Related papers: A note on monotonicity of spatial epidemic models
In epidemic modeling, the term infection strength indicates the ratio of infection rate and cure rate. If the infection strength is higher than a certain threshold -- which we define as the epidemic threshold - then the epidemic spreads…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
The current work deals with an epidemic model on the complete graph K_n on n vertices in a non-homogeneous setting, where the vertices may have distinct types. Different types differ in the probability of getting infected, and/or in the…
Background: Recently developed techniques to study the spread of infectious diseases through networks make assumptions that the initial proportion infected is infinitesimal and the population behavior is static throughout the epidemic. The…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
The ability to directly record human face-to-face interactions increasingly enables the development of detailed data-driven models for the spread of directly transmitted infectious diseases at the scale of individuals. Complete coverage of…
Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of…
We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability…
We introduce a model of epidemics among moving particles on any locally finite graph. At any time, each vertex is empty, occupied by a healthy particle, or occupied by an infected particle. Infected particles recover at rate $1$ and…
The basic contact process with parameter $\mu$ altered so that infections of sites that have not been previously infected occur at rate proportional to $\lambda$ instead is considered. Emergence of an infinite epidemic starting out from a…
We consider the contact process on the preferential attachment graph. The work of Berger, Borgs, Chayes and Saberi [BBCS1] confirmed physicists predictions that the contact process starting from a typical vertex becomes endemic for an…
We prove a Central Limit Theorem for the proportion of infected individuals for an epidemic model by dealing with a discrete time system of simple random walks on a complete graph with n vertices. Each random walk makes a role of a virus.…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise,…
Multigraphs are graphs in which multiple links between pairs of nodes are allowed, whereas they are forbidden in simple graphs, the latter being widely used in network science. Simple graphs generated by the configuration model have served…
For a given, arbitrary graph, what is the epidemic threshold? That is, under what conditions will a virus result in an epidemic? We provide the super-model theorem, which generalizes older results in two important, orthogonal dimensions.…
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the…
We study one specific version of the contact process on a graph. Here, we allow multiple infections carried by the nodes and include a probability of removing nodes in a graph. The removal probability is purely determined by the number of…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
We show that the contact process on a random $d$-regular graph initiated by a single infected vertex obeys the "cutoff phenomenon" in its supercritical phase. In particular, we prove that when the infection rate is larger than the critical…