A Consistent Discrete Version of a Nonautonomous SIRVS Model
A family of discrete nonautonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens nonstandard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. Concern...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2018-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/8152032 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832551643958214656 |
|---|---|
| author | Joaquim Mateus César M. Silva S. Vaz |
| author_facet | Joaquim Mateus César M. Silva S. Vaz |
| author_sort | Joaquim Mateus |
| collection | DOAJ |
| description | A family of discrete nonautonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens nonstandard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. Concerning extinction and persistence, the consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (permanence) for the continuous model, we also have extinction (permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data. |
| format | Article |
| id | doaj-art-f339143589e74ec8a964582c0ac65fad |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f339143589e74ec8a964582c0ac65fad2025-02-03T06:01:02ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/81520328152032A Consistent Discrete Version of a Nonautonomous SIRVS ModelJoaquim Mateus0César M. Silva1S. Vaz2Unidade de Investigação para o Desenvolvimento do Interior (UDI), Instituto Politécnico da Guarda, 6300-559 Guarda, PortugalCentro de Matemática e Aplicações e Departamento de Matemática, Universidade da Beira Interior, 6201-001 Covilhã, PortugalCentro de Matemática e Aplicações e Departamento de Matemática, Universidade da Beira Interior, 6201-001 Covilhã, PortugalA family of discrete nonautonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens nonstandard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. Concerning extinction and persistence, the consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (permanence) for the continuous model, we also have extinction (permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data.http://dx.doi.org/10.1155/2018/8152032 |
| spellingShingle | Joaquim Mateus César M. Silva S. Vaz A Consistent Discrete Version of a Nonautonomous SIRVS Model Discrete Dynamics in Nature and Society |
| title | A Consistent Discrete Version of a Nonautonomous SIRVS Model |
| title_full | A Consistent Discrete Version of a Nonautonomous SIRVS Model |
| title_fullStr | A Consistent Discrete Version of a Nonautonomous SIRVS Model |
| title_full_unstemmed | A Consistent Discrete Version of a Nonautonomous SIRVS Model |
| title_short | A Consistent Discrete Version of a Nonautonomous SIRVS Model |
| title_sort | consistent discrete version of a nonautonomous sirvs model |
| url | http://dx.doi.org/10.1155/2018/8152032 |
| work_keys_str_mv | AT joaquimmateus aconsistentdiscreteversionofanonautonomoussirvsmodel AT cesarmsilva aconsistentdiscreteversionofanonautonomoussirvsmodel AT svaz aconsistentdiscreteversionofanonautonomoussirvsmodel AT joaquimmateus consistentdiscreteversionofanonautonomoussirvsmodel AT cesarmsilva consistentdiscreteversionofanonautonomoussirvsmodel AT svaz consistentdiscreteversionofanonautonomoussirvsmodel |