**5. Conclusions**

In this article we present a stochastic synchronous cellular automaton defined on a square lattice. The automaton rules are based on the SEIR model with probabilistic parameters collected from real human mortality data and SARS-CoV-2 disease characteristics. Automaton rules are presented in Algorithm 1. With computer simulations, we show the influence of the radius of the neighborhood on the number of infected and deceased agents in the artificial population.

The study presented in this paper is based on static automaton. Thus, our approach is equivalent to disease propagation described in terms of conduction-like processes (i.e., the position of each cell is fixed and can infect a neighbor, at distance *r*<sup>E</sup> or *r*<sup>I</sup> ). The latter is a natural way to model with the cellular automata technique. However, we note that also convection-like processes (i.e., the population can flow within the system) may play a crucial role at both large [53] and local scales [19,54].

Further enrichment of the model can lead to the introduction of additional components, including the compartment V that describes the vaccinated agents. This model improvement allows us to study scenarios with limited and unlimited vaccine supply [20] or the existence and stability of steady states [55,56]. Vaccinations seem to be particularly effective when the vaccination campaign starts early and with a large number of vaccinated individuals [20]. Moreover, the realistic models should take into account people's attitudes to vaccination programs [57,58].

In conclusion, increasing the radius of the neighborhood (and the number of agents interacting locally) favors the spread of the epidemic. However, for a wide range of interactions of exposed agents, even isolation of infected agents cannot prevent successful disease propagation. This supports aggressive testing against disease as one of the useful strategies to prevent large peaks of infection in the spread of SARS-CoV-2-like disease. The latter can have devastating consequences for the health care system, in particular for the availability of hospital beds for SARS-CoV-2 and other diseases.

**Author Contributions:** Conceptualization, K.M.; Investigation, S.B.; Methodology, K.M.; Software, S.B.; Visualization, S.B.; Writing-original draft, K.M.; Writing-review & editing, S.B. and K.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** The theoretical data generated by cellular automata simulations is available from the authors upon a reasonable request. The real-world data is based on [44,50].

**Acknowledgments:** The authors are grateful to Zdzisław Burda for critical reading of the manuscript and fruitful discussion.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

