**Core Concept**
The question requires knowledge of epidemiological measures, specifically the calculation of disease incidence. Disease incidence is a key concept in epidemiology, representing the number of new cases of a disease occurring within a specified population over a defined period.

**Why the Correct Answer is Right**
Incidence is typically calculated using the formula: incidence rate = (number of new cases) / (person-time at risk). Person-time at risk refers to the total number of years or months that individuals in the study population are at risk of developing the disease. This method allows for the calculation of incidence, which is essential for understanding the burden of disease and evaluating the effectiveness of interventions. In the context of epidemiological research, incidence is a critical measure that helps identify the risk factors and potential causes of a disease.

**Why Each Wrong Option is Incorrect**
* **Option A:** Prevalence is the total number of cases of a disease in a population at a given time, not the new cases occurring within a specified period. Prevalence does not account for the duration of disease.
* **Option B:** Mortality rate is the number of deaths due to a specific disease or cause per unit population over a specified time period. While related to disease incidence, mortality rate does not directly measure the new cases occurring within a population.

**Clinical Pearl / High-Yield Fact**
It's essential to distinguish between incidence and prevalence, as they provide different insights into the burden of disease. Incidence measures the risk of developing a disease, whereas prevalence reflects the total number of cases, including both new and existing cases.

**Correct Answer:** C.