**4. Discussion**

Let us start the discussion with comparing the leftmost (Figure 6a,d,g,j,m) and the middle (Figure 6b,e,h,k,n) columns of Figure 6. The comparison reveals that quarantining or limiting the connectivity of agents in the I state (both infected and informed) may bring good or even very good results in preventing disease propagation, depending on the arrangement of the other parameters. For *r*<sup>E</sup> = 1.5, this completely brought the epidemic to a halt, which would otherwise affect more than half the population. With *r*<sup>E</sup> = 2, it makes it possible to reduce the share of infected agents in the population from 75% to 50%. The effects on *r*<sup>E</sup> = 2.5 and *r*<sup>E</sup> = 3 are similar—instead of the total population, less than 90% of population became infected. When the *r*<sup>E</sup> = 1.5 pandemic duration was significantly shortened, it is because the virus was unable to survive, and the disease was extinct. In other cases, the duration of the epidemic increased; the restrictions introduced for agents in the I state did not completely extinguish the disease, but allowed to slow it down and mitigate its effects.

For low values of the probability of infection (*p*<sup>E</sup> = *p*<sup>I</sup> = 0.005), that is, in a situation where the transmission of the virus is not too high, even a slight limitation of the contact among agents allows for a complete inhibition of the disease and protection of the society against its negative effects (see Figure 5). We note that manipulating the *p*<sup>E</sup> and/or *p*<sup>I</sup> parameters may reflect changes in disease transition rates with their low values corresponding to wild variant of the SARS-CoV-2 virus while higher values correspond to the fiercer (including delta and specially omicron) variants of the SARS-CoV-2 virus. For instance, for a fixed radius of interaction (*r*<sup>I</sup> = *r*<sup>E</sup> = 3) for low values of *p*<sup>E</sup> = *p*<sup>I</sup> = 0.005 nearly 75% of the population reached the R state (Figure 5e) while increasing infection rates to *p*<sup>E</sup> = 0.03 and *p*<sup>I</sup> = 0.02 caused the entire population to fall ill (Figure 6m). The summed values of the fractions *n*<sup>E</sup> of exposed and *n*<sup>I</sup> infected agents at the peaks of disease are 6.6% (for *p*<sup>E</sup> = *p*<sup>I</sup> = 0.005, Figure 5e) and 39% (for *p*<sup>E</sup> = 0.03 and *p*<sup>I</sup> = 0.02, Figure 6m) of the population.

The results presented in Figures 5 and 6 are summarized in Figure 7, where the maximum fraction of agents in state I vs. the neighbours number *z* for various sets of parameters is presented. We observe a gradual increase in the maximum number of infected agents (up to 30%) as the number of agents in the neighborhood increases. An exception to this rule is observed only when *r*<sup>E</sup> = 3, when the maximum level of infections is constant and it does not change with the increase of the range of the interaction of agents in state I.

**Figure 7.** Maximal fraction *n*<sup>I</sup> of agents in state I as dependent on the number of agents' neighbours *z* in the neighborhood. (**a**) *<sup>p</sup>*<sup>E</sup> = *<sup>p</sup>*<sup>I</sup> = 0.005, *zE* = *<sup>z</sup>*<sup>I</sup> = *<sup>z</sup>*, (**b**) *<sup>p</sup>*<sup>E</sup> = *<sup>p</sup>*<sup>I</sup> = 0.01, *zE* = *<sup>z</sup>*<sup>I</sup> = *<sup>z</sup>*, (**c**) *<sup>p</sup>*<sup>E</sup> = 0.03, *<sup>p</sup>*<sup>I</sup> = 0.02, *zE* = *<sup>z</sup>*<sup>I</sup> = *<sup>z</sup>*, (**d**) *<sup>p</sup>*<sup>E</sup> = 0.03, *<sup>p</sup>*<sup>I</sup> = 0.02, *zE* = *<sup>z</sup>*, *<sup>z</sup>*<sup>I</sup> = 4, (**e**) *<sup>p</sup>*<sup>E</sup> = 0.03, *<sup>p</sup>*<sup>I</sup> = 0.02, *zE* = 24, *<sup>z</sup>*<sup>I</sup> = *<sup>z</sup>*.
