Open AccessSEIPR-Mathematical Model of the Pneumonia Spreading in Toddlers with Immunization and Treatment Effects
Author(s) -
Rusniwati S. Imran,
Resmawan Resmawan,
Novianita Achmad,
Agusyarif Rezka Nuha
Publication year - 2020
Publication title -
jurnal matematika, statistika dan komputasi/jurnal matematika statistik dan komputasi
Language(s) - English
Resource type - Journals
eISSN - 2614-8811
pISSN - 1858-1382
DOI - 10.20956/jmsk.v17i2.11166
Subject(s) - equilibrium point , basic reproduction number , pneumonia , population , immunization , disease , stability (learning theory) , medicine , mathematics , computer science , immunology , differential equation , environmental health , mathematical analysis , machine learning , antigen
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.