7 papers
A Perron-Frobenius strong threshold theorem for (A, B, P, Ï) balanced bilinear models, and the role of left and right Perron eigenvectors in mathematical epidemiology
Florin Avram, Rim Adenane, Andrei-Dan Halanay +2
This paper started as a review of seven results pertaining to a family of bilinear models with rank one NGM introduced by Fall, Iggidr, Sallet and Bonzi, which utilize the explicit…
A cocktail of chemical reaction networks and mathematical epidemiology tools for positive ODE stability problems
Florin Avram, Rim Adenane, Andrei-Dan Halanay
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 o…
Relay transitions and invasion thresholds in multi-strain rumor models: a chemical reaction network approach
Florin Avram, Rim Adenane, Andrei-Dan Halanay
The historical quest for unifying the concepts and methods of Chemical Reaction Networks theory (CRNT), Mahematical Epidemiology (ME) and ecology has received increased attention i…
On the Similarity between Epidemiologic Strains, Minimal Self-Replicable Siphons, and autocatalytic cores in (Chemical) Reaction Networks: Towards a Unifying Framework
Florin Avram, Rim Adenane, Lasko Basnarkov +1
We aim to study boundary stability and persistence of positive odes in mathematical epidemiology models by importing structural tools from chemical reaction networks. This is large…
The Boundary Reproduction Number for Determining Boundary Steady State Stability in Chemical Reaction Systems
Matthew D. Johnston, Florin Avram
We introduce the boundary reproduction number, adapted from the next generation matrix method, to assess whether an infusion of species will persist or become exhausted in a chemic…
Stability in Reaction Network Models via an Extension of the Next Generation Matrix Method
Florin Avram, Rim Adenane, Andrei D. Halanay +1
In this essay, we investigate some relations between Chemical Reaction Networks (CRN) and Mathematical Epidemiology (ME) and report on several pleasant surprises which we had simpl…