Dynamic Modelling of Infectious Diseases

Pradas-Velasco, Roberto; Antoñanzas, Fernando; Martínez-Zárate, María Puy

doi:10.2165/00019053-200826010-00005

Cited by 36 publications

(26 citation statements)

References 28 publications

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“…Supplementing these real-world observations, simulation studies on influenza frequently reported strong indirect effects: even relatively low vaccine coverage rates have been shown to yield important public health benefits in the US [5]. Indirect effects can even exceed direct effects [6]. Modeling studies of pediatric vaccination in the UK predicted more indirect than direct effects [7].…”

Section: Introductionmentioning

confidence: 99%

Direct and indirect effects of influenza vaccination

Eichner

Schwehm

Eichner³

et al. 2017

BMC Infect Dis

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BackgroundAfter vaccination, vaccinees acquire some protection against infection and/or disease. Vaccination, therefore, reduces the number of infections in the population. Due to this herd protection, not everybody needs to be vaccinated to prevent infections from spreading.MethodsWe quantify direct and indirect effects of influenza vaccination examining the standard Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) model as well as simulation results of a sophisticated simulation tool which allows for seasonal transmission of four influenza strains in a population with realistic demography and age-dependent contact patterns.ResultsAs shown analytically for the simple SIR and SIRS transmission models, indirect vaccination effects are bigger than direct ones if the effective reproduction number of disease transmission is close to the critical value of 1. Simulation results for 20–60% vaccination with live influenza vaccine of 2–17 year old children in Germany, averaged over 10 years (2017–26), confirm this result: four to seven times as many influenza cases are prevented among non-vaccinated individuals as among vaccinees. For complications like death due to influenza which occur much more frequently in the unvaccinated elderly than in the vaccination target group of children, indirect benefits can surpass direct ones by a factor of 20 or even more than 30.ConclusionsThe true effect of vaccination can be much bigger than what would be expected by only looking at vaccination coverage and vaccine efficacy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12879-017-2399-4) contains supplementary material, which is available to authorized users.

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Section: Introductionmentioning

confidence: 99%

Direct and indirect effects of influenza vaccination

Eichner

Schwehm

Eichner³

et al. 2017

BMC Infect Dis

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“…Eight studies reported data useful for the estimation of a mathematical function [13,19-25], 8 studies reported point estimate data on herd effect at a community level [11,23-29] and 8 studies in 9 publications reported point estimate data on herd effect in subpopulations [17,18,21,30-35]. These studies are summarised in Table 1.…”

Section: Resultsmentioning

confidence: 99%

“…Of the remaining six studies, two provided a graphical illustration [21,22], three reported data that allowed the estimation of a graphical illustration [23-25] and one provided other relevant data [13]. The studies included are described in more detail in Additional file 1.…”

Section: Resultsmentioning

confidence: 99%

“…Thus, the absolute values of the point estimates reported for this study in Figure 2 are not accurate, but the linear relationship is still valid. One study, comparing a static and a dynamic model, revealed that with low levels of effective coverage a high percentage of the total vaccination effect is due to herd effect [13] (see Additional file 1 for more details).…”

Section: Resultsmentioning

confidence: 99%

“…Static models are most often used to evaluate the cost-effectiveness of mass vaccination against seasonal influenza, whereas dynamic models are most often used to evaluate the impact of vaccination on transmission and disease incidence. However, static cohort models cannot dynamically capture the effect of vaccination on transmission and therefore fail to account for herd effect [12,13]. As such, static models generally underestimate the total reduction in the number of incident cases likely to result from vaccination.…”

Section: Introductionmentioning

confidence: 99%

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An approximation of herd effect due to vaccinating children against seasonal influenza – a potential solution to the incorporation of indirect effects into static models

Vlaenderen¹,

Bellinghen²,

Meier

et al. 2013

BMC Infect Dis

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BackgroundIndirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination.MethodsTwo previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals.ResultsThe literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation.ConclusionsThis method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

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Dynamic versus static models in cost‐effectiveness analyses of anti‐viral drug therapy to mitigate an influenza pandemic

2009

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Conventional (static) models used in health economics implicitly assume that the probability of disease exposure is constant over time and unaffected by interventions. For transmissible infectious diseases this is not realistic and another class of models is required, so-called dynamic models. This study aims to examine the differences between one dynamic and one static model, estimating the effects of therapeutic treatment with antiviral (AV) drugs during an influenza pandemic in the Netherlands. Specifically, we focus on the sensitivity of the cost-effectiveness ratios to model choice, to the assumed drug coverage, and to the value of several epidemiological factors. Therapeutic use of AV-drugs is cost-effective compared with non-intervention, irrespective of which model approach is chosen. The findings further show that: (1) the cost-effectiveness ratio according to the static model is insensitive to the size of a pandemic, whereas the ratio according to the dynamic model increases with the size of a pandemic; (2) according to the dynamic model, the cost per infection and the life-years gained per treatment are not constant but depend on the proportion of cases that are treated; and (3) the age-specific clinical attack rates affect the sensitivity of cost-effectiveness ratio to model choice.

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Dynamic Modelling of Infectious Diseases

Cited by 36 publications

References 28 publications

Direct and indirect effects of influenza vaccination

Direct and indirect effects of influenza vaccination

An approximation of herd effect due to vaccinating children against seasonal influenza – a potential solution to the incorporation of indirect effects into static models

Dynamic versus static models in cost‐effectiveness analyses of anti‐viral drug therapy to mitigate an influenza pandemic

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