*3.3. r*<sup>E</sup> ≥ *r*<sup>I</sup>

In the middle column of Figure 6 the dynamics of the state fractions *n*S, *n*<sup>E</sup> , *n*<sup>I</sup> , *n*<sup>R</sup> for various values of the neighborhood radius *r*<sup>E</sup> are presented. We assume *p*<sup>E</sup> = 0.03 and *p*<sup>I</sup> = 0.02. For this set of plots, *r*<sup>I</sup> has been predefined as 1 and only *r*<sup>E</sup> changes. Translating this into a description of the real world, sick agents who have disease symptoms are aware of their illness (infected) and limit their contact with the environment to a minimum, while oblivious agents (exposed) do not realize that they can transmit the disease. In each of the tested parameter sets, agents in the I state can infect only four of their closest neighbors.

The case illustrated in Figure 6b was analyzed in Section 3.2 in Figure 6a.

The plot in Figure 6e shows the situation where agents in the state E can infect up to eight agents in their neighborhood. We see irregularities in the shapes of the curves showing the fraction of agents in the states I and E, and the duration of the epidemic is relatively long, over 400 days. However, the values shown in the graphs show that the pandemic was not dangerous for the entire population. Death from the disease was recorded on average in less than eight agents, the maximum number of sick agents in one day was just over six, and the total number of infected agents in the entire epidemic was so low that the deviation of the curve representing the number of agents in the state S from the top of the graph is almost imperceptible.

In Figure 6h, the plots for further extension (to the third coordination zone, with *z* = 12 neighbors) of the radius of the neighborhood of exposed agents (in the state E) are presented. The curves are much smoother than those presented in Figure 6e; however, we can still see some irregularities in the curves describing agents in the E and I states. The duration of the longest simulation was approximately 700 days, the number of deaths was less than 330, and at the peak of the pandemic, approximately 220 agents were simultaneously ill. The curves presenting the fraction of agents in the states of S and R almost perfectly line up on the right side of the chart, meaning that half of the population contracted the disease while the other half remained healthy throughout the epidemic.

The case where agents in the state E can infect agents within a radius of 2.5 is shown in Figure 6k. The epidemic was definitely more dynamic than in the previously studied case (Figure 6h), lasting only a little over two hundred days, and the maximum number of sick agents in one day *<sup>n</sup>*<sup>I</sup> *<sup>L</sup>*<sup>2</sup> reached almost 1500 agents. The sum of those who died from the coronavirus was less than 600, and during the pandemic, approximately 85% of the population became recovered (and earlier exposed and/or infected).

Finally, for the radius *r*<sup>E</sup> increased to three (see Figure 6n) we did not observe too many changes compared to the previous case (Figure 6k). The epidemic was even shorter, it lasted a little more than 150 days, the number of deaths was very similar (it could be estimated at 600), slightly more than 85% of agents in the population were infected, and at the hardest moment of the pandemic there were at the same time about 2370 sick agents (in the I state). The results are therefore almost identical to those of *r*<sup>E</sup> = 2.5, except that disease propagation is faster.

The right column of Figure 6 shows cases with predetermined *r*<sup>E</sup> = 3 and various *r*<sup>I</sup> . We keep *p*<sup>E</sup> = 0.03 and *p*<sup>I</sup> = 0.02

All graphs are very similar to each other, as a large range of infections of agents in the state E makes the influence of *r*<sup>I</sup> on epidemic evolution only marginal. This can be easily observed by comparing the scales presented in all subfigures. The assumed range of infection *r*<sup>E</sup> = 3 is large enough (at least for assumed values of transmission rates *p*<sup>E</sup> and *p*<sup>I</sup> ) to prevent any observable influence of *r*<sup>I</sup> on epidemic trajectories.
