Related papers: Existence, multiplicity and stability of endemic s…
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…
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…
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.…
In this manuscript we consider an age structured epidemic system modelling the dynamics of transmission of immunizing disease like Hepatitis B virus. Our model takes into account age as well as two classes of infected individuals (chronic…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…
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 propose and investigate an SEI infection's age model with a general class of nonlinear incidence rates. We give a necessary and sufficient condition for global asymptotic stability of the free-equilibrium related to the basic…
Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this…
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…
We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when $R_0 >…
In this paper, we investigate an SVIRS epidemic model that incorporates both temporary immunity and an age-structured recovery process. By reformulating the system as a non-densely defined abstract Cauchy problem, we establish the existence…
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…
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…
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…
What is the long term dynamics of the Covid-19 pandemic? How will it end? Here we constructed an infectious disease model with testing and analyzed the existence and stability of its endemic states. For a large parameter set, including…
In the present paper, we are concerned with an SIS epidemic reaction-diffusion model governed by mass action infection mechanism and linear birth-death growth with no flux boundary condition. By performing qualitative analysis, we study the…
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 focus on susceptible-infected-susceptible dynamics on metapopulation networks, where nodes represent subpopulations, and where agents diffuse and interact. Recent studies suggest that heterogeneous network structure…
In this article, we construct an age-structured model for COVID-19 with vaccination and analyze it from multiple perspectives. We derive the unique disease-free equilibrium point and the basic reproduction number $ \mathscr{R}_0 $, then we…
Medical statistics reveal a significant dependence of hospitalized dengue patient on the patient's age. To incorporate an age-dependence into a mathematical model, we extend the classical ODE system of disease dynamics to a PDE system. The…