## Abstract

Pneumococcal pneumonia is a type of community-acquired pneumonia which is an acute respiratory infection caused by Streptococcus pneumoniae bacteria. In this study, a mathematical model on the spread of Pneumococcal pneumonia is constructed by considering vaccination and hospital care interventions. The model is formed by dividing the human population based on their health status. We consider several things in the model's construction, such as asymptomatic individuals, the latent phase during infection, and interventions of vaccination and hospitalization. Analytical studies are carried out to find and analyze the existence and local stability of the equilibrium points, determining the basic reproduction number (R_{0}), and investigate the type of bifurcation of the model. We find that the model exhibits a forward bifurcation when R_{0} = 1. These result means that we have to reduce the value of R_{0} as large as possible using vaccination and/or hospitalization to avoid the existence of Pneumococcal pneumonia in the community. Several numerical experiments are shown to see the visualization of the model. The simulation results show that the rate of vaccination and the rate of hospitalization only have a very significant effect at the beginning in reducing the value of R_{0}, but not as significant when the value of the two rates given is large enough. It is also concluded that an increase in the rate of vaccination is more successful in reducing the number of individuals infected with Pneumococcal pneumonia compared to an increase in the rate of hospitalization. Thus, it will be more effective for intervention in the field to rely on vaccination compared to hospitalization. The type of vaccine used in the vaccination process also has a significant effect in reducing the value of R_{0}. This is because the elasticity value of the parameter ζ, which is the infection reduction value because the effectiveness of the vaccine, has the most significant effect in reducing the value of R_{0} compared to the parameters that indicate the rate of vaccination and the rate of hospitalization.

Original language | English |
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Title of host publication | 8th Symposium on Biomathematics, Symomath 2021 |

Subtitle of host publication | Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration |

Editors | Noorma Yulia Megawati, Nanang Susyanto, Dwi Ertiningsih, Eminugroho Ratna Sari, Fitriana Yuli Saptaningtyas, Made Tantrawan, Oki Almas Amalia, Susiana |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735443648 |

DOIs | |

Publication status | Published - 2 Aug 2022 |

Event | 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021 - Yogyakarta, Indonesia Duration: 16 Jul 2021 → 17 Jul 2021 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2498 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 8th Symposium on Biomathematics: Bridging Mathematics and Covid-19 Through Multidisciplinary Collaboration, Symomath 2021 |
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Country/Territory | Indonesia |

City | Yogyakarta |

Period | 16/07/21 → 17/07/21 |

## Keywords

- equilibrium points
- mathematical model
- Pneumococcal pneumonia
- SIR