TY - JOUR
T1 - Improved Contact Tracing SIR Model for Randomly Mixed Populations
AU - Li , Meili
AU - Yu , Boxiang
AU - Ma , Junling
AU - Wang , Manting
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 666
EP - 679
PY - 2025
DA - 2025/04
SN - 7
DO - http://doi.org/10.12150/jnma.2025.666
UR - https://global-sci.org/intro/article_detail/jnma/24021.html
KW - Compartmental disease model, control reproduction number, pair
dynamics.
AB - <p style="text-align: justify;">Contact tracing allows for more efficient quarantine and isolation,
and is thus a key control measure in combating infectious diseases. Mathematical models that accurately describe the contact tracing process are important
tools for studying the effectiveness of contact tracing. Recently, we developed
a novel contact tracing SIR model based on pair dynamics, which uses pairs
(two-individual) interactions to approximate triple (three-individual) interactions to close the model. However, the pair approximation used in the model
is only a crude estimate. We extend this model to improve the approximation.
Specifically, the new model tracks infectious individuals who have or have not
infected others, as they play different roles in triples. We conduct a theoretical
analysis to calculate the control reproduction number. The results of the new
model are compared with those of the original model by numerical analysis.
We find that the two models yield a similar epidemic final size. However, the
original model yields a larger control reproduction number and thus underestimates the effect of contact tracing. This discrepancy increases as contact
tracing is strengthened.</p>