Exploring the Dynamics of Mass Action Systems

Maler, Oded; Halász, Ádám; Lebeltel, Olivier; Maler, Ouri

doi:10.4204/eptcs.125.6

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Each reaction indicates the transformation that is likely to take place when individuals of specific types come into contact." (Maler, Halasz, Lebeltel, & Maler, 2013) In this model, two separate populations are tracked, In the original form, this is the human population which is the primary concern and the Mosquito population, the vector. In our version, the venue population is our primary customer, and the user population is our vector.…”

Section: Mathematical Description and Solution Approach Fermi Estimationmentioning

confidence: 99%

Using the SIR Epidemiology Model with Vector Transmission to Predict the Effectiveness of a Viral Marketing Campaign and the Spread of Product Adoption

Freed¹

2019

UJMM

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Stevelab, LLC is working on an app that will be released within the year. For planning purposes, the company needs to be able to predict how well the app will spread in its initial phase. Because the pilot launch will be limited to Hillsborough County, FL, there is a limited population. The marketing strategy is to sell the application to places where people gather to mingle and socialize, with a particular focus to the bar scene. Customers of the bar can use the app for free. In addition to our direct sales efforts, we can expect the bar owners to talk to other owners, users will talk to other people, and users will talk to other bar employees creating a web of additional growth. These components are very similar to an SIR model used to predict the spread of infection by dividing a population into 3 categories, Susceptible, Infected, and Recovered. Ratios are applied to show how each division interacts with the other two. (Nicho, 2010) Adding a vector as a means of transmission gives a second population to track divided into 3 similar categories. (Wei, Li, & Martcheva, 2007) In addition to reactions among these three, there are also constants to represent how the two populations interact. This study tests the viability of using an SIR vector model to predict sales of our new app. We conclude that there are good matches between the biological data points and the business data points making the use of an SIR model for this purpose plausible and a prediction can be made. Due to pervasive estimations in actual figures, the predictions are not expected to be extremely accurate at this time. However, we have the ability to directly monitor all of these points as they happen, meaning we can use the same model with increasing accuracy as business progresses, even as early as our first week.

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Section: Mathematical Description and Solution Approach Fermi Estimationmentioning

confidence: 99%

Using the SIR Epidemiology Model with Vector Transmission to Predict the Effectiveness of a Viral Marketing Campaign and the Spread of Product Adoption

Freed¹

2019

UJMM

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“…The steady state of the system defined above (and the complete model in [21]) has been investigated in [24] and a version of the (2.24) model with two domains was studied in [12]; however, we were unable to provide a definite answer regarding bistability.…”

Section: Putting Things Togethermentioning

confidence: 99%

Reducing Spatial Stochastic Models of Membrane Receptors to Approximately Equivalent Chemical Reaction Networks through Coarse Graining

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Computational models are necessary for understanding how biological functionality emerges from a complex network of molecular interactions such as in cell signaling. Due to the complexity of biological systems, the normal scientific method of hypothesizing then testing predictions is becoming increasingly difficult. The large number of processes limits the level of modeling detail; signaling models typically adopt a non-spatial representation where each molecular process is characterized by a few parameters. However, modern microscopic imaging of receptors on cell membranes reveals an intricate structure of microdomains. Receptors, such as epidermal growth factor receptor (EGFR), vascular endothelial growth factor receptor (VEGFR), and others, tend to be grouped in the microdomains as clusters that range from a few to hundreds of biomolecules. While the origin of these clusters is not well understood, a likely explanation is the existence of microdomains with an affinity for the receptors. Using this hypothesis, we can ignore the underlying cause of the microdomains. The size and geometry of these domains can be inferred directly from microscopy; however, the relevant physical properties can only be verified through simulations. In this thesis, I propose a flexible approach to performing such simulations in a coarse grained model that is validated through solving the differential equations when possible and through equilibrium calculations when not. Due to the non-trivial nature of these cell membrane features, fully spatial models need to be used to address these issues. However, fully spatial models are computationally intense and little insight can be gained from them, because of this I propose a method to construct the well-mixed model from the spatial one. The primary issue is the difficulty of extracting the correct kinetic coefficients and that limits the predictive power of spatial models due to the inherent challenges of estimating dynamical parameters. I will use the Metropolis-Hastings Algorithm to extract these parameters from the fully spatial simulations. I use the spatial model as an intermediary step because the spatial simulations can be matched to experimental techniques that provide molecular level resolution, such as single particle tracking (SPT) data. I will then discuss issues that emerge from a baseline comparison between spatial and non-spatial simulations of a simple reversible dimerization process; the spatial simulation employed an algorithm similar to Smoldyn.

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Exploring Synthetic Mass Action Models

Maler

Halász

Lebeltel

et al. 2015

Hybrid Systems Biology

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Exploring the Dynamics of Mass Action Systems

Abstract: We present the Populus toolkit for exploring the dynamics of mass action systems under different assumptions.Comment: In Proceedings HSB 2013, arXiv:1308.572

Cited by 4 publications

References 8 publications

Using the SIR Epidemiology Model with Vector Transmission to Predict the Effectiveness of a Viral Marketing Campaign and the Spread of Product Adoption

Using the SIR Epidemiology Model with Vector Transmission to Predict the Effectiveness of a Viral Marketing Campaign and the Spread of Product Adoption

Reducing Spatial Stochastic Models of Membrane Receptors to Approximately Equivalent Chemical Reaction Networks through Coarse Graining

Exploring Synthetic Mass Action Models

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