Deficiency Theory in Chemical Reaction Networks: the Analogy of Chemical Kinetics of Models of Infectious Disease Transmission

Abstract

of chemical reaction networks. This research explores the concept of de ciency theory in chemical reaction networks(CRNs) and its analogy with models of infectious disease transmission. In this study, we begin by introducing the fundamental principles of CRNs and the concept of de ciency, which is a combinatorial parameter that measures the network’s potential for complex dynamical behavior. Chemical reaction networks are commonly studied through their reaction rate equations, which are typically described by mass action kinetics. These reactions can be mathematically represented using systems of ordinary di erential equations (ODEs), where the de ciency theory characterizes the topological properties of the network. The de ciency, determined by the stoichiometry matrix, provides valuable insights into the network’s stability and its capacity to exhibit complex dynamics Interestingly, infectious disease transmission models, particularly those based on compartmental frameworks e.g. SIR, also involve systems of ODEs to describe the interactions between di erent compartments representing susceptible, infected, and recovered individuals. These models employ parameters that de ne the transmission and recovery rates, analogous to the reaction rates in chemical kinetics. This comparative analysis between de ciency theory in chemical reaction networks and infectious disease transmission models o ers a fresh perspective on both domains and presents a promising avenue for interdisciplinary research at the interface of mathematics, chemistry, and epidemiology.