Probing the effects of the well-mixed assumption on viral infection dynamics.

  title={Probing the effects of the well-mixed assumption on viral infection dynamics.},
  author={Catherine A. A. Beauchemin},
  journal={Journal of theoretical biology},
  volume={242 2},
  • C. Beauchemin
  • Published 23 May 2005
  • Biology
  • Journal of theoretical biology

Figures and Tables from this paper

Spatiotemporal modelling of viral infection dynamics
A simple two-dimensional cellular automaton model of viral infections was developed and was validated against clinical immunological data for uncomplicated influenza A infections and shown to be accurate enough to adequately protect against emerging spatial structures such as localized populations of dead cells.
A simulation framework to investigate in vitro viral infection dynamics
Modeling HIV-1 Dynamics and Fitness in Cell Culture Across Scales
This article addresses the question how the heterogeneity of the underlying system affects the estimated parameter values of the ODE model, and on the other hand, what information about the microscopic system can be drawn from these values.
A Simulation Framework to Investigate in vitro Viral Infection Dynamics
Choice of spatial discretisation influences the progression of viral infection within multicellular tissues
It is shown that the resolution of spatial discretisation modulates the timescale of infection, and identified the mechanisms by which this occurs, and provides theory to inform the development of multicellular models of viral dynamics, which is in short supply in the literature.
Spatiotemporal Dynamics of Virus Infection Spreading in Tissues
The mathematical model described in this work consists of reaction-diffusion equations with a delay that shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response.
A review of mathematical models of influenza A infections within a host or cell culture: lessons learned and challenges ahead
This work explores the symbiotic role of mathematical models and experimental assays in improving the quantitative understanding of influenza infection dynamics, and discusses the challenges in developing better, more comprehensive models for the course of influenza infections within a host or cell culture.


A simple cellular automaton model for influenza A viral infections.
Spatial models of virus-immune dynamics.
Spatiotemporal dynamics of HIV propagation.
A cellular automaton model of viral propagation based on the known biophysical properties of HIV is introduced, which includes the competition between viral lability and Brownian motion and finds that propagation is limited by viral stability at low cell density and by geometry at high cell density.
Dynamics of HIV infection: a cellular automata approach.
It is found that the infected cells organize themselves into spatial structures, which are responsible for the decrease on the concentration of uninfected cells, leading to AIDS.
Spatial heterogeneity in epidemic models.
  • A. LloydR. May
  • Environmental Science
    Journal of theoretical biology
  • 1996
It is demonstrated that the inclusion of seasonal forcing in deterministic models can lead to the maintenance of phase differences between patches, and chaotic solutions are observed for weaker seasonal forcing; these solutions have a more realistic minimum number of infectives.
Kinetics of Influenza A Virus Infection in Humans
A series of mathematical models of increasing complexity, which incorporate target cell limitation and the innate interferon response, are utilized to examine influenza A virus kinetics in the upper respiratory tracts of experimentally infected adults to suggest that antiviral treatments have a large hurdle to overcome in moderating symptoms and limiting infectiousness.
Mathematical model of influenza A virus production in large-scale microcarrier culture.
Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.
Spatial heterogeneity and the persistence of infectious diseases.
The Importance of Being Discrete (and Spatial)
Abstract We consider and compare four approaches to modeling the dynamics of spatially distributed systems: mean field approaches (described by ordinary differential equations) in which every