A symbiosis between cellular automata and dynamic weighted multigraph with application on virus spread modeling

The pattern of coronavirus spread at different geographical scales verifies that travel or shipment by air, sea or road are potential to transmit viruses from one location to somewhere far away in a very short time. Simulation and analysis of such a situation requires the development of models that support long distance transmission of viruses. Cellular Automata (CA) are a family of spatiotemporal computational models frequently employed in analysis of biomedical systems. A CA consists of a topological combination of units called cells as well as a transition function that propagates the configuration of cells locally and step by step. In this paper, we first present some patterns that show the local interaction between CA cells is not sufficient for virus spread modeling, especially at large spatial scales. Then, we generalize the concept of CA by providing a symbiosis between the neighborhood relationship of cells and the transmission channels represented by a dynamic weighted multigraph. Furthermore, we characterize the capabilities of the proposed modeling tool in simulation of the virus spread, and estimating the risk control during the movement restrictions and related health protocols. Finally, we simulate the coronavirus outbreak in the five study areas including three states and two countries. Our experiments using the proposed model verify that the proposed model is capable of formulating different ways of virus transmission, including long-distance transmission, and supports high-precision simulation of the pandemic.