TY - JOUR
T1 - Optimal control applied to a visceral leishmaniasis model
AU - Pantha, Buddhi
AU - Agusto, Folashade B.
AU - Elmojtaba, Ibrahim M.
N1 - Funding Information:
This work was assisted through participation of the authors in an Investigative Workshop on Malaria-Leishmania Co-infection (May 26-28, 2015) at the National Institute for Mathematical and Biological Synthesis, an institute sponsored by the National Science Foundation, the U.S. Department of Home-land Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville. The research of I.M. ELmojtaba is supported by Sultan Qaboos University grant number: IG/SCI/DOMS/16/16.
Publisher Copyright:
© 2020 Texas State University.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
KW - Canine reservoir
KW - Optimal control
KW - PKDL
KW - Vaccination
KW - Visceral leishmanisis
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M3 - Article
AN - SCOPUS:85090631938
SN - 1072-6691
VL - 2020
SP - 1
EP - 24
JO - Electronic Journal of Differential Equations
JF - Electronic Journal of Differential Equations
M1 - 80
ER -