System Dynamics Tipping-Point Analysis of Epidemiological Wastewater Time-Series

System Dynamics Tipping-Point Analysis of Epidemiological Wastewater Time-Series

Mathematical Modeling of COVID-19 Outbreak Dynamics (ARA Werdhölzli, Autumn 2020) Compared to

Telecommunication Network Thresholds and 25% Lineage Displacement Dynamics

Forschungsgruppe Systemdynamik & Netzwerkanalyse  Dr. Theodor Heutschi  | www.heutschi.com
Datum: Juli 2026 

Abstract

In this working paper, we investigate the identification of critical phase transitions (tipping points) in 
biological-epidemiological systems using passive, unbiased wastewater measurements from the ARA 
Werdhölzli wastewater treatment plant (autumn 2020). Conventional individual test data suffer from 
systematic selection and testing capacity biases (ascertainment bias). We demonstrate that the 
wastewater viral load (SARS-N1/N2) provides an ideal, aggregated signal for determining the exact 
tipping point of the outbreak dynamics using derivative analysis (jerk j(t)) and System Dynamics. At the 
end of October 2020, the system tipped from linear to highly exponential growth at a NLS-smoothed, 
flow-normalised concentration of C = 39.2 ng/L. We calculate the cumulative prevalence at this tipping 
point to be 0.43% of the total population in the catchment area (exactly 2,021 cumulative cases out of 
470,000 inhabitants), corresponding to an effective reproduction number of Rₑff ≈ 1.8–2.2. The Rₑff 
calculation is based on NLS-smoothed trend values rather than raw measurements, which exhibit high 
stochastic day-to-day variation (absolute gene copies ranging from 4.1×10⁶ to 48.6×10⁶ within 72 hours). 
Furthermore, we extend the modelling to include the displacement dynamics of new viral variants: as 
soon as the signal share of a new mutant exceeds the critical threshold of 25%, the logistic substitution 
curve reaches its maximum surge, after which complete dominance (>80%) becomes mathematically 
deterministic. Finally, we compare this epidemiological outbreak threshold (<0.5%) and the 25% 
substitution threshold with the empirically determined critical mass in mobile networks (25%–27% 
market penetration) and highlight the fundamental systemic similarities and universal acceleration 
principles governing complex adaptive systems.