Global dynamics of a SEIR model with varying total population size |
| |
Authors: | Michael Y Li John R Graef Liancheng Wang Jnos Karsai |
| |
Institution: | Department of Mathematics and Statistics, Mississippi State University 39762, USA. mli@math.ms-state.edu |
| |
Abstract: | A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied. The force of infection is of proportionate mixing type. A threshold sigma is identified which determines the outcome of the disease; if sigma < or = 1, the infected fraction of the population disappears so the disease dies out, while of sigma > 1, the infected fraction persists and a unique endemic equilibrium state is shown, under a mild restriction on the parameters, to be globally asymptotically stable in the interior of the feasible region. Two other threshold parameters sigma' and sigma are also identified; they determine the dynamics of the population sizes in the cases when the disease dies out and when it is endemic, respectively. |
| |
Keywords: | Epidemic models Endemic equilibrium Latent period Global stability Compound matrices |
本文献已被 ScienceDirect 等数据库收录! |