相关论文: Duality for some models of epidemic spreading

This paper presents an analytical comparison of active and passive receiver models in diffusive molecular communication. In the active model, molecules are absorbed when they collide with the receiver surface. In the passive model, the…

Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…

At non-equilibrium phase transitions into absorbing (trapped) states, it is well known that the directed percolation (DP) critical scaling is shared by two classes of models with a single (S) absorbing state and with infinitely many (IM)…

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum…

We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…

We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of…

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems…

The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…

Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process (CP) where the contagion is expanded at…

Bulk topology and criticality can both lead to nontrivial boundary effects. Topological orders are often characterized by their robust edge states, while bulk critical points can have different boundary scalings governed by boundary…

Diffusive molecular communication (DMC) is envisioned as a promising approach to help realize healthcare applications within bounded biological environments. In this paper, a DMC system within a biological spherical environment is…

We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…

For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of…

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

By a detailed study of the mathematical structure of the cumulant generating function (CGF) of particle transfer in the non-interacting case we show that it satisfies duality relations connecting the CGFs of two different realizations of…

Epidemic spreading and cascading failure are two important dynamical processes over complex networks. They have been investigated separately for a long history. But in the real world, these two dynamics sometimes may interact with each…

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…

We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo…

We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…