Global stability of an SVIR model with age of vaccination

In this paper, an epidemiological model with age of infection and disease relapse is investigated. The basic reproduction number for the model is identified, and it is shown to be a sharp threshold to completely determine the global dynamics of the model. By analysing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By means of suitable Lyapunov functionals and LaSalle's invariance principle, it is verified that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable, and hence the disease dies out; if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable and the disease becomes endemic.

Section: Introductionmentioning

confidence: 99%

Global dynamics of an epidemiological model with age of infection and disease relapse

2017

“…A Lyapunov functional was used in [28] to show that the endemic steady state is globally stable. Recently, much attention has been paid to the modelling and analysis on infectious disease dynamics with age dependence (see, for example, [8,13,[15][16][17]27,36]).…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of a tuberculosis model with fast and slow progression and age-dependent latency and infection

Yang

Tian

et al. 2019

In this paper, a mathematical model describing tuberculosis transmission with fast and slow progression and age-dependent latency and infection is investigated. It is assumed in the model that infected individuals can develop tuberculosis by either of two pathogenic mechanisms: direct progression or endogenous reactivation. It is shown that the transmission dynamics of the disease is fully determined by the basic reproduction number. By analyzing corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state of the model is established. By using the persistence theory for infinite dimensional system, it is proved that the system is uniformly persistent when the basic reproduction number is greater than unity. By constructing suitable Lyapunov functionals and using LaSalle's invariance principle, it is verified that the global dynamics of the system is completely determined by the basic reproduction number.

“…Xiang et al [33] dealt with the global property of a drinking model with public health educational campaigns and concluded that the public health educational campaigns of drinking individuals could slow down the drinking dynamics. For other related alcoholism models or epidemic models, we refer to [1,3,[6][7][8]11,13,14,16,[21][22][23]28,31,39,40].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity

Hong

Cui

Huo

2019

A more realistic alcoholism model on scale-free networks with demographic and nonlinear infectivity is introduced in this paper. The basic reproduction number R 0 is derived from the next-generation method. Global stability of the alcohol-free equilibrium is obtained. The persistence of our model is also derived. Furthermore, the SAITS model with nonlinear infectivity is also investigated. Stability of all the equilibria and persistence are also obtained. Some numerical simulations are also presented to verify and extend our theoretical results.