Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis
This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpop...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6653796 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849399303405043712 |
|---|---|
| author | Ebrima Kanyi Ayodeji Sunday Afolabi Nelson Owuor Onyango |
| author_facet | Ebrima Kanyi Ayodeji Sunday Afolabi Nelson Owuor Onyango |
| author_sort | Ebrima Kanyi |
| collection | DOAJ |
| description | This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R0, is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R0>1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R0<1, and the unique endemic equilibrium point is locally asymptotically stable whenever R0>1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R0=1, the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis. |
| format | Article |
| id | doaj-art-9c9f8638d2dc4718b00d784d64c0d3fa |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9c9f8638d2dc4718b00d784d64c0d3fa2025-08-20T03:38:22ZengWileyJournal of Applied Mathematics1110-757X1687-00422021-01-01202110.1155/2021/66537966653796Mathematical Modeling and Analysis of Transmission Dynamics and Control of SchistosomiasisEbrima Kanyi0Ayodeji Sunday Afolabi1Nelson Owuor Onyango2Department of Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation, Box 62000-00200, Nairobi, KenyaDepartment of Mathematical Sciences, Federal University of Technology Akure, P.M.B. 704, Akure, Ondo State, NigeriaSchool of Mathematics, College of Biological and Physical Science, University of Nairobi, Box 30197-00100, Nairobi, KenyaThis paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R0, is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R0>1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R0<1, and the unique endemic equilibrium point is locally asymptotically stable whenever R0>1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R0=1, the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis.http://dx.doi.org/10.1155/2021/6653796 |
| spellingShingle | Ebrima Kanyi Ayodeji Sunday Afolabi Nelson Owuor Onyango Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis Journal of Applied Mathematics |
| title | Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis |
| title_full | Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis |
| title_fullStr | Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis |
| title_full_unstemmed | Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis |
| title_short | Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis |
| title_sort | mathematical modeling and analysis of transmission dynamics and control of schistosomiasis |
| url | http://dx.doi.org/10.1155/2021/6653796 |
| work_keys_str_mv | AT ebrimakanyi mathematicalmodelingandanalysisoftransmissiondynamicsandcontrolofschistosomiasis AT ayodejisundayafolabi mathematicalmodelingandanalysisoftransmissiondynamicsandcontrolofschistosomiasis AT nelsonowuoronyango mathematicalmodelingandanalysisoftransmissiondynamicsandcontrolofschistosomiasis |