id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-010712-6idcbl66	Fennell, Peter G.	Limitations of discrete-time approaches to continuous-time contagion dynamics	2016-11-16		.txt	text/plain	5614	351	62	Allen, in her work [33] , shows that discrete-time susceptible-infectedsusceptible (SIS) and susceptible-infected-recovered (SIR) models can produce complex behavior such as period doubling and chaotic effects for sufficiently large values of the time step and/or contact rate. These deviations arise through both the transition probabilities, which are used in place of transition rates, as well as the parallel (synchronous) state changes in discrete-time systems that are uncharacteristic of continuous-time dynamics. We illustrate this with an example from the literature, also showing how synchronous updating simulation schemes can favour discrete-time formalisms leading to biased conclusions when comparing against continuous-time theories. In the next section, we fix the time step at t = 1 and show how the accuracy breaks down when the infection and recovery rates are too large, showing that discrete-time formalisms using this approach are limited in the ranges of the rate parameters that they can study and thus their ability to match continuoustime dynamics.	./cache/cord-010712-6idcbl66.txt	./txt/cord-010712-6idcbl66.txt