**Core Concept**
The question is testing the understanding of the cellular response to viral infections, specifically the mechanism of viral clearance. **Apoptosis**, or programmed cell death, is a critical process that eliminates virus-infected cells to prevent further viral replication and spread. This process involves a series of cellular and molecular events that ultimately lead to the death of the infected cell.

**Why the Correct Answer is Right**
The correct answer is **Cytokine-induced apoptosis**. When a cell is infected with a virus, it undergoes significant changes in its gene expression and cellular metabolism. This leads to the activation of pro-apoptotic signaling pathways, which are amplified by the release of cytokines such as TNF-alpha and IFN-gamma. These cytokines bind to their respective receptors on the surface of the infected cell, triggering a cascade of intracellular events that ultimately lead to the activation of caspases and the initiation of apoptosis. This process is crucial for eliminating virus-infected cells and preventing the spread of the virus.

**Why Each Wrong Option is Incorrect**
**Option A:** **Lysosomal degradation** is not a primary mechanism for eliminating virus-infected cells. While lysosomes can play a role in the degradation of viral particles and infected cellular components, they are not the primary mechanism for inducing apoptosis in virus-infected cells.

**Option B:** **Innate immune response** is a broader term that encompasses the initial response of the immune system to viral infections, including the activation of cytokines and the recruitment of immune cells to the site of infection. However, it is not a specific mechanism for eliminating virus-infected cells.

**Option D:** **Complement system** is a component of the innate immune system that plays a role in eliminating pathogens, including viruses, through the formation of the membrane attack complex (MAC). However, the complement system is not the primary mechanism for inducing apoptosis in virus-infected cells.

**Clinical Pearl / High-Yield Fact**
One key fact to remember is that the **cytokine-induced apoptosis** pathway is a critical mechanism for eliminating virus-infected cells and preventing the spread of viral infections. This process is mediated by cytokines such as TNF-alpha and IFN-gamma, which play a crucial role in the immune response to viral infections.

**Correct Answer: C. Cytokine-induced apoptosis**