Heterogeneous individual-based epidemic models via matrix equations

Heterogeneity in human societies plays an important role in epidemic spreading process. Compared to differential equation models, individual-based epidemic models have the advantage of providing a more detailed depiction of realities to capture heterogeneity across a population. However, the higher granularity and resolution of individual-based models come with the cost of increased computational complexities, which result in difficulty in formulating individual-based models usingmathematics. Moreover, a great effort is needed to understand existing individual-based epidemic models that are presented by previous researches. In this paper, we realize the mathematical formulation of heterogeneous individual-based epidemic models by using matrix equations. We employ matrices and vectors to represent individual attributes and behaviors, derive analytical results from the matrix-based representation of individuals, and design algorithms to derivethe computation of individual-based epidemic models. At last, we study the effect of non-pharmaceutical interventions on epidemic outbreaks by using heterogeneous individual-based epidemic models via matrix equations, including contact tracing and workplace closing.