Moghadas, Seyed M.; Alexander, Murray E. Bifurcations of an epidemic model with non-linear incidence and infection-dependent removal rate. (English) Zbl 1098.92058 Math. Med. Biol. 23, No. 3, 231-254 (2006). Summary: An epidemic model with generalized nonlinear incidence is extended to incorporate the effect of an infection-dependent removal strategy, which is defined as a function of the number of infected individuals. It is assumed that the removal rate decreases from a maximum capacity for removing infected individuals as their number increases. The existence and stability of the associated equilibria are analysed, and the basic reproductive number (\({\mathcal R}_0\)) is formulated. It is shown that \({\mathcal R}_0\) is independent of the functional form of the incidence, but depends on the removal rate. Normal forms are derived to show the different types of bifurcation the model undergoes, including transcritical, generalized Hopf (Bautin), saddle-node and Bogdanov-Takens. A degenerate Hopf bifurcation at the Bautin point, where the first Lyapunov coefficient vanishes, is discussed. Sotomayor’s theorem is applied to establish a saddle-node bifurcation at the turning point of backward bifurcation. The Bogdanov-Takens normal form is derived, from which the local bifurcation curve for a family of homoclinic orbits is formulated. Bifurcation diagrams and numerical simulations, using parameter values estimated for some infectious diseases, are also presented to provide more intuition to the theoretical findings. The results show that sufficiently increasing the removal rate can reduce \({\mathcal R}_0\) below a subthreshold domain, which leads to disease eradication. Cited in 15 Documents MSC: 92D30 Epidemiology 34C23 Bifurcation theory for ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D23 Global stability of solutions to ordinary differential equations Keywords:epidemic models; nonlinear incidence; removal rate; Hopf bifurcation; saddle-node bifurcation; Bogdanov-Takens bifurcation; disease-free equilibrium PDFBibTeX XMLCite \textit{S. M. Moghadas} and \textit{M. E. Alexander}, Math. Med. Biol. 23, No. 3, 231--254 (2006; Zbl 1098.92058) Full Text: DOI