Related papers: Global stability in a competitive infection-age st…
In this paper we consider a competition system in which two diseases spread by contact. We characterize the system behavior, establishing that only some configurations are possible. In particular we discover that coexistence of the two…
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…
In this article, we study the global dynamics of a discrete two dimensional competition model. We give sufficient conditions on the persistence of one species and the existence of local asymptotically stable interior period-2 orbit for this…
For classic Lotka-Volterra systems governing many interacting species, we establish an exclusion principle that rules out the existence of linearly asymptotically stable steady states in subcommunitites of communities that admit a stable…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…
This paper studies a two microbial species model in competition for a single resource in the chemostat including general interspecific density-dependent growth rates with distinct removal rates for each species. We give the necessary and…
In many natural situations one observes a local system with many competing species which is coupled by weak immigration to a regional species pool. The dynamics of such a system is dominated by its stable and uninvadable (SU) states. When…
We extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain…
We will study a mathematical model of the human immunodeficiency virus (HIV) infection in the presence of combination therapy that includes within-host infectious dynamics. The deterministic model requires us to analyze asymptotic stability…
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 develop a new perturbation method for studying quasi-neutral competition in a broad class of stochastic competition models, and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a…
We investigate the long-time dynamics of a SIR epidemic model with infinitely many pathogen variants infecting a homogeneous host population. We show that the basic reproduction number $\mathcal{R}_0$ of the pathogen can be defined in that…
It is known that the competitive exclusion principle holds for a large kind of models involving several species competing for a single resource in an homogeneous environment. Various works indicate that the coexistence is possible in an…
We study the global stability of a class of models for in-vivo virus dynamics, that take into account the CTL immune response and display antigenic variation. This class includes a number of models that have been extensively used to model…
The stochastic extinction and stability in the mean of a family of SEIRS malaria models with a general nonlinear incidence rate is presented. The dynamics is driven by independent white noise processes from the disease transmission and…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
Public health services are constantly searching for new ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine (isolation) and treatment of symptomatic individuals. Epidemic…
This study examines the behavior of solutions in a multi-patch epidemic model that includes a saturation incidence mechanism. When the fatality rate due to the disease is not null, our findings show that the solutions of the model tend to…
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…