A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number 0 R is calculated. It is shown that this number characterizes the disease transmission dynamics: if 0 1 R , there only exists the disease-free equilibrium which is globally asymptotically stable; if 0 1 R , there is a unique endemic equilibrium and the disease persists,...

ABSTRACT Mathematical epidemiological models for the dynamics of infections that induce lifelong immunity have been extensively developed. In this work, we consider a nonlinear SIR model given by a nonlinear system describing the dynamics of the interaction between susceptible and infective individuals in population. We analyze the dynamical behavior of the nonlinear system and then use two typ...

During the course of a day an individual typically mixes with different groups of individuals. Epidemic models incorporating population structure with individuals being able to infect different groups of individuals have received extensive attention in the literature. However, almost exclusively the models assume that individuals are able to simultaneously infect members of all groups, whereas ...

Theoretical results show that the measles 'pulse' vaccination strategy can be distinguished from the conventional strategies in leading to disease eradication at relatively low values of vaccination. Using the SIR epidemic model we showed that under a planned pulse vaccination regime the system converges to a stable solution with the number of infectious individuals equal to zero. We showed tha...

Epidemic modeling in complex networks has become one of the latest topics recent times. The Susceptible-Infectious-Recovered (SIR) model and its variants are often used for epidemic modeling. One important issue is determination spreading ability nodes network. Thus, example, can be detected early stages. In this study, we developed a centrality measure called Lexical Sorting Centrality (LSC) t...

A simplified susceptible-infected-recovered (SIR) epidemic model and a small-world model are applied to analyse the spread and control of Severe Acute Respiratory Syndrome (SARS) for Hong Kong in early 2003. From data available in mid April 2003, we predict that SARSwould be controlled by June and nearly 1700 persons would be infected based on the SIR model. This is consistent with the known da...

It has been known that epidemic outbreaks in the SIR model on networks are described by phase transitions. Despite the similarity with percolation transitions, whether an epidemic outbreak occurs or not cannot be predicted with probability one in the thermodynamic limit. We elucidate its mechanism by deriving a simple Langevin equation that captures an essential aspect of the phenomenon. We als...

Infectious diseases spread through human networks. Susceptible-InfectedRemoved (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken i...