MODEL EPIDEMI SIRS DENGAN TIME DELAY PADA PERIODE KESEMBUHAN

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 recovery. 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 recovered 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  > 0 when
the number of numbers is R0<1. It can be said that the time delay of the recovery
period cannot affect the stability of disease-free equilibrium. In other words, the
effect of the time delay recovery 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 recovery period.