Steady State Stability Analysis of a Chagas Disease Model
Chagas disease is caused by the parasite Trypanosoma cruzi, which is spread primarily by domestic vectors in the reduviid family. This work presents a model of the dynamics of Chagas disease in a rural village. The model consists of a nonlinear delay logistic-type differential equation for the pop...
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| Format: | Article |
| Language: | English |
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Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2014-06-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/184 |
| _version_ | 1797721169665720320 |
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| author | Daniel James Coffield Jr. Anna Maria Spagnuolo |
| author_facet | Daniel James Coffield Jr. Anna Maria Spagnuolo |
| author_sort | Daniel James Coffield Jr. |
| collection | DOAJ |
| description | Chagas disease is caused by the parasite Trypanosoma cruzi, which is spread primarily by domestic vectors in the reduviid family. This work presents a model of the dynamics of Chagas disease in a rural village. The model consists of a nonlinear delay logistic-type differential equation for the population of total vectors and three nonlinear differential equations for the populations of infected vectors, infected humans, and infected domestic mammals. Steady state solutions for the model are derived and analyzed. Stability numbers are provided with necessary and sufficient conditions for local asymptotic stability and partial results for global asymptotic stability. Numerical simulation results are presented, verifying the theoretical results. |
| first_indexed | 2024-03-12T09:30:02Z |
| format | Article |
| id | doaj.art-fd59487230ff4dc28e3dc965c827b431 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T09:30:02Z |
| publishDate | 2014-06-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-fd59487230ff4dc28e3dc965c827b4312023-09-02T13:55:34ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182014-06-013110.11145/j.biomath.2014.05.261234Steady State Stability Analysis of a Chagas Disease ModelDaniel James Coffield Jr.0Anna Maria Spagnuolo1University of Michigan-FlintOakland UniversityChagas disease is caused by the parasite Trypanosoma cruzi, which is spread primarily by domestic vectors in the reduviid family. This work presents a model of the dynamics of Chagas disease in a rural village. The model consists of a nonlinear delay logistic-type differential equation for the population of total vectors and three nonlinear differential equations for the populations of infected vectors, infected humans, and infected domestic mammals. Steady state solutions for the model are derived and analyzed. Stability numbers are provided with necessary and sufficient conditions for local asymptotic stability and partial results for global asymptotic stability. Numerical simulation results are presented, verifying the theoretical results.http://www.biomathforum.org/biomath/index.php/biomath/article/view/184Chagas diseaseepidemic dynamicsdelay logistic modelsteady statesnonlinear dynamical system |
| spellingShingle | Daniel James Coffield Jr. Anna Maria Spagnuolo Steady State Stability Analysis of a Chagas Disease Model Biomath Chagas disease epidemic dynamics delay logistic model steady states nonlinear dynamical system |
| title | Steady State Stability Analysis of a Chagas Disease Model |
| title_full | Steady State Stability Analysis of a Chagas Disease Model |
| title_fullStr | Steady State Stability Analysis of a Chagas Disease Model |
| title_full_unstemmed | Steady State Stability Analysis of a Chagas Disease Model |
| title_short | Steady State Stability Analysis of a Chagas Disease Model |
| title_sort | steady state stability analysis of a chagas disease model |
| topic | Chagas disease epidemic dynamics delay logistic model steady states nonlinear dynamical system |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/184 |
| work_keys_str_mv | AT danieljamescoffieldjr steadystatestabilityanalysisofachagasdiseasemodel AT annamariaspagnuolo steadystatestabilityanalysisofachagasdiseasemodel |