Related papers: Stationary states and spatial patterning in an $SI…
We show the existence of traveling front solutions in a diffusive classical SIS epidemic model and the SIS model with a saturating incidence in the size of the susceptible population. We investigate the situation where both susceptible and…
Some recent works reveal that there are models of differential equations for the mean and variance of infected individuals that reproduce the SIS epidemic model at some point. This stochastic SIS epidemic model can be interpreted as a…
Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of…
In previous work, we developed the scaled SIS process, which models the dynamics of SIS epidemics over networks. With the scaled SIS process, we can consider networks that are finite-sized and of arbitrary topology (i.e., we are not…
The COVID-19 pandemic provided many modeling challenges to investigate the evolution of an epidemic process over areal units. A suitable encompassing model must describe the spatio-temporal variations of the disease infection rate of…
The spread of an infectious disease is known to change people's behavior, which in turn affects the spread of disease. Adaptive network models that account for both epidemic and behavior change have found oscillations, but in an extremely…
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,…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…
In this paper we analyze continuous-time SIS epidemics subject to arrivals and departures of agents, by using an approximated process based on replacements. In defining the SIS dynamics in an open network, we consider a stochastic setting…
This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private…
In this paper we study the diffusion of an SIS-type epidemics on a network under the presence of a random environment, that enters in the definition of the infection rates of the nodes. Accordingly, we model the infection rates in the form…
This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection…
We propose a new stochastic epidemiological model defined in a continuous space of arbitrary dimension, based on SIS dynamics implemented in a spatial $\Lambda$-Fleming-Viot (SLFV) process. The model can be described by as little as three…
We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we…
In this paper, we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology. We focus our study on the adaptive susceptible-infected-susceptible (ASIS) model, where healthy individuals are allowed to…
I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
We introduce and investigate an SIS-type model for the spread of an infectious disease, where the infected population is structured with respect to the different strain of the virus/bacteria they are carrying. Our aim is to capture the…
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional…