Analysis of the permanence of an SIR epidemic model with logistic process and distributed time delay

Global stability analysis for a generalized delayed SIR model with vaccination and treatment

“…From the fact that P(0) = (μ+c+γ +T (0))(1-R 0 ) < 0 if R 0 > 1 and lim λ− →+∞ P(λ) = +∞, we conclude that there is at least one positive root of (9). Hence, if R 0 > 1, E 0 is unstable.…”

“…It is known that the function forms of the incidence rate of the infection have a crucial role in the modeling of the infection dynamics, many forms of incidence function have been considered by the researchers in mathematical epidemiology, for example, the bilinear incidence rate βSI, where β is the transmission rate of infection, the saturated incidence rate βSI 1+αI , with α defined as the inhibitory coefficient, and many other forms (see [1][2][3][4][5][6][7]). To make a model more realistic, the introduction of the time delay is more interesting, and considerable attention has been paid by several authors to studying the dynamics of epidemic models with discrete or distributed time delay (see [3,4,[8][9][10][11]). Vaccination and treatment are the two main public health control strategies that help to minimize the burden of an infectious disease spread and to delay a possible outbreak.…”

SIRS Model of Passengers’ Panic Propagation under Self-Organization Circumstance in the Subway Emergency

“…Moreno et al [38,39] confirmed that there exist a certain number of infected nodes in the end, even if the initial infection is very low by applying the SIR model. Li et al [40] believed that, in real life, there are some viruses that cannot be immune for all life and built a complex heterogeneous network SIRS epidemic model to a more realistic portrayal of the spread of infection. Based on this work, Zhao et al [24,26,39] applied the epidemic model to the study of spread of rumors issues.…”

“…In the study of the propagation of the disease, taking into account the nonuniform interaction between nodes, Dybiec [23] extended the classical SIR model. Sekiguchi et al [40,42,43] studied the distributed delay characteristics of infectious diseases in the model. Tchuenche et al [44][45][46][47] believed that the total population is changing in real life due to the birth and death rates.…”

Dynamics in a Lotka-Volterra Predator-Prey Model with Time-Varying Delays

“…Teng et al [31] addressed the permanence criteria for delayed discrete nonautonomous-species Kolmogorov systems. For more research on the permanence behavior of predator-prey models, one can see [32][33][34][35][36][37][38][39][40].…”