Sufficient conditions are given which guarantee that the trivial solution x = 0 for a nonlinear integro–differential system is globally attracting. As an example, this result is applied to a SIRS epidemic model with subpopulations to show that, under certain conditions, the endemic equilibrium is globally asymptotically stable.

An SIRS type model of disease transmission in an open environment is discussed. We use the Poincaré index together with a perturbation method to show that the endemic proportions need not be unique.

Dear Sirs, Research serves a vital purpose in furthering the knowledge base on which medicine is practised. Furthermore it may be defined as the method to which we inform our action. In order for us to practice evidence-based medicine, we must be informing our action, which is reliant on robust and rigorous research. Tomorrow’s Doctors 2009 relates to three domains: the scholar, the scientist a...

This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical...

We consider SIR and SIRS models with differential mortality. Global stability of equilibria is established by using Lyapunov’s method.

OBJECTIVE The relationship between food insecurity and obesity is discussed in the literature. The objective of this study was to determine whether food insecurity and obesity were associated in the Paris metropolitan area. METHODS We used data from third wave of the Health, Inequalities and Social Ruptures (SIRS) cohort study, a longitudinal population-based, representative health and socioe...

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We con...

Blocking the effects of cytokines is a potential new therapeutic avenue for the treatment of Gram-negative sepsis. Three classes of agents are currently being evaluated: antibodies, circulating inhibitors, and receptor antagonists. Data in the current literature support the consideration of these agents as potential therapeutic agents in Gram-negative sepsis. The clinical utility of these agent...