  This monograph provides an overview of the mathematical theories and
computational algorithm design for contagion source detection in large
networks. By leveraging network centrality as a tool for statistical inference,
we can accurately identify the source of contagions, trace their spread, and
predict future trajectories. This approach provides fundamental insights into
surveillance capability and asymptotic behavior of contagion spreading in
networks. Mathematical theory and computational algorithms are vital to
understanding contagion dynamics, improving surveillance capabilities, and
developing effective strategies to prevent the spread of infectious diseases
and misinformation.
