# A Generalized Framework for the Estimation of Edge Infection Probabilities
## 4 Evaluation
### Complex Networks
Since we are running the same infection tasks on the same network with different infection models, if we increase  
\begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Task** & **IC** & & & **SIR 2** & & & **SEIR 2, 3** & & **SI** & \\
**Init/Prob** & **Real** & **Binary** & **Real** & **Binary** & **Real** & **Binary** & **Real** & **Binary** \\ \hline
33/0.75 & 0.024 & \(1\) & 0.019 & 1 & 0.016 & 1 & 0.018 & 1 \\
33/0.50 & 0.040 & \(1\) & 0.033 & 1 & 0.03 & 1 & 0.02 & 1 \\
33/0.25 & 0.079 & \(1\) & 0.041 & 1  
the infectious period, we can expect a greater prevalence of vertex infections; therefore, we are seeing the same phenomenon as with the size of infections. To confirm this, we show the average infection probability of the nodes for the different tasks in Table 3.  
The results for the fully observed real-valued scenarios are shown in Figure 4. The error is computed for the observations at each time step, \(T:\{1\ldots 10\}\), for the SIR model. All infection scenarios were run for 10 iterations. The same performance behavior was observed for the other infection models, and they are, therefore, not presented separately. Figure 4 illustrates the significant difference in the behavior of the inverse infection tasks with sparse and dense infections. When the infections are large, in the first few observations, the error increases and then steadily decreases to its final value. With sparse infections, the situation is more similar to what we observed in trees; the error continuously increases until the end of the infection process. The tasks with dense initial infections and sparse infection spreading behave somewhat like a combination of the two. If the initially infected nodes are far apart from each other, the first few steps of the process behave very much like what we saw with the trees of the previous section, and the reasoning remains the same. Furthermore, if the infection probabilities are small, the infections remain local, centered around the initially infected nodes. However, if the infections originating from multiple sources reach each other, the probability of being infected rises significantly due to multiple independent infection paths connecting each node. However, if the infections are dense enough, again, a sizable fraction of the nodes will have an infection value close to one, making the optimization task easier and explaining the improvement in model performance seen in Figure 4 for more aggressive infection processes. Finally, from the optimization perspective, the task is moderately difficult for the FPSO algorithm. The performance varies depending on the task: the binary ones are easy, always taking less than two hundred iterations to conclude, while the real-valued scenarios with sparse infections are the most difficult, often requiring over a thousand iterations. The accuracy of the predictions is acceptable; for the majority of the test runs, the error remains below 5%, but there are cases where the search is less successful, for example, the 10/0.25 scenario for the IC model. Nonetheless, we can conclude that the optimization method performs well in this application. \begin{table}
\begin{tabular}{c c c c c} \hline
**Task** & **IC** & **SIR 2** & **SEIR 2, 3** & **SI** \\
**Init/Prob** & & & & \\ \hline
33/0.75 & 0.78 & 0.87 & 0.91 & 0.9 \\
33/0.50 & 0.65 & 0.8 & 0.86 & 0.88 \\
33/0.25 & 0.46 & 0.65 & 0.72 & 0.72 \\ \hline
10/0.75 & 0.69 & 0.83 & 0.88 & 0.85 \\
10/0.50 & 0.51 & 0.72 & 0.8 & 0.79 \\
10/0.25 & 0.22 & 0.46 & 0.6 & 0.56 \\ \hline
2/0.75 & 0.68 & 0.82 & 0.88 & 0.85 \\
2/0.50 & 0.50 & 0.72 & 0.8 & 0.79 \\
2/0.25 & 0.20 & 0.45 & 0.6 & 0.56 \\ \hline \end{tabular}
\end{table} 
Table 3: Average node infection value for the last observation for all infection models. As before, the numbers of the inverse infection tasks correspond to the scenarios described in this section. The first number denotes the percentage of initially infected nodes, and the second one indicates the maximum value of the edge infection probability.