Influence of high-order nonlinear fluctuations in the multivariate susceptible-infectious-recovered master equation.
We perform a high-order analytical expansion of the epidemiological susceptible-infectious-recovered multivariate master equation and include terms up to and beyond single-particle fluctuations. It is shown that higher order approximations yield qualitatively different results than low-order approximations, which is incident to the influence of additional nonlinear fluctuations. The fluctuations can be related to a meaningful physical parameter, the basic reproductive number, which is shown to dictate the rate of divergence in absolute terms from the ordinary differential equations more so than the total number of persons in the system. In epidemiological terms, the effect of single-particle fluctuations ought to be taken into account as the reproductive number approaches unity.
Intellectual Ventures Laboratory, 1600 132nd Avenue NE, Bellevue, Washington 98004, USA.
Basil S
BS
Bayati
Philip A
PA
Eckhoff
D000465:Algorithms; D001703:Biophysics / Q000379:methods; D003141:Communicable Diseases / Q000453:epidemiology*; D004812:Epidemiologic Methods; D006801:Humans; D015233:Models, Statistical; D015999:Multivariate Analysis; D017711:Nonlinear Dynamics; D011634:Public Health / Q000379:methods; D012984:Software; D013269:Stochastic Processes