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Mathematical Model, Optimal Control and Transmission Dynamics of Avian Spirochaetosis
- Source :
- Journal of Applied Mathematics and Physics. :270-293
- Publication Year :
- 2020
- Publisher :
- Scientific Research Publishing, Inc., 2020.
-
Abstract
- Avian Spirochaetosis is an acute endemic tick-borne disease of birds, caused by Borrelia anserins, a species of Borrelia bacteria. In this paper, we present a compartmental mathematical model of the disease for the bird population and Tick population. The disease steady-state and the conditions for reaching a stable disease-free steady state are determined. The analysis by Lyapunov method shows both local and global stability. Further investigation involves the introduction of controls to the model; the existence and uniqueness of optimal control are established. Finally, the effect of the controls is investigated using numerical solutions.
- Subjects :
- Lyapunov function
education.field_of_study
010102 general mathematics
Population
Dynamics (mechanics)
Biology
Optimal control
biology.organism_classification
01 natural sciences
Stability (probability)
010305 fluids & plasmas
law.invention
symbols.namesake
Transmission (mechanics)
law
Borrelia
0103 physical sciences
symbols
Applied mathematics
Uniqueness
0101 mathematics
education
Subjects
Details
- ISSN :
- 23274379 and 23274352
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Mathematics and Physics
- Accession number :
- edsair.doi...........542058b69fc9a3474ddfcaa12b1a242e