## 1 Background  
Multiple studies show that mathematical models and computer simulations are powerful tools for policy makers to investigate pandemic spread and different PIPs with their outcomes in a fast, cheap, and controlled manner [18; 19; 21]. There are multiple modeling approaches for epidemiological dynamics [22; 23; 24]. The leading approach is extending the \(SIR\) model [20] with sociological [19], economic [25], biological [18], and clinical [26] dynamics to name a few. [PERSON] and [PERSON] [27] introduced a vaccinated (V) stage to the \(SIR\) model, resulting in an \(SIRV\) model for the polio pandemic. The authors took into consideration the spontaneous occurrence of strains during the pandemic. [PERSON] and [PERSON] [28] proposed a two-age group extension for the \(SIR\) model, also for the polio pandemic spread. The authors were able to explain the sharp increase in the number of analytic polio cases that emerged at the beginning of the 20 th century using the separation of children and adult age groups. For the influenza viruses, [PERSON] et al. [29] developed a multi-scale immuno-epidemiological model which takes into consideration direct and environmental transmission of the pathogen. Using their model, the authors showed that two time-since-infection structural variables outperform classical \(SIR\) models for the case of influenza. [PERSON] and [PERSON] [30] fitted a multi-strain stochastic \(SIR\) model onto the COVID-19 pandemic in China. The authors showed that their extended model provides a more accurate prediction of pandemic spread over a longer period of time. More often than not, these models obtain relatively poor results for medium and long prediction periods. One explanation for this shortcoming is the assumption that the population is well mixed which is known to be false even for small population sizes and spatial locations [31; 32; 33; 34; 35; 36]. Indeed, [PERSON] et al. (2020) used the _SIR_ model on the COVID-19 pandemic while relaxing the assumption that the population is mixing homogeneously, showing a fair fitting on six countries with improved results compared to the classical _SIR_ model [37]. Due to statistical fluctuations, long time periods are difficult to predict. To tackle this challenge, several models introduced spatial dynamics to the spread of a pandemic which can be divided into two main groups: graph-based and metric space. Graph-based models take an abstract approach to modeling the locations in which individuals can be located. Usually, it is assumed that each node in the spatial graph represents a physical location (such as a room, street, city, or even a country) and that the population is well-mixed in each node [21; 33]. This approach more often than not ignores the physical properties and dynamics that occur in the location represented by the graph's nodes. For instance, [PERSON] et al. (2021b) proposed a two-age-group extended _SIR_ model with a three-node graph representing a school, a home, and a workplace, such that the individuals move between them according to their age group and time of day [38]. [PERSON] and [PERSON] (2000) studied several models of disease transmission in small-world networks, in which either the probability of infection by a disease or the probability of its transmission is varied, or both [39]. The authors conducted a numerical analysis which results in similar behavior to the reported data by [32]. [PERSON] et al. (1994) defined and explored the stochastic _SIR_ model on a graph of interactions to represent the pandemic in a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale [34]. The authors used real data on trade-related cattle movements from a densely populated livestock farming region in western France and epidemiological parameters corresponding to an infectious epizootic disease, obtaining fair prediction accuracy. Additionally, [PERSON] and [PERSON] (2022) proposed a graph-based extended _SIR_ model where each node represents a room in a building [31].