Analisis Kestabilan Model Matematika Ko-infeksi Virus Influenza A dan Pneumokokus pada Sel Inang

Co-infection of influenza A virus and pneumococcus is caused by influenza A virus and pneumococcus bacteria which infected host cell at the same time. The purpose of this thesis is to analyze stability of equilibrium point on mathematical model within-host co-infection of influenza A and pneumococcus. Based on anlytical result of the model there are four quilibrium points, non endemic co-infection equilibrium (E₀), endemic influenza A virus equilibrium (E₁), endemic pneumococcus equilbrium (E₂) and endemic co-infection equilibrium (E₃). By Next Generation Matrix (NGM), we obtain two basic reproduction number, which are basic reproduction number for influenza A virus (R_0v) and basic reproduction number for pneumococcus (R_0b). Existence of equilibrium point and local stability of equilibrium point dependent on basic reproduction number. Non endemic co-infection equilibrium is locally asymtotically stable if R_0v < 1 and R_0b < 1; influenza A virus endemic equilibrium is locally asymtotically stable if R_0v > 1 and R_0b > 1; pneumococcus endemic equilibrium is locally asymtotically stable if R_0v < 1 and R_0b > 1. Meanwhile, the co-infection endemic equilibrium is locally asymtotically stable if R_0v > 1 and R_0b > 1. From the numerical simulation result, it was shown that increasing the number of influenza A virus and pneumococcus made the number of population cell infected by influenza A virus and pneumococcus (co-infection) also increased.