Related papers: Finding bifurcations in mathematical epidemiology …
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…
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 case that mathematical epidemiology (ME), and also related…
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 simply by putting these two topics together. Firstly, we propose…
The historical quest for unifying the concepts and methods of Chemical Reaction Networks theory (CRNT), Mahematical Epidemiology (ME) and ecology has received increased attention in the last years and has led in particular to the…
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 largely a review work, which attempts to bring closer together…
Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…
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 theory and Lagrange-Hamilton geometry. Through a synthesis…
In this paper, the main purpose is to explore an SIRS epidemic model with a general nonlinear incidence rate $f(I)S=\beta I(1+\upsilon I^{k-1})S$ ($k>0$). We analyzed the existence and stability of equilibria of the epidemic model. Local…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…
The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However,…
We address the question of which small, bimolecular, mass action chemical reaction networks (CRNs) are capable of Andronov-Hopf bifurcation (from here on abbreviated to "Hopf bifurcation"). It is easily shown that any such network must have…
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…
Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a…
Key processes in biological and chemical systems are described by networks of chemical reactions. From molecular biology to biotechnology applications, computational models of reaction networks are used extensively to elucidate their…
A chemical reaction network (CRN) is composed of reactions that can be seen as interactions among entities called species, which exist within the system. Endowed with kinetics, CRN has a corresponding set of ordinary differential equations…
The ever-changing world of disease study heavily relies on mathematical models. They are key in finding and controlling infectious diseases. We aim to explore these mathematical tools used for studying disease spread in biology. The SEIR…
In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
We consider the SIRWJS epidemiological model that includes the waning and boosting of immunity via secondary infections. We carry out combined analytical and numerical investigations of the dynamics. The formulae describing the existence…
We address a fundamental question: under which conditions do the dynamics and thermodynamics of open chemical reaction networks (CRNs), grounded on the notion of idealized chemostats that exchange selected species, emerge from underlying…