Optimal control applied to a visceral leishmaniasis model
In this article, we developed a deterministic model for the transmission dynamics of visceral leishmaniasis in humans, canine reservoirs and sandflies, which is the only vector that transmits the disease parasite. The theoretical and epidemiological findings of this study indicates that the dise...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/80/abstr.html |
| _version_ | 1819175287132258304 |
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| author | Buddhi Pantha Folashade B. Agusto Ibrahim M. Elmojtaba |
| author_facet | Buddhi Pantha Folashade B. Agusto Ibrahim M. Elmojtaba |
| author_sort | Buddhi Pantha |
| collection | DOAJ |
| description | In this article, we developed a deterministic model for the transmission dynamics
of visceral leishmaniasis in humans, canine reservoirs and sandflies, which is
the only vector that transmits the disease parasite.
The theoretical and epidemiological findings of this study indicates that the
disease-free equilibrium of the model is locally and globally asymptotically stable
when the associated reproduction number is less than unity. We perform sensitivity
analysis on the model parameter to determine the parameter with the most impact on
the reproduction number. Following the results obtained from the sensitivity analysis,
we apply optimal control theory using three time dependent control variables
representing personal protection, insecticide spraying and culling of infected canine
reservoirs. Simulation results are presented for various outbreak scenarios which
indicates that leishmaniasis can be eliminated from a region by the application of
three time dependent controls representing respectively, personal protection,
insecticide spraying and culling infected canine reservoir. |
| first_indexed | 2024-12-22T20:52:28Z |
| format | Article |
| id | doaj.art-8e1739058a5d4bd99cee7bbbd0dc29cd |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T20:52:28Z |
| publishDate | 2020-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-8e1739058a5d4bd99cee7bbbd0dc29cd2022-12-21T18:13:03ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-07-01202080,124Optimal control applied to a visceral leishmaniasis modelBuddhi Pantha0Folashade B. Agusto1Ibrahim M. Elmojtaba2 Abraham Baldwin Agricultural College, Tifton, GA, USA Univ. of Kansas, Lawrence KS, USA Sultan Qaboos Univ., Muscat, Oman In this article, we developed a deterministic model for the transmission dynamics of visceral leishmaniasis in humans, canine reservoirs and sandflies, which is the only vector that transmits the disease parasite. The theoretical and epidemiological findings of this study indicates that the disease-free equilibrium of the model is locally and globally asymptotically stable when the associated reproduction number is less than unity. We perform sensitivity analysis on the model parameter to determine the parameter with the most impact on the reproduction number. Following the results obtained from the sensitivity analysis, we apply optimal control theory using three time dependent control variables representing personal protection, insecticide spraying and culling of infected canine reservoirs. Simulation results are presented for various outbreak scenarios which indicates that leishmaniasis can be eliminated from a region by the application of three time dependent controls representing respectively, personal protection, insecticide spraying and culling infected canine reservoir.http://ejde.math.txstate.edu/Volumes/2020/80/abstr.htmlvisceral leishmanisispkdlvaccinationcanine reservoiroptimal control |
| spellingShingle | Buddhi Pantha Folashade B. Agusto Ibrahim M. Elmojtaba Optimal control applied to a visceral leishmaniasis model Electronic Journal of Differential Equations visceral leishmanisis pkdl vaccination canine reservoir optimal control |
| title | Optimal control applied to a visceral leishmaniasis model |
| title_full | Optimal control applied to a visceral leishmaniasis model |
| title_fullStr | Optimal control applied to a visceral leishmaniasis model |
| title_full_unstemmed | Optimal control applied to a visceral leishmaniasis model |
| title_short | Optimal control applied to a visceral leishmaniasis model |
| title_sort | optimal control applied to a visceral leishmaniasis model |
| topic | visceral leishmanisis pkdl vaccination canine reservoir optimal control |
| url | http://ejde.math.txstate.edu/Volumes/2020/80/abstr.html |
| work_keys_str_mv | AT buddhipantha optimalcontrolappliedtoavisceralleishmaniasismodel AT folashadebagusto optimalcontrolappliedtoavisceralleishmaniasismodel AT ibrahimmelmojtaba optimalcontrolappliedtoavisceralleishmaniasismodel |