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

2019 ◽  
Vol 13 (1) ◽  
pp. 675-705
Author(s):  
Rui Xu ◽  
Junyuan Yang ◽  
Xiaohong Tian ◽  
Jiazhe Lin
Keyword(s):  
Global Dynamics ◽  
Tuberculosis Model ◽  
Slow Progression ◽  
Age Dependent

GLOBAL DYNAMICS OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH AGE-DEPENDENT LATENCY AND ACTIVE INFECTION

2019 ◽  
Vol 27 (04) ◽  
pp. 503-530
Author(s):  
RUI XU ◽  
NING BAI ◽  
XIAOHONG TIAN
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Feasible Region ◽  
Global Dynamics ◽  
Active Infection ◽  
Age Dependent ◽  
Latent Tb ◽  
Latent Tb Infection ◽  
The Basic Reproduction Number

In this paper, mathematical analysis is carried out for a mathematical model of Tuberculosis (TB) with age-dependent latency and active infection. The model divides latent TB infection into two stages: an early stage of high risk of developing active TB and a late stage of lower risk for developing active TB. Infected persons initially progress through the early latent TB stage and then can either progress to active TB infection or progress to late latent TB infection. The model is formulated by incorporating the duration that an individual has spent in the stages of the early latent TB, the late latent TB and the active TB infection as variables. By constructing suitable Lyapunov functionals and using LaSalle’s invariance principle, it is shown that the global dynamics of the disease is completely determined by the basic reproduction number: if the basic reproduction number is less than unity, the TB always dies out; if the basic reproduction number is greater than unity, a unique endemic steady state exists and is globally asymptotically stable in the interior of the feasible region and therefore the TB becomes endemic. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Global Dynamics of an SVEIR Model with Age-Dependent Vaccination, Infection, and Latency

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
Rodrigue Yves M’pika Massoukou ◽  
Suares Clovis Oukouomi Noutchie ◽  
Richard Guiem
Keyword(s):  
Infectious Diseases ◽  
Differential Equations ◽  
Reproduction Number ◽  
Coupled System ◽  
Hyperbolic Partial Differential Equations ◽  
Global Dynamics ◽  
Lyapunov Functionals ◽  
Age Dependent ◽  
Induced Immunity ◽  
The Basic Reproduction Number

Vaccine-induced protection is substantial to control, prevent, and reduce the spread of infectious diseases and to get rid of infectious diseases. In this paper, we propose an SVEIR epidemic model with age-dependent vaccination, latency, and infection. The model also considers that the waning vaccine-induced immunity depends on vaccination age and the vaccinated individuals fall back to the susceptible class after losing immunity. The model is a coupled system of (hyperbolic) partial differential equations with ordinary differential equations. The global dynamics of the model is established through construction of appropriate Lyapunov functionals and application of Lasalle’s invariance principle. As a result, the global stability of the infection-free equilibrium and endemic equilibrium is obtained and is fully determined by the basic reproduction number R0.

Global stability of an age-structured SVEIR epidemic model with waning immunity, latency and relapse

2017 ◽  
Vol 10 (03) ◽  
pp. 1750038 ◽  
Author(s):  
Lili Liu ◽  
Xianning Liu
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Epidemic Model ◽  
Uniform Persistence ◽  
Global Dynamics ◽  
Sharp Threshold ◽  
Age Dependent ◽  
Waning Immunity ◽  
Age Structured ◽  
Disease Free

The global dynamics of an SVEIR epidemic model with age-dependent waning immunity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed.

GLOBAL DYNAMICS OF NONLINEAR TWO-STAGED AGE-DEPENDENT POPULATIONS

2008 ◽  
Vol 01 (04) ◽  
pp. 449-461 ◽  
Author(s):  
ZE-RONG HE
Keyword(s):  
Laplace Transforms ◽  
Evolution Process ◽  
Global Behavior ◽  
Global Dynamics ◽  
Population System ◽  
Density Dependent ◽  
Age Dependent ◽  
Asymptotic Dynamics

We investigate the global behavior for a population whose members are divided into two classes: juveniles and adults, with mortalities age- and density-dependent. Laplace transforms are used to examine the asymptotic dynamics of age profiles, which describes completely the evolution process of the nonlinear population system. Our result can be viewed as a generalization of Sharp–Lotka theorem in some nonlinear situations.

Effects of Hyperoxia on Lung Utrastructure

1970 ◽  
Vol 28 ◽  
pp. 26-27
Author(s):  
Gladys Harrison
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Light Microscopy ◽  
Oxygen Effects ◽  
Age Dependent ◽  
The Central Nervous System ◽  
The Subject ◽  
Space Age ◽  
Alveolar Septa ◽  
Extensive Damage

With the advent of the space age and the need to determine the requirements for a space cabin atmosphere, oxygen effects came into increased importance, even though these effects have been the subject of continuous research for many years. In fact, Priestly initiated oxygen research when in 1775 he published his results of isolating oxygen and described the effects of breathing it on himself and two mice, the only creatures to have had the “privilege” of breathing this “pure air”.Early studies had demonstrated the central nervous system effects at pressures above one atmosphere. Light microscopy revealed extensive damage to the lungs at one atmosphere. These changes which included perivascular and peribronchial edema, focal hemorrhage, rupture of the alveolar septa, and widespread edema, resulted in death of the animal in less than one week. The severity of the symptoms differed between species and was age dependent, with young animals being more resistant.

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