Detecting change points in epidemic models has been studied by many scholars. Yao (1993) summarized five existing test statistics in the literature. Out of those test statistics, it was observed that the likelihood ratio statistic showed its standout power. However, all of the existing test statistics are based on an assumption that population variance is known, which is an unrealistic assumption in practice. To avoid assuming known population variance, a new test statistic for detecting epidemic models is studied in this thesis. The new test statistic is a parameter-free test statistic which is more powerful compared to the existing test statistics. Different sample sizes and lengths of epidemic durations are used for the power comparison purpose. Monte Carlo simulation is used to find the critical values of the new test statistic and to perform the power comparison. Based on the Monte Carlo simulation result, it can be concluded that the sample size and the length of the duration have some effect on the power of the tests. It can also be observed that the new test statistic studied in this thesis has higher power than the existing test statistics do in all of cases.