A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling

Abstract

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks.

BeyondR0: heterogeneity in secondary infections and probabilistic epidemic forecasting

“…As a result, relying on R 0 alone is often misleading when comparing different pathogens or outbreaks of the same pathogen in different settings [13][14][15]. This is especially critical considering that many outbreaks are not shaped by the 'average' individuals but rather by a minority of super-spreading events [13,16,17].…”

Beyond R0: Heterogeneity in secondary infections and probabilistic epidemic forecasting

“…Unfortunately, the equation relating R 0 to final outbreak size from Kermack and McKendrick is only valid when all the above assumptions hold, which is rarely the case in practice. As a result, relying on R 0 alone is often misleading when comparing different pathogens or outbreaks of the same pathogen in different settings [1][2][3]. This is especially critical considering that many outbreaks are not shaped by the "average" individuals but rather by a minority of super-spreading events [1,16].…”

“…As a result, relying on R 0 alone is often misleading when comparing different pathogens or outbreaks of the same pathogen in different settings [1–3]. This is especially critical considering that many outbreaks are not shaped by the “average” individuals but rather by a minority of super-spreading events [1, 16].…”

“… The basic reproductive number — R 0 — is one of the most common and most commonly misapplied numbers in public health. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same R 0 [1–3]. Here, we show how to predict outbreak size using estimates of the distribution of secondary infections, leveraging both its average R 0 and the underlying heterogeneity.…”

EoN (Epidemics on Networks): a fast, flexible Python package for simulation, analytic approximation, and analysis of epidemics on networks

“…This follows [22]. return float('Inf') N = 10**6 #number of individuals kave = 5 #expected number of partners print('generating graph G with {} nodes'.format(N)) G = nx.fast_gnp_random_graph(N, kave/(N-1)) #Erdo''s-Re'nyi graph tau = 0.3 for cntr in range (10)…”