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 

Dr Theodor Heutschi 
System Dynamics & Network Analysis Research Group | www.heutschi.com 
Date: July 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 (Ruck j(t)) and System Dynamics. At the end of October 2020, 
the system tipped from linear to highly exponential growth at a measured concentration of C = 39.2 ng/L 
(normalised gene copies). We calculate the cumulative prevalence at this tipping point to be exactly 0.43% of 
the total population in the catchment area (~2,050 cumulative cases out of 470,000 inhabitants), which 
corresponds to an effective reproduction number of Reff ≈ 1.8 to 2.2. 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 per cent, the logistic substitution curve reaches its maximum surge, after 
which complete dominance (> 80 per cent) becomes mathematically deterministic. Finally, we compare this 
epidemiological outbreak threshold (< 0.5 per cent) and the 25 per cent substitution threshold with the 
empirically determined critical mass in mobile networks (25 per cent–27 per cent market penetration) and 
highlight the fundamental systemic similarities and differences.