Open Access
2019 Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays
Fulgensia Kamugisha Mbabazi, Joseph Y. T. Mugisha, Mark Kimathi
Abstr. Appl. Anal. 2019: 1-21 (2019). DOI: 10.1155/2019/3757036


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.


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Fulgensia Kamugisha Mbabazi. Joseph Y. T. Mugisha. Mark Kimathi. "Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays." Abstr. Appl. Anal. 2019 1 - 21, 2019.


Received: 12 September 2018; Accepted: 18 December 2018; Published: 2019
First available in Project Euclid: 15 March 2019

zbMATH: 07054487
MathSciNet: MR3914231
Digital Object Identifier: 10.1155/2019/3757036

Rights: Copyright © 2019 Hindawi

Vol.2019 • 2019
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