The analysis of the SIRS alcoholism models with relapse on weighted networks

Two SIRS alcoholism models with relapse on networks with fixed and adaptive weight are introduced. The spread of alcoholism threshold R 0 is calculated by the next generation matrix method. For the model with fixed weight, we prove that when R 0 < 1 , the alcohol free equilibrium is globally asym...

Full description

Saved in:
Bibliographic Details
Published in:SpringerPlus 2016-06, Vol.5 (1), p.722-722, Article 722
Main Authors: Huo, Hai-Feng, Liu, Ying-Ping
Format: Article
Language:English
Subjects:
Applied Mathematics
Humanities and Social Sciences
multidisciplinary
Science
Science (multidisciplinary)
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Two SIRS alcoholism models with relapse on networks with fixed and adaptive weight are introduced. The spread of alcoholism threshold R 0 is calculated by the next generation matrix method. For the model with fixed weight, we prove that when R 0 < 1 , the alcohol free equilibrium is globally asymptotically stable, then the drinking crowd gradually disappear. When R 0 > 1 , the alcoholism equilibrium is global attractivity, then the density of alcoholics will remain in a stable value. For the model with adaptive weight, we only make some numerical simulations. We also give two effective strategies. Our results show that the treatment of recuperator for stopping relapsing and preventing the susceptible people to drink are two effective measures to eliminate alcoholism problem, and preventing the susceptible people to drink is more effective when the proportion of recuperator to accept treatment is equal to the proportion of susceptible people to refuse drinking alcohol.
ISSN:2193-1801
2193-1801
DOI:10.1186/s40064-016-2308-0