MODEL EPIDEMI SIRS DENGAN TIME DELAY PADA INFECTED (Terinfeksi Penyakit)

Abstract

This study aims to identify whether the healing time delay period affects or does not affect the stability of disease-free equilibrium and the equilibrium of disease endemic. Time delay in the sense of this study is the time period of infected. Time delay in this study is focused on a single specific model, by calculating the temporary and permanent state of the spread of the disease.

            The SIRS model used in this study with the assumption that all individuals who have infected do not have permanent immunity to the disease, so they will return to the disease-prone class. The SIRS epidemic model divides the population into four subpopulations namely Susceptible, Infective, Recovered and Susceptible.

            This research was conducted by revising the SIRS epidemic model compartment which was then used to determine the model development equations represented in differential equation systems. The system describes the interaction between subpopulations with other populations.

The results show that global disease-free equilibrium is stable for all t > 0 when the number of numbers is R₀<1. It can be said that the time delay of the infected period cannot affect the stability of disease-free equilibrium. In other words, the effect of the time delay infected period can be negligible for R₀ <1. However, when, R₀> 1 the stability of endemic equilibrium will be affected by the time delay of the infected period.