Epidemic characteristics of two classic models and the dependence on the initial conditions
The epidemic characteristics, including the epidemic final size, peak, andturning point, of two classical SIR models with disease-induced death are investigated when asmall initial value of the infective population is released. The models have mass-action (i.e.bilinear), or density dependent (i.e. s...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2016-06-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016027 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590037810675712 |
|---|---|
| author | Jianquan Li Yiqun Li Yali Yang |
| author_facet | Jianquan Li Yiqun Li Yali Yang |
| author_sort | Jianquan Li |
| collection | DOAJ |
| description | The epidemic characteristics, including the epidemic final size, peak, andturning point, of two classical SIR models with disease-induced death are investigated when asmall initial value of the infective population is released. The models have mass-action (i.e.bilinear), or density dependent (i.e. standard) incidence, respectively. For the two models, theconditions that determining whether the related epidemic characteristics of an epidemicoutbreak appear are explicitly determine by rigorous mathematical analysis. The dependenceof the epidemic final size on the initial values of the infective class is demonstrated. The peak,turning point (if it exists) and the corresponding time are found. The obtained results suggestthat their basic reproduction numbers are one factor determining the epidemic characteristics,but not the only one. The characteristics of the two models depend on the initial values andproportions of various compartments as well. At last, the similarities and differences of theepidemic characteristics between the two models are discussed. |
| format | Article |
| id | doaj-art-3a383adb76dc4ff999a07a1dcba7480f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3a383adb76dc4ff999a07a1dcba7480f2025-01-24T02:36:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-06-01135999101010.3934/mbe.2016027Epidemic characteristics of two classic models and the dependence on the initial conditionsJianquan Li0Yiqun Li1Yali Yang2Science College, Air Force Engineering University, Xi'an 710051Science College, Air Force Engineering University, Xi'an 710051College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062The epidemic characteristics, including the epidemic final size, peak, andturning point, of two classical SIR models with disease-induced death are investigated when asmall initial value of the infective population is released. The models have mass-action (i.e.bilinear), or density dependent (i.e. standard) incidence, respectively. For the two models, theconditions that determining whether the related epidemic characteristics of an epidemicoutbreak appear are explicitly determine by rigorous mathematical analysis. The dependenceof the epidemic final size on the initial values of the infective class is demonstrated. The peak,turning point (if it exists) and the corresponding time are found. The obtained results suggestthat their basic reproduction numbers are one factor determining the epidemic characteristics,but not the only one. The characteristics of the two models depend on the initial values andproportions of various compartments as well. At last, the similarities and differences of theepidemic characteristics between the two models are discussed.https://www.aimspress.com/article/doi/10.3934/mbe.2016027epidemic modelspeakturning point.epidemic final size |
| spellingShingle | Jianquan Li Yiqun Li Yali Yang Epidemic characteristics of two classic models and the dependence on the initial conditions Mathematical Biosciences and Engineering epidemic models peak turning point. epidemic final size |
| title | Epidemic characteristics of two classic models and the dependence on the initial conditions |
| title_full | Epidemic characteristics of two classic models and the dependence on the initial conditions |
| title_fullStr | Epidemic characteristics of two classic models and the dependence on the initial conditions |
| title_full_unstemmed | Epidemic characteristics of two classic models and the dependence on the initial conditions |
| title_short | Epidemic characteristics of two classic models and the dependence on the initial conditions |
| title_sort | epidemic characteristics of two classic models and the dependence on the initial conditions |
| topic | epidemic models peak turning point. epidemic final size |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016027 |
| work_keys_str_mv | AT jianquanli epidemiccharacteristicsoftwoclassicmodelsandthedependenceontheinitialconditions AT yiqunli epidemiccharacteristicsoftwoclassicmodelsandthedependenceontheinitialconditions AT yaliyang epidemiccharacteristicsoftwoclassicmodelsandthedependenceontheinitialconditions |