# Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications
## 5 Evaluation
### Impact of Utilization  
We first evaluate the dynamics of an infection using the epidemic model introduced in the previous section under different utilization percentages of the contact tracing mobile application. The idea is to provide a better understanding of the dynamics of the spread disease, and the people quarantined using contact tracing. We start analyzing the situation when no measures are taken: that is, individuals are neither detected nor quarantined (\(\delta=q_{i}=q_{s}=0\)). Figure 2a show these results. It clearly depicts the evolution of the deterministic SIR epidemic model where most individuals gets infected due to the COVID-19's high reproductive number (\(R_{0}\)). Figure 2b represents the case where a proportion of the infected individuals are being detected and isolated (i.e., with a detection rate of \(\delta=0.05\)). This simple measure reduces the percentage of individuals infected (about 60%), flattening the curve of infected individuals. Such an effect of flattening the curve means that the infection is lengthier. Now, we assess the effect that smartphone-based contact tracing has in the spread of the infection. We consider an optimistic utilization of the application of 75% (\(U=0.75\)), and that the ratio of users checking the application is also high (\(RC=0.8\)). Using Equations (2) and (3) with these values, we obtain \(q_{i}=0.19\) and \(q_{s}=0.47\). We consider also a short average tracing time of one day (\(1/\tau_{T}=1\)). The results are presented in Figure 2c, showing that the infected curve has been mostly flattened, and the percentage of infected individuals is also reduced to about 20% of the population. Nevertheless, if we consider a non-optimistic utilization of the contact tracing application (\(U=0.5\) and \(RC=0.5\)), we can see in Figure 2d that the reduction is relatively small (about 40%) when compared to the results shown in Figure 2b. In order to control the outbreak of the disease, a non-realistic utilization close to 100% is required (not displayed for being completely flat curves). The threshold utilization values for controlling a COVID-19 outbreak can be obtained using Equation (6). The results are those in Figure 3, showing the threshold values for the application utilization (\(U\)) and user checking (\(RC\)). The presented results are very significant. For an initial outbreak, that is when all nodes are susceptible (\(S/N=1\)), we can see that the required utilization is unrealistically high (greater than 90%). Fortunately, using some mild measure of social distancing, the effective reproductive number can be reduced significantly. In the paper, we use the notation \(R_{0}\) for both the basic reproductive number and effective reproductive number, although the basic reproductive ratio is when no measures are taken. Additionally, note that by taking measures such as social distancing, the number of contacts (\(k\)) and the probability to transmit the disease (\(b\)) are reduced, and these are the main components of the reproductive number. It is also foreseeable, that for future outbreaks, some proportion of the population has gained immunity after being recovered, and so the ratio \(S/N\) could be smaller. We can see in Figure 3 that, for \(R_{0}=2\), the required utilization can be 60% considering also an RC of 60%. Additionally, if we consider that 10% of the population has gained immunization, the required utilization can be above 40%. These scenarios are highly probable, making mobile contact tracing a feasible solution for new \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Estimated Value** \\ \hline \(R_{0}\) & 3 (1.5–6) \\ \(\gamma\) & 1/15 \\ \(\beta\) & 0.52 \\ \(\tau_{Q}\) & 1/14 \\ \(\delta\) & 0.05 (0.02–0.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Some estimated parameters for COVID-19 (the time unit is days) [29; 36; 42]. outbreaks. Now, we evaluate the scenario when the infection could not be controlled and most people are getting infected.