A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis
A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | AppliedMath |
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| Online Access: | https://www.mdpi.com/2673-9909/4/1/6 |
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| author | Kabiru Michael Adeyemo Kayode Oshinubi Umar Muhammad Adam Adejimi Adeniji |
| author_facet | Kabiru Michael Adeyemo Kayode Oshinubi Umar Muhammad Adam Adejimi Adeniji |
| author_sort | Kabiru Michael Adeyemo |
| collection | DOAJ |
| description | A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to the equilibria. Employing a Lyapunov function, we demonstrated that the disease-free equilibrium (DFE) is globally asymptotically stable; that is, the related basic reproduction number is less than unity. When it is bigger than one, we use a suitable nonlinear Lyapunov function to demonstrate the existence of a globally asymptotically stable endemic equilibrium (EE). Furthermore, the necessary conditions for the presence of optimum control and the optimality system for the co-infection model are established using Pontryagin’s maximum principle. The model is quantitatively analyzed by studying how sensitive the basic reproduction number is to the model parameters and the model simulation using Runge–Kutta technique of order 4 is also presented to study the effects of the treatments. We deduced from the quantitative analysis that, if there is an effective treatment and diagnosis of those exposed to and infected with the disease, the spread of the viral disease can be effectively managed. The results presented in this work will be useful for the proper mitigation of the disease. |
| first_indexed | 2024-04-24T18:36:54Z |
| format | Article |
| id | doaj.art-99518e629ecb4e1eb2e5499eff1add49 |
| institution | Directory Open Access Journal |
| issn | 2673-9909 |
| language | English |
| last_indexed | 2024-04-24T18:36:54Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj.art-99518e629ecb4e1eb2e5499eff1add492024-03-27T13:18:49ZengMDPI AGAppliedMath2673-99092024-01-01418911910.3390/appliedmath4010006A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control AnalysisKabiru Michael Adeyemo0Kayode Oshinubi1Umar Muhammad Adam2Adejimi Adeniji3Department of Mathematics, Hallmark University, Ijebu-Itele 122101, NigeriaSchool of Informatics, Computing, and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USADepartment of Mathematics, Federal University, Dutse 720222, NigeriaDepartment of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0083, South AfricaA co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to the equilibria. Employing a Lyapunov function, we demonstrated that the disease-free equilibrium (DFE) is globally asymptotically stable; that is, the related basic reproduction number is less than unity. When it is bigger than one, we use a suitable nonlinear Lyapunov function to demonstrate the existence of a globally asymptotically stable endemic equilibrium (EE). Furthermore, the necessary conditions for the presence of optimum control and the optimality system for the co-infection model are established using Pontryagin’s maximum principle. The model is quantitatively analyzed by studying how sensitive the basic reproduction number is to the model parameters and the model simulation using Runge–Kutta technique of order 4 is also presented to study the effects of the treatments. We deduced from the quantitative analysis that, if there is an effective treatment and diagnosis of those exposed to and infected with the disease, the spread of the viral disease can be effectively managed. The results presented in this work will be useful for the proper mitigation of the disease.https://www.mdpi.com/2673-9909/4/1/6onchocerciasisLassa feverco-infectionglobal stabilityoptimal controlperiodic variational vectors |
| spellingShingle | Kabiru Michael Adeyemo Kayode Oshinubi Umar Muhammad Adam Adejimi Adeniji A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis AppliedMath onchocerciasis Lassa fever co-infection global stability optimal control periodic variational vectors |
| title | A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis |
| title_full | A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis |
| title_fullStr | A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis |
| title_full_unstemmed | A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis |
| title_short | A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis |
| title_sort | co infection model for onchocerciasis and lassa fever with optimal control analysis |
| topic | onchocerciasis Lassa fever co-infection global stability optimal control periodic variational vectors |
| url | https://www.mdpi.com/2673-9909/4/1/6 |
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