# High-Performance Computing and ABMS for High-Resolution COVID-19 Spreading Simulation
## 1 Introduction  
In the earliest months of 2020, the unexpected COVID-19 spreading put all the world's countries in difficulties because of the lack of countermeasures and knowledge about this novel virus to model its spreading. Moreover, since SARS-CoV-2 is an air-borne disease, it spreads among people due to everyday social interactions that represent themselves as a complex system to be modeled and simulated. Classical methods based on dynamic models like the Susceptible-Exposed-Infectious-Removed (SEIR) model [1; 2] can only help with several limitations when high simulation resolution (fine-grained) is desired. Indeed, the class of SEIR models has to be extended to model particular conditions like social distancing, lockdown policies, and mask wearing. Although these extensions are easy to implement with additional equations in the basic model, these models do not still address the primary issue related to the basic reproduction number (R_0), which is not policy-invariant. Indeed, it depends on the average number of contacts among people, assuming that the population distribution is uniformly mixed. Moreover, the contact distribution is mixed heterogeneously in a natural population and shows some complex network characteristics.  
Therefore, to avoid the problems of dynamic models, a different modeling and simulation approach should be used. Agent-based modeling and simulation (ABMS) is a better choice because it can model single individuals' characteristics and behaviors with a common trade-off between resolution and population size [3]. This paper proposes a novel case study based on ABMS and on previous experiences to increase the simulation resolution in the same large-scale context of COVID-19 spreading in Italy. Therefore, to avoid the problems of dynamic models, a different modeling and simulation approach should be used. Agent-based modeling and simulation (ABMS) is a better choice because it can model single individuals' characteristics and behaviors with a common trade-off between resolution and population size [3]. This paper proposes a novel case study based on ABMS and on previous experiences to increase the simulation resolution in the same large-scale context of COVID-19 spreading in Italy. The main contributions of our work are the following: (a) a software solution to model and execute millions of concurrent agents using the high-performance computing that maps individuals' behavior to a high simulation resolution; (b) providing a simulator for COVID-19 based on our framework that reaches interesting performances when used to forecast new infections cases using only few days of real data for the initialization; and (c) we propose a commuting model that is suitable for the epidemic context but that can be reused also in different domains.  
On the contrary to previous works, we did not assume an underlying network of contacts, modeling social meetings as a function of the geographical distance among the individuals exploiting the commuting properties at different resolution levels (municipalities and provinces). We defined a commuting mechanism combining two distance-based models: the radiation model [4] and the gravity model [5]. To achieve this goal, we implemented a spreading simulator using ActoDemic [6] and validated it on two of the most populated Italian regions: Lombardy and Emilia-Romagna. The next section shows the features of ABMS, and Section 3 introduces the main epidemic models. Section 4 discusses the use of actors in ABMS application. Section 4 introduces the case study and discusses the development. Sections 5 and 6 discuss the features of our simulation model and introduces two simulation use cases. Section 7 discussed the results of the simulations of COVID-19 spreading in the Emilia Romagna and Lombardy regions. Finally, Section 8 concludes the paper by discussing its main features and the directions for future work.