# Investigating Dynamics of COVID-19 Spread and Containment with Agent-Based Modeling
## 3 Results
### Applying Containment Strategies to Flatten the Curve
#### 3.2.1 Testing and Contact Tracing  
While merely testing individuals will not stop the spread of the disease, WHO recommends a combination of testing and tracing the contacts of individuals that have been tested positive [41]. The successful containment of COVID-19 in some countries such as South Korea are attributed to their rigorous testing and contact tracing and isolation strategy [42]. In this section, we apply this testing and contact tracing strategy on the proposed model and investigate the results. The parameters used in this model are all fixed on 0.2, that is to say \(\lambda_{1}=\lambda_{2}=H=0.2\). Per-contact disease transmission rate (\(\beta\)) and per-contact fear transmission rate (\(\alpha\)) are also fixed on 0.2. two quantities determine the experiment: _daily testing size_ and _number of contacts tracing_. In each timestep, a number of agents, the number of which is determined by _daily testing size_, are chosen and tested for being infected with the disease. If they are tested positive, that is to say they have a state of E, EF, I, or IF, they are then put into isolation (QEF, or QIF), and their previous contacts are traced, tested, and put into isolation either if they are also positive. The number of their previous contacts which are traced, is determined by _number of contacts tracing_ parameter.  
Three daily testing size of 1, 100, and 200 were tested. Also, three number of contact tracing sized were tested: 1, 10, and 20. Each experiment was run 2000 times (a total of \(3\times 3\times 2000\) = 18,000 simulations) and the quantity that was recorded in each experiment, as explained in Section 3.2, is _peak infection_(the maximum number of people that are infected with the disease at any time during the course of the simulation).  
Figure 2: Two waves of infection. (**a**) shortly after the number of infected agents starts decreasing, quarantined agents start coming out of self isolation, a sudden increase in parameter \(H\), which results in occurrence of a second wave of infections. (**b**) a sudden decrease in \(\lambda_{1}\) parameter, which show the rate at which agents in a state of fear quarantine themselves, produces a second wave of infection. These two scenarios describe how a second wave can be produced under different parameterizations.  
Figure 3 shows the results of the simulation. For each parameter setting, peak infection number in all 2000 experiments are recorded and then probability density function (PDF) of peak infection is drawn. The results of the experiment show that, as the size of daily testing size increases, the median of peak infection also decreases (compare the median of 1774 when daily testing size and contact tracing numbers are 1, with the median of 1384 when daily testing size is 200 and number of contact tracing is set on 20). A Mann-Whitney U test between the two distributions (distribution 1: daily size = 200 and tracing size = 20 and distribution 2: daily size = 1 and tracing size = 1) was conducted and a \(p\)-value of \(2.28\times 10^{-123}\) shows that the two distributions are significantly different. Perhaps, the most interesting result of this experiment is that the importance of contact tracing is revealed with large daily testing size. Increasing daily testing size, needs to be joined with contact tracing, in order to be really effective. This effect is pronounced with higher daily testing size numbers (Figure 3b,c). A Mann-Whitney U test between the two distributions (distribution 1: daily size = 200 and tracing size = 20 and distribution 2: daily size = 200 and tracing size = 1) were conducted and a \(p\)-value of \(1.24\times 10^{-25}\) shows that the difference between the two distributions is statistically significant.