Related papers: A geometric analysis of the SIRS epidemiological m…
We study fast-slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is…
Although we have made progress in understanding disease spread in complex systems with non-Poissonian activity patterns, current models still fail to capture the full range of recovery time distributions. In this paper, we propose an…
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR…
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…
We propose a novel slow-fast SIRS compartmental model with demography, by coupling a slow disease spreading model and a fast information and misinformation spreading model. Beside the classes of susceptible, infected and recovered…
We study the long-time behavior of solutions of the SIRS model, a reaction-diffusion system that appears in epidemiology to describe the spread of epidemics. We allow the system to be heterogeneous periodic. Under some hypotheses on the…
We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological…
We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
We introduce a fast simulation technique for modeling epidemics on adaptive networks. Our rejection-based algorithm efficiently simulates the co-evolution of the network structure and the epidemic dynamics. We extend the classical SIS model…
Empirical studies suggest that contact patterns follow heterogeneous inter-event times, meaning that intervals of high activity are followed by periods of inactivity. Combined with birth and death of individuals, these temporal constraints…
In this paper, we study the trajectory of a classic SIR epidemic on a family of dynamic random graphs of fixed size, whose set of edges continuously evolves over time. We set general infection and recovery times, and start the epidemic from…
We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we…
For a susceptible-infectious-susceptible (SIS) infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
Network epidemiology has become a core framework for investigating the role of human contact patterns in the spreading of infectious diseases. In network epidemiology represents the contact structure as a network of nodes (individuals)…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…