scholarly journals Numerical approximation of the basic reproduction number for a class of age-structured epidemic models

2017 ◽  
Vol 73 ◽  
pp. 106-112 ◽  
Author(s):  
Toshikazu Kuniya
Keyword(s):  
Basic Reproduction Number ◽  
Numerical Approximation ◽  
Reproduction Number ◽  
Epidemic Models ◽  
Age Structured ◽  
The Basic Reproduction Number

An age-structured epidemic model with waning immunity and general nonlinear incidence rate

2018 ◽  
Vol 11 (05) ◽  
pp. 1850069 ◽  
Author(s):  
Xia Wang ◽  
Ying Zhang ◽  
Xinyu Song
Keyword(s):  
Steady State ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Waning Immunity ◽  
Age Structured ◽  
The Basic Reproduction Number

In this paper, a susceptible-vaccinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fluctuation lemma and the approach of Lyapunov functionals, we establish a threshold dynamics completely determined by the basic reproduction number. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, and otherwise the endemic steady state is globally asymptotically stable.

scholarly journals Epidemic management with admissible and robust invariant sets

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257598
Author(s):  
Willem Esterhuizen ◽  
Jean Lévine ◽  
Stefan Streif
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Intervention Strategies ◽  
Epidemic Models ◽  
Invariant Sets ◽  
Social Distancing ◽  
The Basic Reproduction Number

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.

ANALYSIS OF AN AGE-STRUCTURED HIV-1 INFECTION MODEL WITH LOGISTIC TARGET CELL GROWTH

2020 ◽  
Vol 28 (04) ◽  
pp. 927-944
Author(s):  
HUIJUAN LIU ◽  
FEI XU ◽  
JIA-FANG ZHANG
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Age Structured ◽  
Hiv 1 ◽  
The Basic Reproduction Number

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

Global threshold dynamics of an age structured alcoholism model

2021 ◽  
pp. 2150013
Author(s):  
Soufiane Bentout ◽  
Salih Djilali ◽  
Abdenasser Chekroun
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Threshold Dynamics ◽  
Global Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Threshold ◽  
Age Structured ◽  
The Basic Reproduction Number ◽  
Proper Strategy

We consider in this research an age-structured alcoholism model. The global behavior of the model is investigated. It is proved that the system has a threshold dynamics in terms of the basic reproduction number (BRN), where we obtained that alcohol-free equilibrium (AFE) is globally asymptotically stable (GAS) in the case [Formula: see text], but for [Formula: see text] we found that the system persists and the nontrivial equilibrium (EE) is GAS. Furthermore, the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated, which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations. The obtained mathematical results are tested numerically next to its biological relevance.

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