Question: An epidemiologist is modeling the spread of a disease across 6 cities. If each city can be in one of two states — infected or uninfected — and the model requires that no two adjacent cities (in a linear arrangement) can both be infected simultaneously, how many valid infection configurations are there?

Sun, 03 May 2026 11:05:30 +0000

**How Many Safe Infection Configurations Exist in This Urban Disease Model?** Have you ever wondered how infection patterns might unfurl across tightly connected communities—especially in a structured city layout? A growing number of public health models now explore precise configurations that prevent adjacent transmission, a critical concept behind disease containment strategies. With rising interest in urban resilience and contact tracing innovation, understanding how many valid infection states exist in a linear city network has become more relevant than ever. When epidemiologists model disease spread across six cities arranged in a straight line, each city can either be infected or uninfected—no in-between. But a strict constraint applies: no two neighboring cities can both be infected at the same time. This simple rule reflects real-world scenarios where physical distance slows contagion. The core question then becomes: how many unique infection states comply with this “no adjacency” rule? **The Math Behind Safe City Configurations**