# An Efficient Geometric Search Algorithm of Pandemic Boundary Detection
## 5 Results and Discussion  
Figures 3 and 4 show the results of full search and geometric search in a single trial, where the population size is 250,000, the duration of the pandemic is 200 days, and the infection probability is 0.1. Figure 2 shows the result when all people are cooperative, whereas Figure 3 shows the result when approximately \(\frac{1}{3}\) of population are non-cooperative. When all people are cooperative, the full search tests 72% of the people within the external boundary, while the geometric search only tests 21% of them. The number of people misclassified as boundary for the full search algorithm is also much higher than that of the geometric search algorithm. When a significant fraction of the population is non-cooperative, the number of people misclassified as boundary does not differ much between the full search and the geometric search algorithms. This is because of the different resolution at which the testsare conducted (the use of supercells). The number of tests conducted is also quite close for both geometric and full search, and both are larger than in the fully cooperative case. In all of our experiments, neither algorithm ever misclassified infected individuals, even in the presence of non-cooperation. In other words, our algorithms have the property that all infected individuals are inside the predicted boundary, regardless of the non-cooperative rate in the population. Figures 5-12 show our results in a number of different settings as a function of the infection probability \(p\). For these plots, each experiment is repeated 20 times. The main curve shown is the median across these experiments with the lighter region surrounding each curve representing the 5 th and 95 th percentiles on the low and high end, respectively. These eight plots demonstrate the differences between the two searching algorithms, for different population sizes, non-cooperative rates and pandemic duration. As we might expect, for each population size and non-cooperative rate, both the MAB rate and the test rate for the geometric search algorithm is lower than that of the full search. In addition, an increase in population size leads to a decrease in both the MAB rate and test rate for both algorithms, holding the non-cooperative rates equal. In contrast, an increase in the non-cooperative rate leads to an increase in both the MAB rate and the test rate for both algorithms, holding the population size equal. While our figures show that there are individuals misclassified as boundary, an additional computation that involves no additional testing can be used to correctly classify these individuals. Nonetheless, we display them in these figures to help illustrate what the searching algorithms are doing. When there are non-cooperative people in the population, our use of supercells means that the radius of the predicted external boundary tends to be large compared to the true external boundary. As mentioned above, in this case, the MAB individuals incorrectly include non-infected people who are inside of the predicted external boundary but outside of the true boundary. Indeed, in such a situation, we would incorrectly demand that these individuals quarantine as well. In Figure 3, the predicted external boundary using the full search has more people than both the true external boundary and the predicted one obtained using geometric search. Taking a closer look at the plot on the lower left in Figure 3, we see that the full search explores many cells inside the external boundary, which increases both the MAB rate and the test rate. The geometric search reduces the cost by prioritizing the testing of individuals further from the center, who are more likely to be part of the true external boundary. Zooming into the lower right of Figure 3, we see that among all external boundary cells that have uninfected neighbors inside the true boundary, most of them take only one step inward. A consequence of this is that geometric search almost always prioritizes the correct paths.