Electron. J. Differential Equations, Vol. 2020 (2020), No. 80, pp. 1-24.

Optimal control applied to a visceral leishmaniasis model

Buddhi Pantha, Folashade B. Agusto, Ibrahim M. Elmojtaba

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.

Submitted January 6, 2019. Published July 28, 2020.
Math Subject Classifications: 35F21, 37N25.
Key Words: Visceral leishmanisis; PKDL; vaccination; canine reservoir; optimal control.

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Buddhi Pantha
Department of Science and Mathematics
Abraham Baldwin Agricultural College
Tifton, GA 31793, USA
email: bpantha@abac.edu
Folashade B. Agusto
Department of Ecology and Evolutionary Biology
University of Kansas
Lawrence KS 66045, USA
email: fbagusto@gmail.com
Ibrahim M. Elmojtaba
Department of Mathematics
Sultan Qaboos University
Al Khoudh 123 - Muscat, Oman
email: elmojtaba@squ.edu.om

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