Global dynamics of a SEIR model with varying total population size.
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.
Li
M Y
MY
Department of Mathematics and Statistics, Mississippi State University 39762, USA. mli@math.ms-state.edu
Graef
J R
JR
Wang
L
L
Karsai
J
J
D004196:Disease Outbreaks; D018562:Disease Transmission, Infectious; D004813:Epidemiology; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics