Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study
Abstract In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of differential equations the model is analyzed qualitatively. The equilibrium points i...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-12-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1877-3 |
| _version_ | 1811269674612031488 |
|---|---|
| author | Priti Kumar Roy Shubhankar Saha |
| author_facet | Priti Kumar Roy Shubhankar Saha |
| author_sort | Priti Kumar Roy |
| collection | DOAJ |
| description | Abstract In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of differential equations the model is analyzed qualitatively. The equilibrium points in the local and global stability proof are found to be stable under certain conditions. Further, we use Pontryagin’s Minimum Principle in the time-dependent constant control case to derive necessary conditions for the optimal control of the disease. Sensitivity analysis is also performed to check the robustness of the model with respect to small changes in parametric values of the system. In order to predict the long term dynamics of the disease, projections are made. These studies reveal that HIV incidence could be substantially reduced by improving the test-and-treat strategy and implication of media awareness. |
| first_indexed | 2024-04-12T21:46:26Z |
| format | Article |
| id | doaj.art-4c932fc7aff641d384e490f38a24c54c |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T21:46:26Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4c932fc7aff641d384e490f38a24c54c2022-12-22T03:15:37ZengSpringerOpenAdvances in Difference Equations1687-18472018-12-012018112010.1186/s13662-018-1877-3Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical studyPriti Kumar Roy0Shubhankar Saha1Department of Mathematics, Jadavpur UniversityDepartment of Mathematics, Jadavpur UniversityAbstract In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of differential equations the model is analyzed qualitatively. The equilibrium points in the local and global stability proof are found to be stable under certain conditions. Further, we use Pontryagin’s Minimum Principle in the time-dependent constant control case to derive necessary conditions for the optimal control of the disease. Sensitivity analysis is also performed to check the robustness of the model with respect to small changes in parametric values of the system. In order to predict the long term dynamics of the disease, projections are made. These studies reveal that HIV incidence could be substantially reduced by improving the test-and-treat strategy and implication of media awareness.http://link.springer.com/article/10.1186/s13662-018-1877-3Epidemic modelHIVDrug-dosingAwareness programsBasic reproductive numberLocal & global stability |
| spellingShingle | Priti Kumar Roy Shubhankar Saha Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study Advances in Difference Equations Epidemic model HIV Drug-dosing Awareness programs Basic reproductive number Local & global stability |
| title | Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study |
| title_full | Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study |
| title_fullStr | Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study |
| title_full_unstemmed | Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study |
| title_short | Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study |
| title_sort | predicting the effectiveness of drug interventions with hiv counseling testing hct on the spread of hiv aids a theoretical study |
| topic | Epidemic model HIV Drug-dosing Awareness programs Basic reproductive number Local & global stability |
| url | http://link.springer.com/article/10.1186/s13662-018-1877-3 |
| work_keys_str_mv | AT pritikumarroy predictingtheeffectivenessofdruginterventionswithhivcounselingtestinghctonthespreadofhivaidsatheoreticalstudy AT shubhankarsaha predictingtheeffectivenessofdruginterventionswithhivcounselingtestinghctonthespreadofhivaidsatheoreticalstudy |