# Dynamic Infection Spread Model Based Group Testing
## 5 Numerical Results
Due to the relatively high number of initial infections in the system, we observe that the dynamic individual testing algorithm performs better than the dynamic Dorfman type group testing algorithm in terms of the average steady state \(\alpha(t)\). In the weak versions of the algorithms, we observe that their performance is strictly worse than their respective original algorithms, at each time instance, in terms of the average \(\alpha(t)\), as expected. The difference of the average \(\alpha(t)\) curves between the original and weak versions of the dynamic Dorfman type group testing algorithm is higher than the difference of the average \(\alpha(t)\) curves between the original and weak versions of the dynamic individual testing algorithm. This is due to the fact that, in the weak dynamic individual testing algorithm, we still utilize \(T\) tests at each time instance but can sample the isolated individuals to test while in the weak dynamic Dorfman type group testing algorithm, we ignore the group tests and only consider \(T/2\) individual tests. However, since the advantage of the group test is not effective for this set of parameters, as we present in Figure 1, even the weak dynamic Dorfman type group testing algorithm provides a reasonable lower bound for its original version. Finally, we observe that our approximation results in Theorem 1 match with the average \(\alpha(t)\) curves in both dynamic Dorfman type group testing and dynamic individual testing algorithms. Similarly, the average \(\alpha(t)\) curves that we obtain from the weak versions of the proposed algorithms are also closely approximated by the results that we obtain in Theorems 2 and 3. In Figure 2, we run the same simulations as in Figure 1, for the parameters \(n=1000\), \(T=80\), \(q=0.0001\) and \(p=0.01\). Now, relative to the first set of parameters, the number of initial infections is lower but the infection spread probability is higher. Because of the targeted individual testing to the positive groups in the dynamic Dorfman type group testing algorithm, it outperforms the dynamic individual testing algorithm for this set of parameters, as we present in Figure 2. Since the advantage of the group testing is more prevalent for this set of parameters, the weak version of the dynamic Dorfman type group testing algorithm results in an average \(\alpha(t)\) curve that is a loose lower bound for the average \(\alpha(t)\) curve of the original version, while the weak dynamic individual testing algorithm results in a proper lower bound for the original version. Furthermore, for this set of parameters, despite the fact that the Theorem 1 approximation matches the average \(\alpha(t)\) curves for both of the original versions of the proposed algorithms, the resulting Theorem 2 and Theorem 3 approximations cannot be used due to the non-convergent exponents in the expressions. In our third and final set of parameters, we consider lower number of test capacity, \(T\), than the first two sets of parameters, high number of initial infections, \(p\), and high infection  
Figure 3: Average values of the random processes \(\alpha(t)\), \(\lambda(t)\) and \(\gamma(t)\), with obtained theoretical approximations given in Theorem 1 when \(n=1000\), \(T=40\), \(q=0.0002\), \(p=0.2\), for (**a**) dynamic Dorfman type group testing algorithm, (**b**) dynamic individual testing algorithm. spread probability, \(q\). As expected, for this set of parameters, for both of the algorithms, system reaches the steady state when almost everyone in the population gets infected. Due to the high number of infections at each time instance in the system, dynamic individual testing algorithm performs slightly better than the dynamic Dorfman type group testing algorithm, even though it still fails to control the infection spread in an effective manner.