A cocktail of chemical reaction networks and mathematical epidemiology tools for positive ODE stability problems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908977497899008 |
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| author | Avram, Florin Adenane, Rim Halanay, Andrei-Dan |
| author_facet | Avram, Florin Adenane, Rim Halanay, Andrei-Dan |
| contents | We continue recent attempts to put together concepts and results of Chemical Reaction Networks theory (CRNT) and Mathematical Epidemiology (ME), for solving problems of stability of positive ODEs.
We provide first an elegant CRN-flavored generalization of the most cited result in ME, the Next Generation Matrix (NGM) theorem.
We review next the "symbolic-numeric approach of Vassena and Stadler, which tackles bifurcation problems by viewing the characteristic polynomial of the Jacobian at fixed points as a formal polynomial in the "symbolic reactivities", and identifies its coefficients as "Child Selection minors of the stoichiometric matrix". We also review two applications of this approach using the Mathematica package Epid-CRN tools from both CRNT and ME. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06778 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A cocktail of chemical reaction networks and mathematical epidemiology tools for positive ODE stability problems Avram, Florin Adenane, Rim Halanay, Andrei-Dan Molecular Networks Dynamical Systems 34C10, 34D23, 34C25, 92C45, 92C60 We continue recent attempts to put together concepts and results of Chemical Reaction Networks theory (CRNT) and Mathematical Epidemiology (ME), for solving problems of stability of positive ODEs. We provide first an elegant CRN-flavored generalization of the most cited result in ME, the Next Generation Matrix (NGM) theorem. We review next the "symbolic-numeric approach of Vassena and Stadler, which tackles bifurcation problems by viewing the characteristic polynomial of the Jacobian at fixed points as a formal polynomial in the "symbolic reactivities", and identifies its coefficients as "Child Selection minors of the stoichiometric matrix". We also review two applications of this approach using the Mathematica package Epid-CRN tools from both CRNT and ME. |
| title | A cocktail of chemical reaction networks and mathematical epidemiology tools for positive ODE stability problems |
| topic | Molecular Networks Dynamical Systems 34C10, 34D23, 34C25, 92C45, 92C60 |
| url | https://arxiv.org/abs/2603.06778 |