Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

“…This type of saturation is a combination of all the previous effects. Our model in the present paper is an extension of the models from [17][18][19][20][21], where the authors considered the same rate of incidence but with different birth rate of the susceptible populations. The paper is organized as follows: in Section II we have formulated the model, in Section III we describe the boundedness and permanence of the solutions.…”

“…In most of the articles researchers considered the constant birth rates of the susceptible populations [12][13][14][15][16][17], which is not realistic in some populations. So the authors in [18][19][20] considered exponential/logistic growth rate of the susceptible populations.…”

Stability analysis for a delayed SIR model with a nonlinear incidence rate

“…Furthermore, the endemic equilibrium may lose its stability under certain conditions if the basic reproduction number is greater than one, which admits periodic behavior. Inspired by the works of Wang et al [24], Enatsu et al [4], Zhang et al [28], and Liu [14], it is reasonable to construct a more realistic disease model with the general nonlinear incidence rate of the…”

“…Moreover, Hopf bifurcation occurs under some conditions. Enatsu et al [4] extended system (1.1) and proposed the following vector-bone disease model with nonlinear incidence rate:…”

Global Hopf bifurcation analysis of an susceptible-infective-removed epidemic model incorporating media coverage with time delay

“…For instance, it can change the stability of equilibrium and thus lead to periodic solutions by Hopf bifurcation [6,[10][11][12]14,17,18,21,[27][28][29][30].…”