7 citations · 11 across the 16 of their papers we have counts for
17 papers
A Perron-Frobenius strong threshold theorem for (A, B, P, ϕ) 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…
Triangularity of the Jacobian on siphon faces, the Metzler property of its transversal component and other results
Florin Avram, Rim Adenane, Andrei-Dan Halanay
We establish two structural properties of the Jacobian of a positive ODE on any invariant boundary face, i.e. on the face defined by a siphon of an associated Chemical Reaction Net…
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…
Advancing Mathematical Epidemiology and Chemical Reaction Network Theory via Synergies Between Them
Florin Avram, Rim Adenane, Mircea Neagu
Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the c…
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…
Advancing Mathematical Epidemic Modeling via synergies with Chemical Reaction Network Theory and Lagrange-Hamilton Geometry
Florin Avram, Rim Adenane, Mircea Neagu
This essay reviews some key concepts in mathematical epidemiology and examines the intersection of this field with related scientific disciplines, such as chemical reaction network…
Finding bifurcations in mathematical epidemiology via reaction network methods
Nicola Vassena, Florin Avram, Rim Adenane
Mathematical Epidemiology (ME) shares with Chemical Reaction Network Theory (CRNT) the basic mathematical structure of its dynamical systems. Despite this central similarity, metho…
Algorithmic approach for an unique definition of the next generation matrix
Florin Avram, Rim Adenane, Lasko Basnarkov +1
The basic reproduction number R0 is a concept which originated in population dynamics, mathematical epidemiology, and ecology and is closely related to the mean number of children…
Dynamics of an SIR epidemic model with limited medical resources, revisited and corrected
Rim Adenane, Florin Avram, Mohamed El Fatini +1
This paper generalizes and corrects a famous paper (more than 200 citations) concerning Hopf and Bogdanov-Takens bifurcations due to L. Zhou and M. Fan, "Dynamics of an SIR epidemi…
Explicit mathematical epidemiology results on age renewal kernels and R0 formulas are often consequences of the rank one property of the next generation matrix
Florin Avram, Rim Adenane, Dan Goreac +1
A very large class of ODE epidemic models (2.2) discussed in this paper enjoys the property of admitting also an integral renewal formulation, with respect to an "age of infection…
On a three-dimensional and two four-dimensional oncolytic viro-therapy models
Rim Adenane, Eric Avila-Vales, Florin Avram +2
We revisit here and carry out further works on tumor-virotherapy compartmental models of [Tian, 2011, Wang et al., 2013, Phan and Tian, 2017, Guo et al., 2019]. The results of thes…
New results and open questions for SIR-PH epidemic models with linear birth rate, loss of immunity, vaccination, and disease and vaccination fatalities
Florin Avram, Rim Adenane, Andrei Halanay
Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical…
Stability analysis of an eight parameter SIR-type model including loss of immunity, and disease and vaccination fatalities
Florin Avram, Rim Adenane, Gianluca Bianchin +1
We revisit here a landmark five parameter SIR-type model of [DvdD93, Sec. 4], which is maybe the simplest example where a complete picture of all cases, including non-trivial bista…
On matrix-SIR Arino models with linear birth rate, loss of immunity, disease and vaccination fatalities, and their approximations
Florin Avram, Rim Adenane, Lasko Basnarkov +3
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have…
A review of matrix SIR Arino epidemic models
Florin Avram, Rim Adenane, David I. Ketcheson
Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain sub-class of compartmental models whose classes may be divide…
Optimizing dividends and capital injections limited by bankruptcy, and practical approximations for the Cramér-Lundberg process
Florin Avram, Dan Goreac, Rim Adenane +1
The recent papers Gajek-Kucinsky(2017) and Avram-Goreac-Li-Wu(2020) investigated the control problem of optimizing dividends when limiting capital injections stopped upon bankruptc…