SEIPR-Mathematical Model of the Pneumonia Spreading in Toddlers with Immunization and Treatment Effects

Rusniwati S. Imran; Resmawan Resmawan; Novianita Achmad; Agusyarif Rezka Nuha

doi:10.20956/jmsk.v17i2.11166

Authors

Rusniwati S. Imran Department of Mathematics, Universitas Negeri Gorontalo
Resmawan Resmawan Department of Mathematics, Universitas Negeri Gorontalo
Novianita Achmad Department of Mathematics, Universitas Negeri Gorontalo
Agusyarif Rezka Nuha Department of Mathematics, Universitas Negeri Gorontalo

DOI:

https://doi.org/10.20956/jmsk.v17i2.11166

Keywords:

Pneumonia, SEIPR Mathematical Model, Equilibrium Point, Basic Reproduction Number

Abstract

This research discussed the SEIPR mathematical model on the spread of pneumonia among children under five years old. The development of the model was done by considering factors of immunization and treatment factors, in an effort to reduce the rate of spread of pneumonia. In this research, mathematical model construction, stability analysis, and numerical simulation were carried out to see the dynamics of pneumonia cases in the population. The model analysis produces two equilibrium points, which are the equilibrium point without the disease, the endemic equilibrium point, and the basic reproduction number ( ) as the threshold value for disease spread. The point of equilibrium without disease reaches a stable state at the moment , which indicates that pneumonia will disappear from the population, while the endemic equilibrium point reaches a stable state at that time , which indicates that the disease will spread in the population. Furthermore, numerical simulations show that increasing the rate parameters of infected individuals undergoing treatment ( ), the treatment success rate ( ), and the immunization proportion ( ), could suppress the basic reproductive number so that control of the disease spread rate can be accelerated.

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