A Mathematical Consideration on the Relation of the Social Structure to the Infection Risk in a Community

Abstract

We construct and analyze a mathematical model to consider the relation of the social structure to the infection risk for a spreading transmissible disease in a community. We take into account different phases of human activity, whether it takes place solely in the private situation or both private and social spheres, followed by the division of the community members into two classes: active and less active. The analysis on our mathematical model implies that there are critical conditions for the class size and human activity with respect to the infection risk for a community. Further, we try to discuss how the social structure and situation could be related to the infection risk for a community.