# Investigating Dynamics of COVID-19 Spread and Containment with Agent-Based Modeling
## 3 Results
### Applying Containment Strategies to Flatten the Curve
#### 3.2.2 Travel Restriction  
Travel restrictions and limitations are among the most common government interventions during the COVID-19 pandemic and it has been shown to be an effective measure [43]. In this section, we simulate application of this intervention in our proposed model and investigate its effect. This experiment could be analogous to travel restriction and human mobility restrictions set in place in some countries such as Italy in earlier days of the pandemic. As mentioned in Section 3.2 the world in which the model is implemented is a \(160\times 160\) grids of patches which form a two dimensional lattice. For this experiment, the world is divided into 4 quadrants: region I with positive x and y coordinates, region II with negative x coordinate and positive y coordinate, region III with negative x and y coordinates, and region IV with positive x coordinate and negative y coordinate. Upon starting the simulation, all 5000 agents are created and randomly put into a patch, which  
Figure 3: The effect of applying containment strategy I (testing and tracing) on the population. Here the effects of daily test size and contact tracing size on pdf (probability density function) of maximum daily number of infected agents during the course of epidemic is shown. (**a**) A daily testing size of 1 is applied with three tracing sizes of 1, 10, and 20. (**b**) Daily test size of 100, with tracing sizes of 1, 10, and 20. (**c**) Daily test size of 200, with tracing sizes of 1, 10, and 20. It can be seen how testing and contact tracing together are required in order to change the distribution. happens to be in one of the four regions. Contrary to the previous experiment in which agents could freely choose another empty patch among all 25,600 patches and move there, in this experiment agents are only allowed to move and change positions within the boundaries in which they were created and are not allowed to change their region. For instance, an agent that is created in position (20,30) is not allowed to move to (\(-\)15,30) or (27,\(-\)48). The model is run for 4000 runs with no restrictions, and 4000 times with the restrictions present, and in each run the peak infection number is recorded. Similar to the previous experiment, all parameters are fixed at 0.2. The results of the simulation are shown in Figure 4. It is observed that by applying the travel restriction, the median of peak infection distribution is moved from 1775 to 1659. A Mann-Whitney U test between the two distributions was conducted and a \(p\)-value of 1.79 \(\times\) 10\({}^{-8}\) shows that the two distributions are significantly different. A more pronounced effect could be reached by applying more extensive restrictions. Figure 5 shows the effectiveness that applying both containment strategies have on _flattening the curve_. In Figure 5a, both simulation runs are performed with the same random number generator seed. As could be observed, test and contact tracing strategy is able to reduce the maximum number of infected agents by 27%. Figure 5 also shows two simulations with the same random number generator seed. The results show that applying travel restriction strategy is also effective in reducing the maximum number of infected agents by 31%. Figure 4: The effect of applying containment strategy II (zoning and travel restriction) on the population. This figure shows the effect of applying travel a restriction strategy on the p.d.f. (probability density function) of maximum daily number of infected agents during the course of epidemic. Here the zoning applies to agents so that they do not cross different areas of the urban space which is anchored from the initial position. Figure 5: The effect of applying containment strategies (test and contact tracing and travel restriction) on the contagion curves. This figure shows the effect of applying the containment strategies on epidemic curves. (**a**) Applying test and contact tracing has reduced the maximum number of infected agents by 27%.