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.
Publisher
University of Nairobi
Rights
Attribution-NonCommercial-NoDerivs 3.0 United StatesUsage Rights
http://creativecommons.org/licenses/by-nc-nd/3.0/us/Collections
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