Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination

Global stability in a tuberculosis model of imperfect treatment with age-dependent latency and relapse

“…Recently, Wang et al [24]- [27] considered the global stability of nonlinear agestructured models, Liu et al [17] introduced age-dependent latency and relapse into an SEIR epidemic model and the local stability and global stability of equilibria are obtained by analyzing the corresponding characteristic equations and constructing the proper Volterra-type Lyapunov functionals, respectively. Wang et al [28] proposed an SV EIR epidemic model with media impact, age-dependent vaccination and latency, and discussed the global dynamics of the age-structure model.…”

“…Substituting (27) and (28) into (25) and solving (25) gives Thus, we know (29) has a unique real root λ * . Obviously,…”

Dynamical behavior of a higher order stochastically perturbed SIRI epidemic model with relapse and media coverage

“…Mass media plays an important role in propagating the nature and the cause of assorted deadly diseases such as respiratory disease, hepatitis diseases, human immunodeficiency syndrome (HIV), Avian influenza A (H7N9), human tuberculosis (TB), acquired immunodeficiency syndrome (AIDS), severe acute respiratory syndrome (SARS), Ebola virus disease (EVD), etc. Recently, numerous mathematical models have been developed to study the influence of media coverage on the dynamics of infection disease [4] , [5] , [6] , [7] , [8] , [9] , [10] . Caraballo et al.…”

“…Note that this model appears when we assume that the parameters μ 1 , μ 2 and μ 3 are disturbed by some stochastic perturbation in each equation, that is to say, we replace μ 1 , μ 2 and μ 3 by in each equation, respectively. A large number of scholars concentrate only on media coverage and they have not considered media coverage with relapse and higher order perturbation [4] , [5] , [6] , [7] , [8] , [9] , [30] . Yet another group of scholars focus only on higher order perturbation [19] , [28] , [31] , [32] , [33] .…”

Optimal control strategy of SEIR endemic model with continuous age‐structure in the exposed and infectious classes

“…Firstly, one can easily apply the proposed method to a number of age‐structured optimal control problems. Secondly, since most of the age‐structured models include the vaccinated and treated population as separate compartments such as in the works of Wang et al and Wang et al, it will reduce the mathematical complexities arising in considering vaccination and treated people as separate classes. It will help authorities working in health sector to develop an effective strategy for control and inhibition of infection.…”