Related papers: A geometric analysis of the SIR, SIRS and SIRWS ep…
We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much…
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…
Traditional studies about disease dynamics have focused on global stability issues, due to their epidemiological importance. We study a classical SIR-SI model for arboviruses in two different directions: we begin by describing an…
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…
We consider a model due to Piero Poletti and collaborators that adds spontaneous human behavioral change to the standard SIR epidemic model. In its simplest form, the Poletti model adds one differential equation, motivated by evolutionary…
The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
An ultrametric model of epidemic spread of infections based on the classical SIR model is proposed. Ultrametrics on a set of individuals based on theire hierarchical clustering relativly to the average time of infectious contact is…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
Mathematical models are instrumental to forecast the spread of pathogens and to evaluate the effectiveness of non-pharmaceutical measures. A plethora of optimal strategies has been recently developed to minimize either the infected peak…
Epidemiological models are best suitable to model an epidemic if the spread pattern is stationary. To deal with non-stationary patterns and multiple waves of an epidemic, we develop a hybrid model encompassing epidemic modeling, particle…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we…
We study a coupled epidemic-mobility model in which, at each time, individuals move in a network of spatially-distributed regions (sub-populations) according to a Continuous Time Markov Chain (CTMC) and subsequently interact with the local…
We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also…
In this paper we consider an SIRS epidemic model under a general assumption of density-dependent mortality. We prove the global stability of the disease-free equilibrium and propose a Lyapunov function that allows to demonstrate the global…
A class of multiple-timescale asymptotic solutions to the equations of the susceptible-infected-recovered (SIR) model is presented for the case of high basic reproduction number, with the inverse of the latter employed as the expansion…
In this work, we use a new approach to study the spread of an infectious disease. Indeed, we study a SIR epidemic model with variable infectivity, where the individuals are distributed over a compact subset $D$ of $\R^d$. We define…
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…
In this work, we study the dynamics of a SEIRS epidemic model with a periodic time-dependent transmission rate. Emphasizing the influence of the seasonality frequency on the system dynamics, we analyze the largest Lyapunov exponent along…