Stability Switches Induced by Cross-Immunity in a Virus Competition Model with Time Delay Calibrated with Wastewater Data

Abstract. We consider the competitive dynamics of two viral strains using compartmental epidemiological models that incorporate temporary cross-immunity with a discrete time delay, and are calibrated using wastewater surveillance data. We identify biological conditions for strain coexistence based on the strain-specific basic reproduction number [Formula: see text]. For instance, [Formula: see text] enables strain 1 persistence. We also demonstrate that immune enhancement of infection ([Formula: see text]) is necessary for the establishment of a less fit strain ([Formula: see text]). We define parameter thresholds that induce stability switches that lead to complex dynamical behaviors such as the emergence of limit cycles around strain 1’s equilibrium. In addition, we perform data fitting, simulations, and global sensitivity analysis to evaluate the influence of the recovered class on wastewater viral signals. Our results illustrate that infection-immune dynamics can naturally give rise to the multiwave epidemic patterns and support the integration of dynamical models in wastewater-based epidemiology.