Related papers: Stochastic and deterministic SIS patch model
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same…
We study the Susceptible-Infected-Susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population and the infectivity. We derive the large-N…
Social networks are an important infrastructure for information, viruses and innovations propagation. Since users behavior has influenced by other users activity, some groups of people would be made regard to similarity of users interests.…
Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe…
We propose a lattice dynamical system that arises in a discrete diffusive two-group epidemic model with latency in a patchy environment. The model considers the SIS form and latency of the disease in group 1, while the SIR form without…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and…
This paper focuses on and analyzes realistic SIR models that take stochasticity into account. The proposed systems are applicable to most incidence rates that are used in the literature including the bilinear incidence rate, the…
We study the Susceptible-Infectious-Susceptible (SIS) model on arbitrary networks. The well-established pair approximation treats neighboring pairs of nodes exactly while making a mean field approximation for the rest of the network. We…
Disease awareness in epidemiology can be modelled with adaptive contact networks, where the interplay of disease dynamics and network alteration often adds new phases to the standard models (Gross et al. 2006, Shaw et al. 2008) and, in…
An epidemic Susceptible-Vaccinated-Infected-Removed-Susceptible (SVIRS) model is presented on a weighted-undirected network with graph Laplacian diffusion. Disease-free equilibrium always exists while the existence and uniqueness of endemic…
We study the spreading of an infection within an SIS epidemiological model on a network. Susceptible agents are given the opportunity of breaking their links with infected agents, and reconnecting those links with the rest of the…
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth…
This paper investigates the spread of infectious diseases within a networked community by integrating epidemic transmission and public opinion dynamics. We propose a novel discrete-time networked SIS (Susceptible-Infectious-Susceptible)…
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic…
The propagation of infectious diseases and its impact on individuals play a major role in disease dynamics, and it is important to incorporate population heterogeneity into efforts to study diseases. As a simplistic but illustrative…
We analyze the critical transitions (a) to endemic states in an SIS epidemiological model, and (b) to full synchronization in an ensemble of coupled chaotic maps, on networks where, at any given time, each node is connected to just one…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…
In this article we mainly extend the deterministic model developed in [10] to a stochastic setting. More precisely, we incorporated randomness in some coefficients by assuming that they follow a prescribed stochastic dynamics. In this way,…