# Dynamic SAFFRON: Disease Control Over Time via Group Testing
## 5 Conclusions  
* We considered a dynamic infection spread model based on the discrete SIR model.
* We aimed to efficiently utilize the available testing capacity \(T\) at each time instance to control disease spread within a community rather than minimize the number of required tests to determine every infection as in the static group testing problem.
* We presented a novel performance metric: \(\epsilon\)-disease control time. Different than our previous metric in [38], which is the expected number of susceptible individuals in the steady state, \(\epsilon\)-disease control time measures the timeliness of the disease control.
* We refined our prior results in [38] and used them to characterize the performance of dynamic individual testing algorithm in terms of the \(\epsilon\)-disease control time metric, in (6).
* We introduced dynamic SAFFRON-based group testing algorithm and presented mean-sense performance results in (12), which can be further used in combination with our previous results regarding symmetric and converging dynamic testing algorithms.
* We simulated our dynamic system, implemented the dynamic individual testing algorithm and dynamic SAFFRON-based group testing algorithm, and presented the numerical results that we obtained.  
Future Work
* Our system model serves as a baseline model for group testing applications in a dynamic setting. For the purpose of expanding this baseline, further dynamic algorithms can be proposed and their performance can be characterized. For varying parameter regimes, proposed dynamic algorithms can be compared.
* Novel performance metrics can be proposed. In this paper, we focus on \(\epsilon\)-disease control time, and in our prior work in [38], we focus on the number of individuals that remain non-infected throughout the process of controlling the infection. Novel performance metrics can be proposed and the performance of proposed dynamic testing algorithms can be characterized in terms of these novel performance metrics.
* Novel variations of the SIR-based disease spread model can be considered. Disease spread characteristics can be challenged and proposed dynamic algorithms can be evaluated over these novel disease spread models.  
Figure 2: Numerical averages of the random processes \(\alpha(t)\), \(\lambda(t)\) and \(\gamma(t)\), with theoretical calculation of \(\lambda(t)\), for the system parameters \(n=1000\), \(T=30\), \(q=0.00001\), \(p=0.2\), for dynamic SAFFRON-based group testing algorithm.  
**Author Contributions:** Conceptualization, B.A. and S.U.; methodology, B.A. and S.U.; software, B.A. and S.U.; validation, B.A. and S.U.; formal analysis, B.A. and S.U.; investigation, B.A. and S.U.; resources, B.A. and S.U.; data curation, B.A. and S.U.; writing--original draft preparation, B.A. and S.U.; writing--review and editing, B.A. and S.U.; visualization, B.A. and S.U.; supervision, S.U.; project administration, S.U.; funding acquisition, S.U. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.