2025-302

Consider the SI model (Susceptible-Infected) under the homogeneous mixing assumption. In this model, the spread of the virus is driven by random contacts between individuals.

You are given the following data for a specific population at time \(t\):

• Total Population (\(N\)): 10,000 individuals

• Current Susceptible individuals (\(S\)): 9,500

• Current Infected individuals (\(I\)): 500

• Average degree (contacts per individual per unit time, \(\langle k\rangle\)): 12

• Transmission probability (\(\beta\)): 0.05

At this specific moment, what is the average rate of new infections?

A) 275

B) 285

C) 570

D) 600

E) None of the above

Original idea by: Alexandre Petrachini