Related papers: Backward bifurcations and multistationarity
This paper carries out an analysis of the global properties of solutions of an in-host model of hepatitis C for general values of its parameters. A previously unknown stable steady state on the boundary of the positive orthant is exhibited.…
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…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
In Systems Biology there is a growing interest in the question, whether or not a given mathematical model can admit more than one steady state. As parameter values are often unknown or subject to a very high uncertainty, one is often…
The COVID-19 pandemic led to widespread interest in epidemiological models. In this context the role of vaccination in influencing the spreading of the disease is of particular interest. There has also been a lot of debate on the role of…
This paper presents a disease-severity-structured epidemic model with treatment necessary only to severe infective individuals to discuss the effect of the treatment capacity on the disease transmission. It is shown that a backward…
We investigate the structure and stability of the steady states for a bacterial colony model with density-suppressed motility. We treat the growth rate of bacteria as a bifurcation parameter to explore the local and global structure of the…
We present a deterministic mathematical model for malaria transmission with waning immunity. The model consists of five non-linear system of differential equations. We used next generation matrix to derive the basic reproduction number…
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an…
Deciding whether and where a system of parametrized ordinary differential equations displays bistability, that is, has at least two asymptotically stable steady states for some choice of parameters, is a hard problem. For systems modeling…
Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
In this paper, we derive and analyze a compartmental model for the control of arboviral diseases which takes into account an imperfect vaccine combined with individual protection and some vector control strategies already studied in the…
In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in a…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
When the steady states at infinity become unstable through a pattern forming bifurcation, a travelling wave may bifurcate into a modulated front which is time-periodic in a moving frame. This scenario has been studied by B.Sandstede and…
Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
We perform a bifurcation analysis on an SIR model involving two pathogens that influences each other. Partial cross-immunity is assumed and coinfection is thought to be less transmittable then each of the diseases alone. The susceptible…