CLT for the proportion of infected incividuals for an epidemic model on a complete graph

We prove a Central Limit Theorem for the proportion of infected individuals for an epidemic model by dealing with a discrete time system of simple random walks on a complete graph with n vertices. Each random walk makes a role of a virus. Individuals are all connected as vertices in a complete graph. A virus duplicates each time it hits a susceptible individual, dying as soon as it hits an already infected individual. The process stops as soon as there is no more viruses. This model is closely related to some epidemiologial models like those for virus dissemination in a computer network.