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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.27 n.1 San José Jan./Jun. 2020

http://dx.doi.org/10.15517/rmta.v27i1.39952 

Artículo

Estimating age-specific hazard rates of infection from cross-sectional observations

Estimación de las tasas de infección de riesgo específicas de la edad a partir de observaciones transversales

Zhilan Feng1 

John W. Glasser2 

1Purdue University, Department of Mathematics, West Lafayette IN, United States; fengz@purdue.edu

2National Center for Immunization and Respiratory Diseases, CDC, Atlanta GA, United States; jglasser@cdc.gov

Abstract

Mathematical models of pathogen transmission in age-structured host populations, can be used to design or evaluate vaccination programs. For reliable results, their forces or hazard rates of infection (FOI) must be formulated correctly and the requisite contact rates and probabilities of infection on contact estimated from suitable observations. Elsewhere, we have described methods for calculating the probabilities of infection on contact from the contact rates and FOI. Here, we present methods for estimating the FOI from cross-sectional serological surveys or disease surveillance in populations with or without concurrent vaccination. We consider both continuous and discrete age, and present estimates of the FOI for vaccinepreventable diseases that confer temporary or permanent immunity.

Keywords: epidemiological model; force of infection; parameter estimation; cross-sectional observations; serology data.

Resumen

Los modelos matemáticos de transmisión de patógenos en poblaciones de huéspedes estructuradas por edad pueden usarse para diseñar o evaluar programas de vacunación. Para obtener resultados confiables, sus fuerzas o tasas de riesgo de infección (FOI) deben formularse correctamente y las tasas de contacto requeridas y las probabilidades de infección en contacto deben estimarse a partir de observaciones adecuadas. En otros lugares, hemos descrito métodos para calcular las probabilidades de infección por contacto a partir de las tasas de contacto y FOI. Aquí, presentamos métodos para estimar el FOI a partir de encuestas serológicas transversales o vigilancia de enfermedades en poblaciones con o sin vacunación concurrente. Consideramos tanto la edad continua como la discreta, y presentamos estimaciones del FOI para enfermedades prevenibles por vacunación que confieren inmunidad temporal o permanente.

Palabras clave: modelo epidemiológico; fuerza de infección; estimación de parámetros; observaciones transversales; datos serológicos.

Mathematics Subject Classification: 34C99, 35Q92, 92B05.

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Acknowledgement

ZF’s research is partially supported by NSF grant DMS-1814545.

References

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Received: May 12, 2019; Revised: August 14, 2019; Accepted: August 31, 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License