Buddhi Pantha, Folashade B. Agusto, Ibrahim M. Elmojtaba
Abstract:
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.
Show me the PDF file (1109 KB), TEX file for this article.
 |
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 |
Return to the EJDE web page