We propose a mathematical model for disease transmission which incorporates the effect of non-compliance of quarantine intervention. This model uses the spread of infection in the form of a nonstandard population dependent ratio, where the total population involved in the infection process becomes dependent on time due to the effect of non-compliance people with the quarantine process. A detailed discussion was carried out on the model analysis regarding the effect of the reproduction number on the existence and stability of the equilibrium points. Model parameters were estimated using COVID-19 daily incidence data in Jakarta. Numerical experiments on the sensitivity analysis and autonomous simulations were given to give a better understanding on the impact of model parameters on disease control strategy. The experiment on the bifurcation diagram indicates the potential for recurring outbreaks in the population. As shown by the results of the sensitivity analysis, it was shown that probability of quarantine compliance has a negative relationship with the basic reproduction number. Numerical results also show that the transmission and recovery rate also have a significant influence on the spread and control of the disease.