# An Efficient Geometric Search Algorithm of Pandemic Boundary Detection
## 5 Results and Discussion
In Figure 4, the difference in test rate between the geometric and full search algorithms is significantly reduced. Recall that in the presence of non-cooperation, both searching algorithms tend to push the predicted external boundary outward and falsely incorporate more non-infected people inside of the predicted external boundary. However, the collapsing of cells into super-cells also reduces the complexity of the graphical structures. Therefore, the full search algorithm no longer has that many inner branches to search, and therefore its test rate is not as different from that of geometric search relative to the fully cooperative setting. Figure 3: Population = 250,000 Non-cooperative Rate = 0. Duration = 200 Infection Probability = 0.1. N: number of people inside and containing the external boundary. Figure 4: Population = 250,000 Non-cooperative Rate = 0.333. Duration = 200 Infection Probability = 0.1. N: number of people inside and containing the external boundary. Figure 5: Number of Tests. Population = 250,000 Non-cooperative Rate = 0. N: number of people inside and containing the external boundary. Figure 6: Number of Tests. Population = 1,000,000 Non-cooperative Rate = 0. N: number of people inside and containing the external boundary. Figure 7: Number of Tests. Population = 250,000 Non-cooperative Rate = 0.333. N: number of people inside and containing the external boundary. Figure 8: Number of Tests. Population = 1,000,000 Non-cooperative Rate = 0.333. N: number of people inside and containing the external boundary. Figure 10: Misclassified As Boundaries. Population = 1,000,000 Non-cooperative Rate = 0. N: number of people inside and containing the external boundary. Figure 9: Misclassified As Boundaries. Population = 250,000 Non-cooperative Rate = 0. N: number of people inside and containing the external boundary. In the settings of Figures 3 and 4, the MIP rates for both algorithms are 0. In other words, all infected individuals are contained in the predicted external boundary and there is no way for undetected infected individuals to spread the disease to the population outside of the predicted external boundary, as long as appropriate social distancing rules are implemented. This is what we had hoped for. A comparison between Figures 5, 7, 9, 11 and Figures 6, 8, 10, 12 shows that as the population becomes denser, each individual is connected with more direct neighbors and therefore has a larger chance of spreading the disease. Thus, the radius of the pandemic tends to be larger. Asymptotically, the numbers of tests and MAB rates are proportional to the length of the external boundary, which is proportional to the radius, whereas the total number of people inside the external boundary is proportional to the square of radius. Therefore, as the radius becomes larger, the MAB rates and test rates tend to be smaller. A comparison between Figures 5, 6, 9, 10 and Figures 7, 8, 11, 12 shows that the MAB rates and test rates increase as the population becomes less cooperative. The reason is that with non-cooperative individuals, we are forced to use supercells to correctly detect the spread of the disease. All curves in Figures 5-12 decrease as the infection probability increases, because the radius of the pandemic increases with the infection probability. Figure 11: Misclassified As Boundaries. Population = 250,000 Non-cooperative Rate = 0.333. N: number of people inside and containing the external boundary. Figure 12: Misclassified As Boundaries. Population = 1,000,000 Non-cooperative Rate = 0.333. N: number of people inside and containing the external boundary. The variance in the results (as represented by the 5-95 percentile regions) also decreases as the population size grows and with cooperation. In particular, the decrease is drastic at \(p=0.075\). All points on the median curves are below 1 when the population size is 1,000,000 or when the infection probability is larger than 0.075.