相关论文: SIR model with vaccination: bifurcation analysis
This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible $\to$ infected $\to$ removed) model for the spread of an epidemic amongst a population of individuals with a random network of social…
We consider an infinite-dimension SIS model introduced by Delmas, Dronnier and Zitt, with a more general incidence rate, and study its equilibria. Unsurprisingly, there exists at least one endemic equilibrium if and only if the basic…
A probabilistic approach to the epidemic evolution on realistic social-contact networks allows for characteristic differences among subjects, including the individual number and structure of social contacts, and the heterogeneity of the…
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected…
We analyze an optimal control version of a simple SIR epidemiology model that includes a partially specified vaccination policy and takes into account fatigue from protracted application of social distancing measures. The model assumes…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
The dynamics of a SIVR model with power relationship incidence rates $(\beta I^p S^q)$ is investigated. It is assumed an individual can be susceptible after receiving the first dose of the vaccine, hence a second dose is required to attain…
Controlling and understanding epidemic outbreaks has recently drawn great interest in a large spectrum of research communities. Vaccination is one of the most well-established and effective strategies in order to contain an epidemic. In the…
The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…
The ever-changing world of disease study heavily relies on mathematical models. They are key in finding and controlling infectious diseases. We aim to explore these mathematical tools used for studying disease spread in biology. The SEIR…
An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…
SIRS epidemic models assume that individual immunity (from infection and vaccination) wanes in one big leap, from complete immunity to complete susceptibility. For many diseases immunity on the contrary wanes gradually, something that's…
Multiple viruses are widely studied because of their negative effect on the health of host as well as on whole population. The dynamics of coinfection is important in this case. We formulated a SIR model that describes the coinfection of…
We study an SAIRS-type epidemic model with vaccination, where the role of asymptomatic and symptomatic infectious individuals are explicitly considered in the transmission patterns of the disease. We provide a global stability analysis for…
This paper considers a mathematical model based on the transmission dynamics of hepatitis C virus (HCV) infection. In addition to the usual compartments for susceptible, exposed, and infected individuals, this model includes compartments…
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…
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the…
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between…
We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous…
We present a series of SIR-network models, extended with a game-theoretic treatment of imitation dynamics which result from regular population mobility across residential and work areas and the ensuing interactions. Each considered…