Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays
Joint Authors
Mbabazi, Fulgensia Kamugisha
Mugisha, Joseph Y. T.
Kimathi, Mark
Source
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-02-03
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed.
The stability theory of delay differential equations is used to analyze the model.
The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio R0 is less than unity and unstable otherwise.
The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions.
The existence of Hopf-bifurcation is investigated and transversality conditions are proved.
The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations.
Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively.
The analytical results are supported by numerical simulations.
American Psychological Association (APA)
Mbabazi, Fulgensia Kamugisha& Mugisha, Joseph Y. T.& Kimathi, Mark. 2019. Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays. Abstract and Applied Analysis،Vol. 2019, no. 2019, pp.1-21.
https://search.emarefa.net/detail/BIM-1114474
Modern Language Association (MLA)
Mbabazi, Fulgensia Kamugisha…[et al.]. Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays. Abstract and Applied Analysis No. 2019 (2019), pp.1-21.
https://search.emarefa.net/detail/BIM-1114474
American Medical Association (AMA)
Mbabazi, Fulgensia Kamugisha& Mugisha, Joseph Y. T.& Kimathi, Mark. Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays. Abstract and Applied Analysis. 2019. Vol. 2019, no. 2019, pp.1-21.
https://search.emarefa.net/detail/BIM-1114474
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1114474