of urbanization and mobility among countries. Since a disease spreading in one country could become a pandemic with a potential worldwide humanitarian…