Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment
Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/3243957 |
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| author | Fulgensia Kamugisha Mbabazi J. Y. T. Mugisha Mark Kimathi |
| author_facet | Fulgensia Kamugisha Mbabazi J. Y. T. Mugisha Mark Kimathi |
| author_sort | Fulgensia Kamugisha Mbabazi |
| collection | DOAJ |
| description | Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0<1, the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if R0>1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia. |
| format | Article |
| id | doaj-art-54b0263145f94c399bb2d00f0d4ada5c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-54b0263145f94c399bb2d00f0d4ada5c2025-08-20T03:34:21ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/32439573243957Global Stability of Pneumococcal Pneumonia with Awareness and Saturated TreatmentFulgensia Kamugisha Mbabazi0J. Y. T. Mugisha1Mark Kimathi2Department of Mathematics, Busitema University, Tororo, UgandaDepartment of Mathematics, Makerere University, Kampala, UgandaDepartment of Mathematics and Statistics, Machakos University, Machakos, KenyaPneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, R0, is computed using the next generation matrix method. The results show that if R0<1, the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if R0>1 the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of R0 on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of R0 on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.http://dx.doi.org/10.1155/2020/3243957 |
| spellingShingle | Fulgensia Kamugisha Mbabazi J. Y. T. Mugisha Mark Kimathi Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment Journal of Applied Mathematics |
| title | Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment |
| title_full | Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment |
| title_fullStr | Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment |
| title_full_unstemmed | Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment |
| title_short | Global Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatment |
| title_sort | global stability of pneumococcal pneumonia with awareness and saturated treatment |
| url | http://dx.doi.org/10.1155/2020/3243957 |
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