ANALYSIS OF SUSCEPTIBLE, INFECTED, RECOVERED, SUSCEPTIBLE (SIRS) MODEL FOR SPREAD OF THE ACUTE RESPIRATORY TRACT INFECTIONS (ARI) DISEASE

ARI is an acute inflammation of the upper and lower respiratory tract caused by infection with microorganisms or bacteria, viruses, and rickets, without or with inflammation of the lung parenchyma, such that it can cause a spectrum of illnesses ranging from asymptomatic disease or mild infection to a deadly disease, depending on the causative pathogen. Therefore, it is necessary to
analyze scientifically acceptable to the events of the spread of respiratory diseases. One of them can be seen in the form of a mathematical model, that is, Susceptible, Infected, Recovered, Susceptible (SIRS) model. Determination of equilibrium points and eigenvalue equation, as well as basic reproduction numbers (R_0) were done to analyze the stability of the model. From the
analysis of model, it found that the free disease equilibrium point, model is asymptotically stable when R_0≤1, while for the endemic equilibrium point, model is asymptotically stable when R_0>1. It indicates that, the Bah Jambi district is free from the ARI disease. Collecting real data and simulation of the spread of ARI using the fourth order Runge-Kutta (RK4) was done to validity of model.