Related papers: Global stability in a competitive infection-age st…
We consider a space-time SI epidemic model with infection age-dependent infectivity and non-local infections constructed on a grid of the torus $\mathbb{T}^1 =(0, 1]^d$, where the individuals may migrate from node to another. The migration…
The mathematical modeling of the propagation of illnesses has an important role from both mathematical and biological points of view. In this article, we observe an SEIR-type model with a general incidence rate and a non-constant…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
We consider SIR and SIRS models with differential mortality. Global stability of equilibria is established by using Lyapunov's method
In this paper, we consider a competition model between $n$ species in a chemostat including both monotone and non-monotone response functions, distinct removal rates and variable yields. We show that only the species with the lowest…
This paper considers the susceptible-infected-susceptible (SIS) epidemic model with an underlying network structure among subpopulations and focuses on the effect of social distancing to regulate the epidemic level. We demonstrate that if…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
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…
The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…
We formulate a multi-group and multi-vector epidemic model in which hosts' dynamics is captured by staged-progression $SEIR$ framework and the dynamics of vectors is captured by an $SI$ framework. The proposed model describes the evolution…
For a non-autonomous SEIRS model with general incidence, that admits [T. Kuniya and Y. Nakata, Permanence and extinction for a nonautonomous SEIRS epidemic model, Appl. Math. Computing 218, 9321-9331 (2012)] as a very particular case, we…
This paper studies the endemic behavior of a multi-competitive networked susceptible-infected-susceptible (SIS) model. In particular, we focus on the case where there are three competing viruses (i.e., the tri-virus system). First, we show…
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $\lambda$ that is used to classify the extinction and permanence of the disease. In…
A stochastic model, describing the growth of two competing infections on $\mathbb{R}^d$, is introduced. The growth is driven by outbursts in the infected region, an outburst in the type 1 (2) infected region transmitting the type 1 (2)…
We propose a system theoretic approach to select and stabilize the endemic equilibrium of an SIRS epidemic model in which the decisions of a population of strategically interacting agents determine the transmission rate. Specifically, the…
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without contacting an infected member of the population. This…
We consider a large population of learning agents noncooperatively selecting strategies from a common set, influencing the dynamics of an exogenous system (ES) we seek to stabilize at a desired equilibrium. Our approach is to design a…
The aims of this work is to analyse of the global stability of the extended model of hepatitis C virus(HCV) infection with cellular proliferation, spontaneous cure and hepatocyte homeostasis. We first give general information about…