An SIR model tracks susceptible, infected, and recovered individuals. A chemical reaction network tracks reactant, intermediate, and product concentrations. Both are positive ODE systems — differential equations where every variable must remain non-negative. Both ask the same stability question: does the system converge to an equilibrium, and which one?
Avram, Adenane, and Halanay argue these aren't analogous — they're identical. The Next Generation Matrix, the workhorse of epidemic threshold analysis (it gives you the basic reproduction number R₀), is a special case of tools from chemical reaction network theory. The stoichiometric matrix that encodes which reactions produce and consume which species is the same mathematical object as the transmission matrix that encodes who infects whom.
The payoff runs both directions. Chemical reaction network theory provides the symbolic-numeric approach of Vassena and Stadler: treat the Jacobian's characteristic polynomial as a formal expression using “symbolic reactivities,” then link its coefficients to “Child Selection minors” of the stoichiometric matrix. This machinery, developed for understanding chemical oscillations and bistability, transfers directly to epidemic models. Bifurcation analysis — asking when the disease-free equilibrium loses stability — becomes a computation in the stoichiometric framework.
And epidemiology returns the favor. The Next Generation Matrix decomposes the dynamics into “new infections” and “transitions” in a way that chemical reaction network theory doesn't naturally distinguish. This decomposition isolates the productive part of the dynamics (what amplifies) from the dissipative part (what decays), giving stability results that pure CRN analysis would have to derive differently.
The structural point: the disciplinary walls between chemical kinetics and epidemiology are accidents of history, not mathematics. The same positive systems, the same stability questions, the same bifurcation machinery. The tools were developed independently because the communities don't talk. A cocktail of both is stronger than either alone — not because it discovers new mathematics, but because it recognizes that the same mathematics was discovered twice.