Related papers: Regime dependent infection propagation fronts in a…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
We consider the class of SIS epidemic models in which a large population of individuals chooses whether to adopt protection or to remain unprotected as the epidemic evolves. For a susceptible individual, adopting protection reduces the…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
We study the spread of stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemics in two types of structured populations, both consisting of schools and households. In each of the types, every individual is part of one school…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
The study proposes a modeling framework for investigating the disease dynamics with adaptive human behavior during a disease outbreak, considering the impacts of both local observations and global information. One important application…
We consider a class of cooperative reaction-diffusion systems with free boundaries in one space dimension, where the diffusion terms are nonlocal, given by integral operators involving suitable kernel functions, and they are allowed not to…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by…
We follow up an earlier work (briefly reviewed below) to investigate the temporal stability of an exact travelling front solution, constructed in the form of an integral expression, for a one-dimensional discrete Nagumo-like model without…
In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call…
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the environmental diffusion coefficient and ignition kernels,…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
We propose a novel SIR epidemic model which is driven by the transmission of infection packets in networks. Specifically, infected nodes generate and deliver infection packets causing the spread of the epidemic, while recovered nodes block…
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.…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
Traveling waves are analyzed in a model of the Hantavirus infection of deer mice. The existence of two kinds of wave phenomena is predicted. An environmental parameter governs a transition between two regimes of propagation. In one of them…
Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In…
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…
We consider a reaction-diffusion system of densities of two types of particles, introduced by Edouard Hannezo et al. in the context of branching morphogenesis. It is a simple model for a growth process: active, branching particles form the…