Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence

Authors:
Ruoyan Sun
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 4
Cited 2

Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission

SIAM Journal on Applied Mathematics
The Mathematics of Infectious Diseases

SIAM Review
Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

Mathematics and Computers in Simulation
Stability of disease free sets in epidemic models

Mathematical and Computer Modelling: An International Journal

Stability analysis for impulsive coupled systems on networks

Neurocomputing
Razumikhin-type theorems on exponential stability of stochastic functional differential equations on networks

Neurocomputing

Quantified Score

Hi-index	0.09

Visualization

Abstract

In this paper, we introduce a basic reproduction number for a multigroup epidemic model with nonlinear incidence. Then, we establish that global dynamics are completely determined by the basic reproduction number R"0. It shows that, the basic reproduction number R"0 is a global threshold parameter in the sense that if it is less than or equal to one, the disease free equilibrium is globally stable and the disease dies out; whereas if it is larger than one, there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population. Finally, a numerical example is also included to illustrate the effectiveness of the proposed result.