scholarly journals Qualitative dynamics of interacting vacuum cosmologies

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
Chakkrit Kaeonikhom ◽  
Phongsaphat Rangdee ◽  
Hooshyar Assadullahi ◽  
Burin Gumjudpai ◽  
Jascha A. Schewtschenko ◽  
...  
Keyword(s):  
Qualitative Dynamics

scholarly journals The Implications of HIV Treatment on the HIV-Malaria Coinfection Dynamics: A Modeling Perspective

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
F. Nyabadza ◽  
B. T. Bekele ◽  
M. A. Rúa ◽  
D. M. Malonza ◽  
N. Chiduku ◽  
...  
Keyword(s):  
Hiv Treatment ◽  
Pathogen Transmission ◽  
Disease Epidemiology ◽  
Qualitative Dynamics ◽  
Potential Impact ◽  
Negative Impacts ◽  
Long Term Behavior ◽  
The Impact ◽  
Multiple Pathogens

Most hosts harbor multiple pathogens at the same time in disease epidemiology. Multiple pathogens have the potential for interaction resulting in negative impacts on host fitness or alterations in pathogen transmission dynamics. In this paper we develop a mathematical model describing the dynamics of HIV-malaria coinfection. Additionally, we extended our model to examine the role treatment (of malaria and HIV) plays in altering populations’ dynamics. Our model consists of 13 interlinked equations which allow us to explore multiple aspects of HIV-malaria transmission and treatment. We perform qualitative analysis of the model that includes positivity and boundedness of solutions. Furthermore, we evaluate the reproductive numbers corresponding to the submodels and investigate the long term behavior of the submodels. We also consider the qualitative dynamics of the full model. Sensitivity analysis is done to determine the impact of some chosen parameters on the dynamics of malaria. Finally, numerical simulations illustrate the potential impact of the treatment scenarios and confirm our analytical results.

scholarly journals A century of transitions in New York City's measles dynamics

2015 ◽  
Vol 12 (106) ◽  
pp. 20150024 ◽  
Author(s):  
Karsten Hempel ◽  
David J. D. Earn
Keyword(s):  
New York ◽  
Infectious Diseases ◽  
Human Population ◽  
Sir Model ◽  
Epidemiological Model ◽  
Qualitative Dynamics ◽  
Measles Incidence

Infectious diseases spreading in a human population occasionally exhibit sudden transitions in their qualitative dynamics. Previous work has successfully predicted such transitions in New York City's historical measles incidence using the seasonally forced susceptible–infectious–recovered (SIR) model. This work relied on a dataset spanning 45 years (1928–1973), which we have extended to 93 years (1891–1984). We identify additional dynamical transitions in the longer dataset and successfully explain them by analysing attractors and transients of the same mechanistic epidemiological model.

scholarly journals A gene regulatory motif that generates oscillatory or multiway switch outputs

2013 ◽  
Vol 10 (79) ◽  
pp. 20120826 ◽  
Author(s):  
Jasmina Panovska-Griffiths ◽  
Karen M. Page ◽  
James Briscoe
Keyword(s):  
Gene Expression ◽  
Transcription Factors ◽  
Spatial Organization ◽  
Formation Mechanisms ◽  
Regulatory Interactions ◽  
Qualitative Dynamics ◽  
Gene Regulatory ◽  
Oscillatory Mechanisms ◽  
Parameter Values ◽  
Natural Way

The pattern of gene expression in a developing tissue determines the spatial organization of cell type generation. We previously defined regulatory interactions between a set of transcription factors that specify the pattern of gene expression in progenitors of different neuronal subtypes of the vertebrate neural tube. These transcription factors form a circuit that acts as a multistate switch, patterning the tissue in response to a gradient of Sonic Hedgehog. Here, by simplifying aspects of the regulatory interactions, we found that the topology of the circuit allows either switch-like or oscillatory behaviour depending on parameter values. The qualitative dynamics appear to be controlled by a simpler sub-circuit, which we term the AC–DC motif. We argue that its topology provides a natural way to implement a multistate gene expression switch and we show that the circuit is readily extendable to produce more distinct stripes of gene expression. Our analysis also suggests that AC–DC motifs could be deployed in tissues patterned by oscillatory mechanisms, thus blurring the distinction between pattern-formation mechanisms relying on temporal oscillations or graded signals. Furthermore, during evolution, mechanisms of gradient interpretation might have arisen from oscillatory circuits, or vice versa.

scholarly journals Parameter inference in dynamical systems with co-dimension 1 bifurcations

2019 ◽  
Vol 6 (10) ◽  
pp. 190747
Author(s):  
Elisabeth Roesch ◽  
Michael P. H. Stumpf
Keyword(s):  
Dynamical Systems ◽  
Kinetic Parameters ◽  
Initial Conditions ◽  
Model Parameters ◽  
Biological Processes ◽  
Parameter Inference ◽  
Qualitative Dynamics ◽  
Small Change ◽  
Bifurcation Behaviour ◽  
Practical Implications

Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in its own right and evaluating the bifurcation behaviour of a given dynamical system can be challenging. An even greater challenge, however, is to learn the bifurcation structure of dynamical systems from data, where the precise model structure is not known. Here, we study one aspects of this problem: the practical implications that the presence of bifurcations has on our ability to infer model parameters and initial conditions from empirical data; we focus on the canonical co-dimension 1 bifurcations and provide a comprehensive analysis of how dynamics, and our ability to infer kinetic parameters are linked. The picture thus emerging is surprisingly nuanced and suggests that identification of the qualitative dynamics—the bifurcation diagram—should precede any attempt at inferring kinetic parameters.

Galerkin Projections for Delay Differential Equations

2004 ◽  
Vol 127 (1) ◽  
pp. 80-87 ◽  
Author(s):  
Pankaj Wahi ◽  
Anindya Chatterjee
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Galerkin Projection ◽  
Shape Functions ◽  
Projection Technique ◽  
Finite Dimensional ◽  
Systems Of Odes ◽  
Qualitative Dynamics ◽  
Delay Differential ◽  
Galerkin Projections

We present a Galerkin projection technique by which finite-dimensional ordinary differential equation (ODE) approximations for delay differential equations (DDEs) can be obtained in a straightforward fashion. The technique requires neither the system to be near a bifurcation point, nor the delayed terms to have any specific restrictive form, or even the delay, nonlinearities, and/or forcing to be small. We show through several numerical examples that the systems of ODEs obtained using this procedure can accurately capture the dynamics of the DDEs under study, and that the accuracy of solutions increases with increasing numbers of shape functions used in the Galerkin projection. Examples studied here include a linear constant coefficient DDE as well as forced nonlinear DDEs with one or more delays and possibly nonlinear delayed terms. Parameter studies, with associated bifurcation diagrams, show that the qualitative dynamics of the DDEs can be captured satisfactorily with a modest number of shape functions in the Galerkin projection.

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