Model Matematika Penyebaran Penyakit Infeksi Saluran Pernapasan Akut (ISPA) Berdasarkan Lokasi Anatomi Akibat Bakteri Streptococcus Pneumoniae

Abstract

Streptococcus pneumoniae is a bacterium that attacks the human respiratory tract. Streptococcus pneumoniae bacteria cause respiratory diseases in the form of pneumonia, otitis media, sinusitis, sepsis, peritonitis, and abscesses. The purpose of this study was to establish, analyze, and interpret the mathematical model of the spread of Acute Respiratory Infections (ARI) based on the anatomical location of the Streptococcus pneumoniae bacteria. In the mathematical population formation model, the human population is divided into six population groups: susceptible, exposes, sinusitis infections, otitis media infections, pneumonia infections, and recovered. An analysis of the stability of the system around the equilibrium point produces two points, namely, disease-free points, which will be asymptotically stable if βπ<μ(μ+ε+ρ). While the endemic point of the desease will be asymptotically stable if βπ-μ(μ+ε+ρ>0.