Abstract
We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates. The second-order approximatio...
Highlights
We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates
The algorithm is implemented for a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model and compared to both the deterministic approximation and the exact simulation
In a broad sense, stochastic population processes correspond to the time-evolution of countable sets of individuals in interaction
Summary
Stochastic population processes correspond to the time-evolution of countable sets (and subsets) of individuals in interaction. Events come in different flavours, characteristic times, and so on and the more accurate the description in biological terms, the larger the number of events that need to be considered The origin of this approach goes back to Kolmogorov (Kolmogoroff, 1931) and, to Feller’s work on stochastic processes (Feller, 1949) developing from the equations that he named Kolmogorov equations. We have developed a Poisson approximation (Solari & Natiello, 2003) to Kendall’s algorithm as well as a general view of approximation methods (Solari & Natiello, 2014) These approximation methods are organised building upon the concept of linear events (those where the probability rate depends linearly on the involved populations) along with a consistent multinomial approximation for the linear situation with constant (in time) coefficients.
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