Related papers: Stochastic epidemic dynamics on extremely heteroge…
In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from…
Contact networks can significantly change the course of epidemics, affecting the rate of new infections and the mean size of an outbreak. Despite this dependence, some characteristics of epidemics are not contingent on the contact network…
Infectious disease superspreading caused by heterogeneity in contact behavior has been observed to be an important determinant of epidemic dynamics and size in both empirical and theoretical settings. However, it has also been observed that…
Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals,…
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…
We propose a network behavioral-feedback Susceptible-Infected-Recovered (SIR) epidemic model in which the interaction matrix describing the infection rates across subpopulations depends in feedback on the current epidemic state. This model…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study…
Epidemics are often modelled using non-linear dynamical systems observed through partial and noisy data. In this paper, we consider stochastic extensions in order to capture unknown influences (changing behaviors, public interventions,…
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…
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…
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the…
Throughout the course of an epidemic, the rate at which disease spreads varies with behavioral changes, the emergence of new disease variants, and the introduction of mitigation policies. Estimating such changes in transmission rates can…
Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an…
We study a well mixed SIR epidemic model with heterogeneous susceptibility and infectivity, allowing for an arbitrary joint distribution of these traits. Using an exact final size formulation and a branching process approximation for early…
Complex networks with pairwise connections have been vastly used for the modeling of interactions within systems. Although these type of models are capable to capture rich structures and different phases within a great variety of…