We show how stiffness manifests itself in the simulation of chemical reactions at both the continuous-deterministic level and the discrete-stochastic level. Existing discrete stochastic simulation methods, such as the stochastic simulation algorithm and the ~explicit! tau-leaping method, are both exceedingly slow for such systems. We propose an implicit tau-leaping method that can take much lar...

The large deviation principle is established for the Poisson–Dirichlet distribution when the parameter θ approaches infinity. The result is then used to study the asymptotic behavior of the homozygosity and the Poisson–Dirichlet distribution with selection. A phase transition occurs depending on the growth rate of the selection intensity. If the selection intensity grows sublinearly in θ, then ...

The emergence of corona virus (COVID-19) has create a great public concern as the outbreak is still ongoing and government are taking actions such as holiday extension, travel restriction, temporary closure of public work place, borders, schools, quarantine/isolation, social distancing and so on. To mitigate the spread, we proposed and analyzed a stochastic model for the continue spread of coro...

The Sellke and Poisson constructions can be used to specify alternative underlying or latent stochastic processes for standard stochastic epidemic models, leading to sampling properties identical to those generated, for example, by Gillespie’s algorithm (Gillespie, 1977). Readers may wish to refer to Svensson (2007) and Sellke (1983) for further discussion of the Poisson and Sellke construction...

This paper presents BetaWB, a framework for modelling and simulating biological processes. The modelling language is based on β-binders, a process calculus developed for better representing biological interactions. In order to provide efficient and accurate stochastic simulation, a new stochastic selection algorithm, based on the Gillespie assumption, is presented. Moreover, two companion graph...

Stochastic simulation of complex biochemical networks is a topic of current interest, in spite of the importance of the Gillespie algorithm it requires substantial amount of computational effort to simulate a complex system, Many algorithms are available now to control the two most important parameters in simulation: speed and accuracy. It can be proved that the stochastic modelling approach pr...

We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density function using a Bethe ansatz, from which the mean square displacement is calculated. The analysis shows the existence of three regimes of drastically different behavior for short, inter...