Reconstruction of the seasonally varying contact rate for measles

Kalivianakis, M; Mous, S.L.J.; Grasman, J.

doi:10.1016/0025-5564(94)90044-2

Cited by 16 publications

(9 citation statements)

References 7 publications

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“…Age structure is a critical factor when analysing the impact of immunization policies [1}6], while seasonality is important for analysing incidence patterns [7,8].…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France

2000

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“…Age structure is a critical factor when analysing the impact of immunization policies [1}6], while seasonality is important for analysing incidence patterns [7,8].…”

Section: Introductionmentioning

confidence: 99%

“…SEIR models have no age structure, but can accommodate rather general time dependence of the contact rate while keeping the number of parameters to a reasonable level. Such an approach was used by Kalivianakis et al [8], who estimated the contact rate function for measles by Kalman "ltering within a SEIR model.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France

2000

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“…Exploring rubella dynamics, a 1980 study used a sinusoidal function to model seasonality of rubella . Overall, 55 studies (40%) explicitly included seasonality by modeling it empirically, using school (or term) timing, assuming a sinusoidal function, exploring multiple formulations, considering the impacts of seasonality in births, or tracing specific agricultural conditions . Despite the number of studies, collectively they provide variable insights about the best strategy.…”

Section: Resultsmentioning

confidence: 99%

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

Thompson¹

2016

Risk Analysis

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The devastation caused by periodic measles outbreaks motivated efforts over more than a century to mathematically model measles disease and transmission. Following the identification of rubella, which similarly presents with fever and rash and causes congenital rubella syndrome (CRS) in infants born to women first infected with rubella early in pregnancy, modelers also began to characterize rubella disease and transmission. Despite the relatively large literature, no comprehensive review to date provides an overview of dynamic transmission models for measles and rubella developed to support risk and policy analysis. This systematic review of the literature identifies quantitative measles and/or rubella dynamic transmission models and characterizes key insights relevant for prospective modeling efforts. Overall, measles and rubella represent some of the relatively simplest viruses to model due to their ability to impact only humans and the apparent life-long immunity that follows survival of infection and/or protection by vaccination, although complexities arise due to maternal antibodies and heterogeneity in mixing and some models considered potential waning immunity and reinfection. This review finds significant underreporting of measles and rubella infections and widespread recognition of the importance of achieving and maintaining high population immunity to stop and prevent measles and rubella transmission. The significantly lower transmissibility of rubella compared to measles implies that all countries could eliminate rubella and CRS by using combination of measles- and rubella-containing vaccines (MRCVs) as they strive to meet regional measles elimination goals, which leads to the recommendation of changing the formulation of national measles-containing vaccines from measles only to MRCV as the standard of care.

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“…We denote the time-dependent transmission parameter by β(t); it is traditionally defined by [20,27] β(t)…”

Section: Motivating Seasonal Seirs Model With Demographymentioning

confidence: 99%

A sensitivity matrix based methodology for inverse problem formulation

Cintrón-Arias¹,

Banks²,

Capaldi³

et al. 2009

Journal of Inverse and Ill-Posed Problems

114

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We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that correspond to sensitivity matrices with full rank. Second, the algorithm involves uncertainty quantification by using the inverse of the Fisher Information Matrix. Nominal values of parameters are used to construct synthetic data sets, and explore the effects of removing certain parameters from those to be estimated using OLS procedures. We quantify these effects via a score for a vector parameter defined using the norm of the vector of standard errors for components of estimates divided by the estimates. In some cases the method leads to reduction of the standard error for a parameter to less than 1% of the estimate.

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Reconstruction of the seasonally varying contact rate for measles

Cited by 16 publications

References 7 publications

Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France

Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France

Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis

A sensitivity matrix based methodology for inverse problem formulation

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