Evaluating the sensitivity of SARS-CoV-2 infection rates on college campuses to wastewater surveillance.

As college campuses reopened in fall 2020, we saw a large-scale experiment unfold on the efficacy of various strategies to contain the SARS-CoV-2 virus. Traditional individual surveillance testing via nasal swabs and/or saliva is among the measures that colleges are pursuing to reduce the spread of the virus on campus. Additionally, some colleges are testing wastewater on their campuses for signs of infection, which can provide an early warning signal for campuses to locate COVID-positive individuals.

Analytic solution of the SEIR epidemic model via asymptotic approximant.

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et al.

Accurate closed-form solution of the SIR epidemic model.

An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et al., 2017). The solution is created by analytically continuing the divergent power series solution such that it matches the long-time asymptotic behavior of the epidemic model.

Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.