Related papers: On equilibria stability in an epidemiological SIR …
Treatment rate has always been one of the most important factors affecting the spread of infectious diseases. In this paper, we study a treatment function SIR model with treatment rate related to the maximum treatment capacity, whose…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…
We propose a mathematical model to analyze the effects of anti-infection behavior on the equilibrium states of an infectious disease. The anti-infection behavior is incorporated into a classical epidemiological SIR model, by considering the…
An SIR model with the coinfection of the two infectious agents in a single host population is considered. The model includes the environmental carry capacity in each class of population. A special case of this model is analyzed and several…
Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion.…
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…
This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously…
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…
In this paper, we give a complete analysis of an SIS epidemiological model in a population of varying size with two dissimilar groups of infective individuals. It is mainly based on the discussion of the existence and stability of…
We consider an epidemiological model that includes waning and boosting of immunity. Assuming that repeated exposure to the pathogen fully restores immunity, we derive an SIRS-type model with discrete and distributed delays. First we prove…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
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…
The focus of this article is on the dynamics of a new susceptible-infected model which consists of a susceptible group ($S$) and two different infectious groups ($I_1$ and $I_2$). Once infected, an individual becomes a member of one of…
We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic…
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…
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…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
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…
In recent years, classical epidemic models, which assume stationary behavior of individuals, have been extended to include an adaptive heterogeneous response of the population to the current state of the epidemic. However, it is widely…
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…