Permanence of a delayed SIR epidemic model with density dependent birth rate
The authors consider the following SIR epidemic model with time delay \[ \frac{dS(t)}{dt}=-\beta S(t)I(t-h)-\mu _1S(t)+b\left( 1-\beta _1\frac{N(t)}{ 1+N(t)}\right), \] \[ \frac{dI(t)}{dt}=\beta S(t)I(t-h)-\mu _2I(t)-\lambda I(t),\quad \frac{dR(t)}{dt}=\lambda I(t)-\mu _3R(t), \] where \(S(t),\) \(I(t)\) and \(R(t)\) denote the numbers of susceptible members to the disease, of infective members and of members who have been removed from the possibility of infection through full immunity, respectively. Some permanence results are established when the positive equilibrium exists.
scientific article; zbMATH DE number 5131571
scientific article