Abstract
Mathematical approaches, such as compartmental models and agent-based models, have been utilized for modeling the spread of the infectious diseases in the computational epidemiology. However, the role of social network structure for transmission of diseases is not explicitly considered in these models. In this paper, the influence maximization problem, considering the diseases starting at some initial nodes with the potential to maximize the spreading in a social network, is adapted to model the spreading process. This approach includes the analysis of network structure and the modeling of connections among individuals with probabilities to be infected. Additionally, individual behaviors that change along the time and eventually influence the spreading process are also included. These considerations are formulated by integer optimization models. Simulation results, based on the randomly generated networks and a local community network under the COVID-19, are performed to validate the effectiveness of the proposed models, and their relationships to the classic compartmental models.