Electron. J. Differential Equations, Vol. 2020 (2020), No. 70, pp. 1-23

Optimal control analysis applied to a two-patch model for Guinea worm disease

Steady Mushayabasa, Anthony A. E. Losio, Chairat Modnak, Jin Wang

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
Anthony A. E. Losio
Department of Mathematics
University of Zimbabwe, P.O. Box MP 167
Harare, Zimbabwe
email: abulelosio@yahoo.com
Chairat Modnak
Department of Mathematics
Faculty of Science
Naresuan University
Phitsanulok 65000, Thailand
email: cmodn001@odu.edu
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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