Special Session 135: Dynamical Systems in Mathematical Biology: Epidemiology, Population Dynamics, and Reaction Networks

Stoichiometric Ruin Theory: Coupling Balanced Bilinear Epidemics with Cramer-Lundberg Processes
Rim Adenane
University Ibn Tofail
Morocco
Co-Author(s):    
Abstract:
This work establishes a formal mathematical bridge between the Next-Generation Matrix (NGM) method, the celebrated cornerstone of mathematical epidemiology (ME), and the stochastic ruin theory of the Cramer-Lundberg process. Drawing on recent developments that prove the NGM is a structural outcome of the siphon property fundamental in Chemical Reaction Networks (CRN), we demonstrate how epidemiological thresholds R_0 can be mapped directly onto insurance solvency metrics. By treating the epidemic as a balanced bilinear model, we prove that the stoichiometric dwell times of the infectious compartments, a concept derived from CRN and ME, determine the asymptotic claim intensity and the adjustment coefficient of the insurer's surplus. This synthesis allows for a "stoichiometric stress test" of insurance portfolios, where financial stability is explicitly linked to the biological reaction kinetics of a pathogen.