The effect of local prevention in an SIS model with diffusion

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.

Original languageEnglish
Pages (from-to)739-746
Number of pages8
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume4
Issue number3
Publication statusPublished - Aug 2004

Fingerprint

SIS Model
Infection
Infectious Diseases
Population Model
Rectangle
Extinction
Contact
Partial
Necessary Conditions

Keywords

  • Epidemics
  • Reaction-diffusion system
  • Spatial heterogenuity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics

Cite this

The effect of local prevention in an SIS model with diffusion. / Sasaki, Toru.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 4, No. 3, 08.2004, p. 739-746.

Research output: Contribution to journalArticle

@article{87e0e94d7eb246fb9c88b04d84b6a9a7,
title = "The effect of local prevention in an SIS model with diffusion",
abstract = "The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.",
keywords = "Epidemics, Reaction-diffusion system, Spatial heterogenuity",
author = "Toru Sasaki",
year = "2004",
month = "8",
language = "English",
volume = "4",
pages = "739--746",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "3",

}

TY - JOUR

T1 - The effect of local prevention in an SIS model with diffusion

AU - Sasaki, Toru

PY - 2004/8

Y1 - 2004/8

N2 - The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.

AB - The effect of spatially partial prevention of infectious disease is considered as an application of population models in inhomogeneous environments. The area is divided into two ractangles, and the local contact rate between infectives and susceptibles is sufficiently reduced in one rectangle. The dynamics of the infection considered here is that described by an SIS model with diffusion. Then the problem can be reduced to a Fisher type equation, which has been fully studied by many authors, under some conditions. The steady states of the linearized equation are considered, and a Nagylaki type result for predicting whether the infection will become extinct over time or not is obtained. This result leads to some necessary conditions for the extinction of the infection.

KW - Epidemics

KW - Reaction-diffusion system

KW - Spatial heterogenuity

UR - http://www.scopus.com/inward/record.url?scp=2942670844&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942670844&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 739

EP - 746

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 3

ER -