Strategies for testing an infected population to mitigate the spread of a pandemic

Many mathematical models have been developed to simulate and predict
the spread of the ongoing COVID-19 pandemic. There has been less work
on on testing as an effective measure to distinguish and isolate
infected patients, and how this might affect disease spread. We
formulate a mathematical model adapted from the classic SIR model
that studies the effect of testing and subsequent isolation confirmed
patients. In order to study how testing and isolation of active
cases can effectively cut off the spreading chain infection, we also
propose and analyze a model that takes into account the social
network structure by considering the heterogeniety arising in the
different numbers of close contacts one has. We perform numerical
simulations and discover that in a heterogeneous social network given
the same amount of testing capacity, different testing strategies
based on the number of close contacts can be devised to optimize the
control of disease spread.