Steady Mushayabasa, Anthony A. E. Losio, Chairat Modnak, Jin Wang
Abstract:
We applied optimal control theory to a mathematical model for guinea worm disease,
to determine the effectiveness of optimal education campaigns on long-term
dynamics of the disease. Our model is concerned with two different host populations,
represented by two patches, sharing a common water source. We computed the basic
reproduction number of the model and demonstrated that whenever the reproduction
number is less than unity the disease dies out in the community. Also we established
that when the basic reproduction number is greater than unity the disease persists.
Utilizing optimal control theory, we explored the potential of time dependent
education to eliminate the disease within 120 months.
The model showed that time dependent education can be successful to minimize
disease prevalence in the two patches, however, its success strongly depends on
the total cost of implementation as well as its maximum strength.
Submitted January 2, 2018. Published July 2, 2020.
Math Subject Classifications: 92D30, 49M05.
Key Words: Mathematical model; Guinea worm disease; optimal control theory.
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Steady Mushayabasa Department of Mathematics University of Zimbabwe, P.O. Box MP 167 Harare, Zimbabwe email: steadymushaya@gmail.com |
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Anthony A. E. Losio Department of Mathematics University of Zimbabwe, P.O. Box MP 167 Harare, Zimbabwe email: abulelosio@yahoo.com |
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Chairat Modnak Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000, Thailand email: cmodn001@odu.edu |
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Jin Wang Department of Mathematics University of Tennessee at Chattanooga 615 McCallie Ave. Chattanooga, TN 37403, USA email: Jin-Wang02@utc.edu |
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