Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis
Abstract In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard–Lindelöf criteria we have proved th...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-01-01
|
| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-51670-y |
| _version_ | 1797350008805130240 |
|---|---|
| author | Shewafera Wondimagegnhu Teklu Abebe Addise Meshesha Saif Ullah |
| author_facet | Shewafera Wondimagegnhu Teklu Abebe Addise Meshesha Saif Ullah |
| author_sort | Shewafera Wondimagegnhu Teklu |
| collection | DOAJ |
| description | Abstract In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard–Lindelöf criteria we have proved the model solutions' existence and uniqueness, using the next generation matrix approach we calculated the model basic reproduction number, we computed the model equilibrium points and investigated their stabilities, using the three time-dependent control variables (prevention measure, non-inflammatory infection treatment measure, and inflammatory infection treatment measure) and from the formulated fractional order model we re-formulated the fractional order optimal control problem. The necessary optimality conditions for the Tinea capitis fractional order optimal control problem and the existence of optimal control strategies are derived and presented by using Pontryagin’s Maximum Principle. Also, the study carried out the sensitivity and numerical analysis to investigate the most sensitive parameters and to verify the qualitative analysis results. Finally, we performed the cost-effective analysis to investigate the most cost-effective measures from the possible proposed control measures, and from the findings we can suggest that implementing prevention measures only is the most cost-effective control measure that stakeholders should consider. |
| first_indexed | 2024-03-08T12:38:35Z |
| format | Article |
| id | doaj.art-9332dd3ee32048438bf31174319e87da |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-08T12:38:35Z |
| publishDate | 2024-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-9332dd3ee32048438bf31174319e87da2024-01-21T12:16:53ZengNature PortfolioScientific Reports2045-23222024-01-0114112310.1038/s41598-024-51670-yAnalysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysisShewafera Wondimagegnhu Teklu0Abebe Addise Meshesha1Saif Ullah2Department of Mathematics, College of Natural and Computational Sciences, Debre Berhan UniversityDepartment of Surgery, College of Health Science, Debre Berhan UniversityDepartment of Mathematics, University of PeshawarAbstract In this study, we have formulated and analyzed the Tinea capitis infection Caputo fractional order model by implementing three time-dependent control measures. In the qualitative analysis part, we investigated the following: by using the well-known Picard–Lindelöf criteria we have proved the model solutions' existence and uniqueness, using the next generation matrix approach we calculated the model basic reproduction number, we computed the model equilibrium points and investigated their stabilities, using the three time-dependent control variables (prevention measure, non-inflammatory infection treatment measure, and inflammatory infection treatment measure) and from the formulated fractional order model we re-formulated the fractional order optimal control problem. The necessary optimality conditions for the Tinea capitis fractional order optimal control problem and the existence of optimal control strategies are derived and presented by using Pontryagin’s Maximum Principle. Also, the study carried out the sensitivity and numerical analysis to investigate the most sensitive parameters and to verify the qualitative analysis results. Finally, we performed the cost-effective analysis to investigate the most cost-effective measures from the possible proposed control measures, and from the findings we can suggest that implementing prevention measures only is the most cost-effective control measure that stakeholders should consider.https://doi.org/10.1038/s41598-024-51670-y |
| spellingShingle | Shewafera Wondimagegnhu Teklu Abebe Addise Meshesha Saif Ullah Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis Scientific Reports |
| title | Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis |
| title_full | Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis |
| title_fullStr | Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis |
| title_full_unstemmed | Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis |
| title_short | Analysis of optimal control strategies on the fungal Tinea capitis infection fractional order model with cost-effective analysis |
| title_sort | analysis of optimal control strategies on the fungal tinea capitis infection fractional order model with cost effective analysis |
| url | https://doi.org/10.1038/s41598-024-51670-y |
| work_keys_str_mv | AT shewaferawondimagegnhuteklu analysisofoptimalcontrolstrategiesonthefungaltineacapitisinfectionfractionalordermodelwithcosteffectiveanalysis AT abebeaddisemeshesha analysisofoptimalcontrolstrategiesonthefungaltineacapitisinfectionfractionalordermodelwithcosteffectiveanalysis AT saifullah analysisofoptimalcontrolstrategiesonthefungaltineacapitisinfectionfractionalordermodelwithcosteffectiveanalysis |