Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics
This article presents and analyzes a deterministic model for malaria transmission that incorporates infected individuals who are unaware of their infectious status (ignorant infected humans) and accounts for relapse dynamics. We explore the invariant region and positivity of the model and calculate...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-01-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2024.1487291/full |
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| author | Getahun Tadesse Haile Purnachandra Rao Koya Fekadu Mosisa Legesse |
| author_facet | Getahun Tadesse Haile Purnachandra Rao Koya Fekadu Mosisa Legesse |
| author_sort | Getahun Tadesse Haile |
| collection | DOAJ |
| description | This article presents and analyzes a deterministic model for malaria transmission that incorporates infected individuals who are unaware of their infectious status (ignorant infected humans) and accounts for relapse dynamics. We explore the invariant region and positivity of the model and calculate the effective reproduction number using the next-generation matrix method. We demonstrate the local and global stability of disease-free equilibrium points using the Routh-Hurwitz criterion and Lyapunov function, respectively. The proposed model shows that a disease-free equilibrium point is globally asymptotically stable when the basic reproduction number Re < 1. We conducted a sensitivity analysis on the effective reproduction number to identify which basic parameter most significantly influences the increase or decrease of malaria cases. This study focuses on individuals who have been treated and cured but continue to carry dormant Plasmodium parasites in their blood, which can potentially cause relapse or reinfection. Additionally, we introduce a protected compartment to carefully evaluate how preventive measures influence the spread and persistence of malaria within the population. |
| format | Article |
| id | doaj-art-e1af960d9d494145aebe905829827e24 |
| institution | Kabale University |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-e1af960d9d494145aebe905829827e242025-01-07T06:50:05ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-01-011010.3389/fams.2024.14872911487291Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamicsGetahun Tadesse HailePurnachandra Rao KoyaFekadu Mosisa LegesseThis article presents and analyzes a deterministic model for malaria transmission that incorporates infected individuals who are unaware of their infectious status (ignorant infected humans) and accounts for relapse dynamics. We explore the invariant region and positivity of the model and calculate the effective reproduction number using the next-generation matrix method. We demonstrate the local and global stability of disease-free equilibrium points using the Routh-Hurwitz criterion and Lyapunov function, respectively. The proposed model shows that a disease-free equilibrium point is globally asymptotically stable when the basic reproduction number Re < 1. We conducted a sensitivity analysis on the effective reproduction number to identify which basic parameter most significantly influences the increase or decrease of malaria cases. This study focuses on individuals who have been treated and cured but continue to carry dormant Plasmodium parasites in their blood, which can potentially cause relapse or reinfection. Additionally, we introduce a protected compartment to carefully evaluate how preventive measures influence the spread and persistence of malaria within the population.https://www.frontiersin.org/articles/10.3389/fams.2024.1487291/fullsensitivity analysiseffective reproduction numberrelapseinfected ignorantlocal stabilityglobal stability |
| spellingShingle | Getahun Tadesse Haile Purnachandra Rao Koya Fekadu Mosisa Legesse Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics Frontiers in Applied Mathematics and Statistics sensitivity analysis effective reproduction number relapse infected ignorant local stability global stability |
| title | Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| title_full | Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| title_fullStr | Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| title_full_unstemmed | Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| title_short | Sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| title_sort | sensitivity analysis of a mathematical model for malaria transmission accounting for infected ignorant humans and relapse dynamics |
| topic | sensitivity analysis effective reproduction number relapse infected ignorant local stability global stability |
| url | https://www.frontiersin.org/articles/10.3389/fams.2024.1487291/full |
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