Concept:
Prevalence refers to the total number of existing cases of a disease in a population at a given time, while incidence refers to the number of new cases occurring over a period.
They are related by the formula:
\[
\text{Prevalence} = \text{Incidence} \times \text{Duration of disease}
\]
Step 1: Understand the relationship.
Prevalence depends directly on both incidence and duration.
Step 2: Analyze the given condition.
If incidence remains constant and duration increases, the product (incidence $\times$ duration) increases.
Step 3: Interpret the result.
An increase in duration means patients live longer with the disease, leading to accumulation of cases.
Step 4: Conclude the answer.
Thus, prevalence increases.