Incorporating social contact data in spatio-temporal models for infectious disease spread

Meyer, Sebastian; Held, Leonhard

doi:10.1093/biostatistics/kxw051

Cited by 49 publications

(74 citation statements)

References 39 publications

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“…Weekly (lab‐confirmed) counts of norovirus infections have been downloaded from https://survstat.rki.de. Our training data – identical to the one described and analysed in Meyer and Held (2017) – are stratified into 6 commonly used age groups (0–4, 5–14, 15–24, 25–44, 45–64 and 65+ years) and 12 city districts (of Berlin) and cover the period from week 2011/27 to week 2015/26. The following year (2015/27 to 2016/26) has been used to assess model predictions (test data).…”

Section: Norovirus Gastroenteritis Surveillance Datamentioning

confidence: 99%

“…An interesting feature of the power law is that it is scale‐free, that is, the power parameter (here −1.59) does not depend on the unit in which the distances d are measured. A power law for areal data has also been proposed and is based on the adjacency order

o_{r^{'} r}

between regions

r^{'}

and r as distance measure:

w_{r^{'} r} = {(o_{r^{'} r} + 1)}^{- ρ} .

Here, adjacent regions r and

r^{'}

have order

o_{r^{'} r} = 1

, regions where we need to traverse one other region are of order 2 and higher orders are defined accordingly. The power parameter ρ is treated as unknown and estimated from the data.…”

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

“…Again, we include an indicator x t for the Christmas break and let seasonal terms enter both components, where we now assume age group‐specific seasonality with coefficients

γ_{g}^{(ν)}

and

δ_{g}^{(ν)}

in the endemic component. Note that the formulation for ϕ g r t extends the one used in Meyer and Held (2017) , because we here also allow for seasonal variation in the epidemic component . The gravity model feature

ϕ_{g r t} \propto e_{g r}^{τ}

causes the amount of disease transmission to scale with the population size e g r of the ‘importing’ age group g in region r – with unknown coefficient τ .…”

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

“…Note that social contacts are reciprocal at the population level, that is, there is an equal number of contacts between age group g and

g^{'}

as between age group

g^{'}

and g , which has been taken into account appropriately . We finally specify a power transformation for the contact matrix ,

c_{g^{'} g} = {(C^{κ})}_{g^{'} g} where C^{κ} : = E {normalΛ}^{κ} E^{- 1},

where Λ is the diagonal matrix of eigenvalues and E is the corresponding matrix of eigenvectors of C . The exponent κ adjusts the amount of transmission between the age groups and is to be estimated as part of the epidemic model component.…”

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

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Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture

2017

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Routine surveillance of notifiable infectious diseases gives rise to daily or weekly counts of reported cases stratified by region and age group. From a public health perspective, forecasts of infectious disease spread are of central importance. We argue that such forecasts need to properly incorporate the attached uncertainty, so they should be probabilistic in nature. However, forecasts also need to take into account temporal dependencies inherent to communicable diseases, spatial dynamics through human travel and social contact patterns between age groups. We describe a multivariate time series model for weekly surveillance counts on norovirus gastroenteritis from the 12 city districts of Berlin, in six age groups, from week 2011/27 to week 2015/26. The following year (2015/27 to 2016/26) is used to assess the quality of the predictions. Probabilistic forecasts of the total number of cases can be derived through Monte Carlo simulation, but first and second moments are also available analytically. Final size forecasts as well as multivariate forecasts of the total number of cases by age group, by district and by week are compared across different models of varying complexity. This leads to a more general discussion of issues regarding modelling, prediction and evaluation of public health surveillance data. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: Norovirus Gastroenteritis Surveillance Datamentioning

confidence: 99%

o_{r^{'} r}

between regions

r^{'}

and r as distance measure:

w_{r^{'} r} = {(o_{r^{'} r} + 1)}^{- ρ} .

Here, adjacent regions r and

r^{'}

have order

o_{r^{'} r} = 1

, regions where we need to traverse one other region are of order 2 and higher orders are defined accordingly. The power parameter ρ is treated as unknown and estimated from the data.…”

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

“…Again, we include an indicator x t for the Christmas break and let seasonal terms enter both components, where we now assume age group‐specific seasonality with coefficients

γ_{g}^{(ν)}

and

δ_{g}^{(ν)}

ϕ_{g r t} \propto e_{g r}^{τ}

causes the amount of disease transmission to scale with the population size e g r of the ‘importing’ age group g in region r – with unknown coefficient τ .…”

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

“…Note that social contacts are reciprocal at the population level, that is, there is an equal number of contacts between age group g and

g^{'}

as between age group

g^{'}

and g , which has been taken into account appropriately . We finally specify a power transformation for the contact matrix ,

c_{g^{'} g} = {(C^{κ})}_{g^{'} g} where C^{κ} : = E {normalΛ}^{κ} E^{- 1},

Section: Endemic–epidemic Models For Infectious Disease Countsmentioning

confidence: 99%

See 2 more Smart Citations

Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture

2017

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“…A common work-around is to introduce predetermined intermittent development stages to account for the different characteristics of each stage and the time it takes to pass from one to another. This approach has been used in various modelling frameworks including deterministic, stochastic, as well as discrete- and continuous-time models 4– 7 . Although intermittent development stages are capable of representing age-structured populations to a certain extent, a large number of age classes are required for accuracy.…”

Section: Introduction: the Age-structured Population Dynamics Modelmentioning

confidence: 99%

sPop: Age-structured discrete-time population dynamics model in C, Python, and R

Erguler

2018

F1000Res

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This article describes the sPop packages implementing the deterministic and stochastic versions of an age-structured discrete-time population dynamics model. The packages enable mechanistic modelling of a population by monitoring the age and development stage of each individual. Survival and development are included as the main effectors and they progress at a user-defined pace: follow a fixed-rate, delay for a given time, or progress at an age-dependent manner. The model is implemented in C, Python, and R with a uniform design to ease usage and facilitate adoption. Early versions of the model were previously employed for investigating climate-driven population dynamics of the tiger mosquito and the chikungunya disease spread by this vector. The sPop packages presented in this article enable the use of the model in a range of applications extending from vector-borne diseases towards any age-structured population including plant and animal populations, microbial dynamics, host-pathogen interactions, infectious diseases, and other time-delayed epidemiological processes.

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A zero‐inflated endemic–epidemic model with an application to measles time series in Germany

Meyer

2023

Biometrical J

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Count data with an excess of zeros are often encountered when modeling infectious disease occurrence. The degree of zero inflation can vary over time due to nonepidemic periods as well as by age group or region. A well‐established approach to analyze multivariate incidence time series is the endemic–epidemic modeling framework, also known as the HHH approach. However, it assumes Poisson or negative binomial distributions and is thus not tailored to surveillance data with excess zeros. Here, we propose a multivariate zero‐inflated endemic–epidemic model with random effects that extends HHH. Parameters of both the zero‐inflation probability and the HHH part of this mixture model can be estimated jointly and efficiently via (penalized) maximum likelihood inference using analytical derivatives. We found proper convergence and good coverage of confidence intervals in simulation studies. An application to measles counts in the 16 German states, 2005–2018, showed that zero inflation is more pronounced in the Eastern states characterized by a higher vaccination coverage. Probabilistic forecasts of measles cases improved when accounting for zero inflation. We anticipate zero‐inflated HHH models to be a useful extension also for other applications and provide an implementation in an R package.

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Incorporating social contact data in spatio-temporal models for infectious disease spread

Cited by 49 publications

References 39 publications

Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture

Probabilistic forecasting in infectious disease epidemiology: the 13th Armitage lecture

sPop: Age-structured discrete-time population dynamics model in C, Python, and R

A zero‐inflated endemic–epidemic model with an application to measles time series in Germany

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