**Core Concept**
The concept of prevalence in epidemiology refers to the total number of cases of a disease in a population at a given time. Prevalence is influenced by various factors, including the duration of illness, the incidence of new cases, and the mortality rate.

**Why the Correct Answer is Right**
An increase in the duration of illness can lead to an increase in the prevalence of a disease. This is because longer duration of illness means that existing cases are not being removed from the population through death or cure, thus contributing to an overall higher number of cases. In contrast, incidence refers to the number of new cases that occur within a population over a specified period. A decrease in the duration of illness would actually lead to a decrease in prevalence, not an increase.

**Why Each Wrong Option is Incorrect**
**Option A:** Immigration of healthy persons would not directly affect the prevalence of a disease. While immigration can impact the incidence of disease, it does not influence the duration of illness or the existing number of cases in a population.

**Option B:** An increased cure rate of disease would actually lead to a decrease in prevalence, as more individuals would be removed from the population of existing cases.

**Option D:** A decrease in population would also lead to a decrease in prevalence, as the total number of individuals affected by the disease would be reduced.

**Clinical Pearl / High-Yield Fact**
When analyzing the impact of various factors on disease prevalence, it is essential to consider the duration of illness as a key determinant. This is because longer duration of illness can lead to an accumulation of existing cases, contributing to an overall increase in prevalence.

**✓ Correct Answer:** C. Longer duration of illness