Multinomial approximation to the Kolmogorov Forward Equation for jump (population) processes

OTERO, MARCELO; BARRIGA, RAÚL H.; NATIELLO, MARIO A.; SOLARI, HERNÁN G.

Cogent Mathematics & Statistics

Taylor and Francis

Año: 2018 vol. 5 p. 1 - 25

anWe develop a simulation method for Markov Jump processes with finitetime steps based in a quasilinear approximation of the process and in multinomialrandom deviates. The second order approximation to the generating function,Error = O ( dt 2 ) , is developed in detail and an algorithm is presented. Thealgorithm is implemented for a Susceptible-Infected-Recovered-Susceptible(SIRS) epidemic model and compared to both the deterministic approximationand the exact simulation. Special attention is given to the problem of extinction ofthe infected population which is the most critical condition for the approximation.Keywords: Jump Processes; Continuous-time Markov Chains; ApproximatingMethods; Multinomial Processes; Feller-Kendall Algorithm; SIRS EpidemicModel