2026-358

Consider a Euclidian TSP with 5 cities located in a 2D plane at the following coordinates:

A (1, 2); B (5, 3); C (6, 7); D (2, 8); E (4, 5).

A delivery starts at city A and uses Nearest Neighbor Heuristic to construct a complete tour. Which alternative represents the total distance (cost) of the resulting tour, rounded to two decimals?

a) 13.31

b) 17.16

c) 15.52

d) 19.39

e) None of the above

Original idea by: Matheus Rufino

2026-357

When modeling the spread of a pathogen or an information cascade, the choice between the SI, SIS, and SIR compartmental frameworks depends entirely on the biological or behavioral traits of the agents involved. Under the homogeneous mixing assumption, each of these three classical models leads to a fundamentally different outcome in its final regime.

Which of the following statements correctly identifies the long-term behavior (final regime) of the SIR model and explains how it differs from the SI and SIS models?

A) In the SIR model, the fraction of infected individuals eventually drops to zero because infected individuals transition into a removed state where they develop permanent immunity or die.

B) The SIR model is the only framework where the entire population eventually ends up infected at the same time, unlike the SIS model which always maintains a mix of healthy and sick individuals.

C) In the final regime of the SIR model, the system reaches a steady endemic state where a fixed, non-zero fraction of the population remains actively infected forever.

D) The SIR model differs because it completely lacks an initial exponential growth regime, making its spread linear and predictable from day one.

E) None of the above.

Original idea by: Maria Luiza Ramos da Silva