Different types of backward bifurcations due to density-dependent treatments
A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-07-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1651 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590093687193600 |
|---|---|
| author | Baojun Song Wen Du Jie Lou |
| author_facet | Baojun Song Wen Du Jie Lou |
| author_sort | Baojun Song |
| collection | DOAJ |
| description | A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads to bistable dynamics. However, this study finds that finds that bistability may not be an option at all; the disease-free equilibrium could be globally stable when there is a backward bifurcation. Furthermore, when a backward bifurcation occurs, the fashion of bistability could be the coexistence of either dual stable equilibria or the disease-free equilibrium and a stable limit cycle. We also extend the formula for mean infection period from density-independent treatments to density-dependent ones. Finally, the modeling results are applied to the transmission of gonorrhea in China, suggesting that these gonorrhea patients may not seek medical treatments in a timely manner. |
| format | Article |
| id | doaj-art-05e032581764493989e248345b5253fd |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-05e032581764493989e248345b5253fd2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61651166810.3934/mbe.2013.10.1651Different types of backward bifurcations due to density-dependent treatmentsBaojun Song0Wen Du1Jie Lou2Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads to bistable dynamics. However, this study finds that finds that bistability may not be an option at all; the disease-free equilibrium could be globally stable when there is a backward bifurcation. Furthermore, when a backward bifurcation occurs, the fashion of bistability could be the coexistence of either dual stable equilibria or the disease-free equilibrium and a stable limit cycle. We also extend the formula for mean infection period from density-independent treatments to density-dependent ones. Finally, the modeling results are applied to the transmission of gonorrhea in China, suggesting that these gonorrhea patients may not seek medical treatments in a timely manner.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1651density-dependentgonorrhea.treatmentbifurcation |
| spellingShingle | Baojun Song Wen Du Jie Lou Different types of backward bifurcations due to density-dependent treatments Mathematical Biosciences and Engineering density-dependent gonorrhea. treatment bifurcation |
| title | Different types of backward bifurcations due to density-dependent treatments |
| title_full | Different types of backward bifurcations due to density-dependent treatments |
| title_fullStr | Different types of backward bifurcations due to density-dependent treatments |
| title_full_unstemmed | Different types of backward bifurcations due to density-dependent treatments |
| title_short | Different types of backward bifurcations due to density-dependent treatments |
| title_sort | different types of backward bifurcations due to density dependent treatments |
| topic | density-dependent gonorrhea. treatment bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1651 |
| work_keys_str_mv | AT baojunsong differenttypesofbackwardbifurcationsduetodensitydependenttreatments AT wendu differenttypesofbackwardbifurcationsduetodensitydependenttreatments AT jielou differenttypesofbackwardbifurcationsduetodensitydependenttreatments |