Effect of incubation delay in an SIRS model: Hopf bifurcation and stability switch (Q6600427)

An delayed SIRS epidemic model is proposed to consider the impact of incubation period on the spread of infectious diseases, where the incidence is of the Monod-Haldane type. First the existence of equilibrium points is discussed. Then their local stability is investigated. Delay can lead to Hopf bifurcation. These theoretical results are illustrated with numerical simulations.\N\NIt should be pointed out that the expression of \(\frac{dN}{dt}\) on page 369 is not correct. It should be\N\[\N\frac {dN}{dt}=bS\left(1-\frac{S}{K}\right)-d(N-S)-\delta I(t+\tau)-\gamma R(t+\tau)+\gamma R.\N\]\NAs the focus of the paper is only about local dynamics, this error does not affect the remaining discussion of the paper.\N\NFor the entire collection see [Zbl 1515.92004].