Appropriate Models for the Management of Infectious Diseases

Abstract

BackgroundMathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models.Methods and FindingsFirst, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options.ConclusionThis work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks.

Effects of the infectious period distribution on predicted transitions in childhood disease dynamics

“…Thus, SI 1 R (n ¼ 1) and SE 1 I 1 R (m ¼ 1, n ¼ 1) denote the standard SIR and SEIR models with exponentially distributed latent and infectious periods. Estimated values of n and m can be inferred from appropriate clinical data and vary widely for different infectious diseases, for example, m ¼ 2, n ¼ 3 for SARS and m ¼ 20, n ¼ 20 for measles [9].…”

“…In our analysis, we use standard Erlang-distributed SIR (equation (1.2)) and SEIR models [6,[8][9][10]23,24]. Here, S, I and R are the numbers of susceptible, infectious and recovered (immune) individuals in the population.…”

“…Nguyen & Rohani [10] found that complex dynamics of whooping cough could be understood based on the multiple coexisting attractors of an SE 1 I 5 R model, whereas the simple SE 1 I 1 R model with the same mean latent and infectious periods always predicts an asymptotically annual cycle. Wearing et al [9] argued that the traditional assumptions of exponentially distributed latent and infectious periods may lead to underestimation of the basic reproduction number, R 0 ; and hence to underestimation of the levels of control required to curtail an epidemic. The primary theme of recent work on SI n R and SE m I n R models has been that the shapes of stage duration distributions can significantly affect the qualitative dynamics of infectious diseases.…”

A susceptible-infected model of early detection of respiratory infection outbreaks on a background of influenza

“…We assumed that the mean duration of infectivity is 7 days, i.e. 1/δ = 7, a clinically sensible assumption for influenza (Steinhoff, 2001;Wearing et al, 2005). Next, we chose a time window of length l for which a system of l−2 such equations was formed, and β was estimated using least-squares regression.…”

“…Thus far, we have examined the sensitivity of our detection algorithm under the assumption that 1/δ = 7, which is clinically a sensible assumption for flu-like respiratory infections (Steinhoff, 2001;Wearing et al, 2005). Here, we examine the effect of varying values of recovery period on the overall sensitivity of the detection system.…”