Global dynamics of delay epidemic models with nonlinear incidence rate and relapse

Impact of heterogeneity on the dynamics of an SEIR epidemic model

“…Epidemic models such as (2.6) with an arbitrarily distributed exposed stage have been studied in the literature; see, for example, [8,14,15]. Recently, a model of this type, but including the possibility of disease relapse, has been proposed in [40,43] to study the transmission and spread of some infectious disease such as herpes, and its global dynamics have been completely investigated in [31,40]. The model in [31,40,43] can be regarded as a generalization of our model (2.6), and thus the stability results there can be immediately applied to our model (2.6) by setting the relapse rate to zero.…”

“…Recently, a model of this type, but including the possibility of disease relapse, has been proposed in [40,43] to study the transmission and spread of some infectious disease such as herpes, and its global dynamics have been completely investigated in [31,40]. The model in [31,40,43] can be regarded as a generalization of our model (2.6), and thus the stability results there can be immediately applied to our model (2.6) by setting the relapse rate to zero. We outline some of their results in the following; their proofs and more detailed study can be found in [31,40].…”

“…The model in [31,40,43] can be regarded as a generalization of our model (2.6), and thus the stability results there can be immediately applied to our model (2.6) by setting the relapse rate to zero. We outline some of their results in the following; their proofs and more detailed study can be found in [31,40]. The existence, uniqueness, and continuity of solutions of system (2.6) follow from the standard theory of Volterra integro-differential equations, see, for example, [36, p.338].…”

“…Proposition 2.1 (van den Driessche et al [40], Liu et al [31]). The following results hold for system (2.6).…”

“…In order to study the dynamical behavior of (2.6) when R 0 > 1, the following limiting system (see [36, p.176]) has been studied as a special case in [31]:…”