In this chapter, we discuss whether or not the epidemic model can give better predictions for Covid-19 to last in a small population size. We take a case study in Brunei Darussalam, with a finite population of around half a million. We compare the predictions made by numerical solutions of the Kermack-McKendrick (KM) SIR epidemic model. The results show that estimating parameter such as rate of infection is a difficult task, which leads to initial predictions far from reality, by taking prevention case. We also conclude that additional factors such as variations in government strict law and policy as well as social network structure such as social distancing have some effects in terms of estimating Covid-19 duration and the number of infected cases.