Optimal Control Analysis of Pneumonia and Meningitis Coinfection
Author
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-09-22
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
In this paper, we proposed a deterministic model of pneumonia-meningitis coinfection.
We used a system of seven ordinary differential equations.
Firstly, the qualitative behaviours of the model such as positivity of the solution, existence of the solution, the equilibrium points, basic reproduction number, analysis of equilibrium points, and sensitivity analysis are studied.
The disease-free equilibrium is locally asymptotically stable if the basic reproduction number is kept less than unity, and conditions for global stability are established.
Then, the basic model is extended to optimal control by incorporating four control interventions, such as prevention of pneumonia as well as meningitis and also treatment of pneumonia and meningitis diseases.
The optimality system is obtained by using Pontryagin’s maximum principle.
For simulation of the optimality system, we proposed five strategies to check the effect of the controls.
First, we consider prevention only for both diseases, and the result shows that applying prevention control has a great impact in bringing down the expansion of pneumonia, meningitis, and their coinfection in the specified period of time.
The other strategies are prevention effort for pneumonia and treatment effort for meningitis, prevention effort for meningitis and treatment effort for pneumonia, treatment effort for both diseases, and using all interventions.
We obtained that each of the listed strategies is effective in minimizing the expansion of pneumonia-only, meningitis-only, and coinfectious population in the specified period of time.
American Psychological Association (APA)
Tilahun, Getachew Teshome. 2019. Optimal Control Analysis of Pneumonia and Meningitis Coinfection. Computational and Mathematical Methods in Medicine،Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1130500
Modern Language Association (MLA)
Tilahun, Getachew Teshome. Optimal Control Analysis of Pneumonia and Meningitis Coinfection. Computational and Mathematical Methods in Medicine No. 2019 (2019), pp.1-15.
https://search.emarefa.net/detail/BIM-1130500
American Medical Association (AMA)
Tilahun, Getachew Teshome. Optimal Control Analysis of Pneumonia and Meningitis Coinfection. Computational and Mathematical Methods in Medicine. 2019. Vol. 2019, no. 2019, pp.1-15.
https://search.emarefa.net/detail/BIM-1130500
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1130500