The COVID-19 pandemic has created a demanding need for fast, sensitive, and reliable diagnostic methods to identify viral infections like SARS-CoV-2. In response, surface plasmon resonance (SPR) biosensors have emerged as effective tools for detecting biomolecules. This theoretical study focuses on designing and refining multilayer SPR biosensor configuration to ensure high sensitivity and stability. The optimized configuration consists of a thin silver layer, a silicon nitride layer, a single graphene layer, and a ssDNA bioreceptor layer, each tailored to improve the effectiveness of the proposed biosensor. The capability of the biosensor to detect SARS-CoV-2 is assessed by analyzing its SPR response, specifically examining variations in resonance angle, attenuation, full width at half maximum, and sensitivity across a range of viral concentrations. Additionally, this study evaluated performance metrics such as refractive index sensitivity, detection accuracy, and quality factor to determine the effectiveness of the biosensor against SARS-CoV-2. Then, this work establishes a basis for further development of SPR biosensors aimed at various viral and biomolecular targets, supporting advances in biosensing technology and the creation of effective diagnostic tools to address current and future health challenges.