Analysis of SI models with multiple interacting populations using subpopulations
Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smalle...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2014-11-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.135 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590153107898368 |
|---|---|
| author | Evelyn K. Thomas Katharine F. Gurski Kathleen A. Hoffman |
| author_facet | Evelyn K. Thomas Katharine F. Gurski Kathleen A. Hoffman |
| author_sort | Evelyn K. Thomas |
| collection | DOAJ |
| description | Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smaller subsystems and captures theinteractions between the smaller systems as external forces using an approximate model. We bound the basic reproductive numbers of the full system in terms of the basic reproductive numbers of the smaller systems and use the alternate model to provide approximations for the endemic equilibrium. In addition to creating algebraically tractable reproductive numbers and endemic equilibria, we can demonstrate the influence of the interactions between subpopulations on the basic reproductive number of the full system. The focus of this paper is to provide analytical tools to help guide public health decisions with limited intervention resources. |
| format | Article |
| id | doaj-art-d3488caf5b5e4ea7af2ae56b89b0b576 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-d3488caf5b5e4ea7af2ae56b89b0b5762025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-0112113516110.3934/mbe.2015.12.135Analysis of SI models with multiple interacting populations using subpopulationsEvelyn K. Thomas0Katharine F. Gurski1Kathleen A. Hoffman2Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250Department of Mathematics, Howard University, Washington, DC 20059Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21250Computing endemic equilibria and basic reproductive numbers for systems of differential equations describing epidemiological systems with multiple connections between subpopulations is often algebraically intractable. We present an alternative method which deconstructs the larger system into smaller subsystems and captures theinteractions between the smaller systems as external forces using an approximate model. We bound the basic reproductive numbers of the full system in terms of the basic reproductive numbers of the smaller systems and use the alternate model to provide approximations for the endemic equilibrium. In addition to creating algebraically tractable reproductive numbers and endemic equilibria, we can demonstrate the influence of the interactions between subpopulations on the basic reproductive number of the full system. The focus of this paper is to provide analytical tools to help guide public health decisions with limited intervention resources.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.135si modelreproductive numberstabilitycompartmental modelspread of hiv. |
| spellingShingle | Evelyn K. Thomas Katharine F. Gurski Kathleen A. Hoffman Analysis of SI models with multiple interacting populations using subpopulations Mathematical Biosciences and Engineering si model reproductive number stability compartmental model spread of hiv. |
| title | Analysis of SI models with multiple interacting populations using subpopulations |
| title_full | Analysis of SI models with multiple interacting populations using subpopulations |
| title_fullStr | Analysis of SI models with multiple interacting populations using subpopulations |
| title_full_unstemmed | Analysis of SI models with multiple interacting populations using subpopulations |
| title_short | Analysis of SI models with multiple interacting populations using subpopulations |
| title_sort | analysis of si models with multiple interacting populations using subpopulations |
| topic | si model reproductive number stability compartmental model spread of hiv. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.135 |
| work_keys_str_mv | AT evelynkthomas analysisofsimodelswithmultipleinteractingpopulationsusingsubpopulations AT katharinefgurski analysisofsimodelswithmultipleinteractingpopulationsusingsubpopulations AT kathleenahoffman analysisofsimodelswithmultipleinteractingpopulationsusingsubpopulations |