Dynamics of a delayed epidemic model with non-monotonic incidence rate

Global stability of a delayed SIRS epidemic model with a non-monotonic incidence rate

“…In this paper, for the basic reproduction number R 0 > 1 of system (1.1), applying both of new monotone iterative techniques which are improved versions of Xu and Ma [8] (see also Xu and Ma [7]), and Lyapunov functional techniques in McCluskey [5], we obtain two types of sufficient conditions for the global asymptotic stability of endemic equilibrium E * of system (1.1) which is a partial answer to the open problem in Huo and Ma [4] and also Yang and Xiao [9]. The first main theorem is established by applying new monotone iterative techniques (see Lemma 3.4 in Section 3) such that the each lower and upper bounds for each S(t), I(t) and R(t) of system (1.1) for a sufficiently large t 0, approach to an endemic steady state by simple conditions of contractive convergence for suitable monotone iterations (see (3.9)).…”

“…We solve the open question for an example offered by Huo and Ma [4,Example], because we can see that this example ,…”

“…If R 0 > 1, then system (1.1) has a unique endemic equilibrium E * = (S * , I * , R * ) (see Huo and Ma [4]), where…”

“…Many authors have proposed various kinds of epidemic models to understand the mechanism of disease transmission (see [1][2][3][4][5][6][7][8] and references therein).…”

Analysis of stability and bifurcation for an SEIR epidemic model with saturated recovery rate

“…After that, a tremendous number of models have been formulated, analyzed and applied to a variety of infectious diseases qualitatively and quantitatively. Mathematical models have become important tools in analyzing the spread and control of infectious diseases [4][5][6]. Furthermore, mathematical models have been used in comparing, planning, implementing, evaluating, and optimizing various detection, prevention, therapy, and control programs [7][8][9].…”