Estimating the Attack Ratio of Dengue Epidemics under Time-varying Force of Infection using Aggregated Notification Data

Quantifying the attack ratio of disease is key to epidemiological inference and public health planning. For multi-serotype pathogens, however, different levels of serotype-specific immunity make it difficult to assess the population at risk. In this paper we propose a Bayesian method for estimation of the attack ratio of an epidemic and the initial fraction of susceptibles using aggregated incidence data. We derive the probability distribution of the effective reproductive number, Rt, and use MCMC to obtain posterior distributions of the parameters of a single-strain SIR transmission model with time-varying force of infection. Our method is showcased in a data set consisting of 18 years of dengue incidence in the city of Rio de Janeiro, Brazil. We demonstrate that it is possible to learn about the initial fraction of susceptibles and the attack ratio even in the absence of serotype specific data. On the other hand, the information provided by this approach is limited, stressing the need for detailed serological surveys to characterise the distribution of serotype-specific immunity in the population.

[1]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[2]  R. Nogueira,et al.  Dengue virus type 4 arrives in the state of Rio de Janeiro: a challenge for epidemiological surveillance and control. , 2011, Memorias do Instituto Oswaldo Cruz.

[3]  N Mantel,et al.  Confidence limits on the ratio of two Poisson variables. , 1974, American journal of epidemiology.

[4]  F. B. Santos,et al.  Dengue virus surveillance: the co-circulation of DENV-1, DENV-2 and DENV-3 in the State of Rio de Janeiro, Brazil. , 2004, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[5]  Sataya D. Dubey,et al.  Compound gamma, beta and F distributions , 1970 .

[6]  O. Bjørnstad,et al.  Dynamics of measles epidemics: Estimating scaling of transmission rates using a time series sir model , 2002 .

[7]  M. Ravenel.  The Principles of Epidemiology and the Process of Infection , 1931 .

[8]  Aaron A. King,et al.  Time-varying, serotype-specific force of infection of dengue virus , 2014, Proceedings of the National Academy of Sciences.

[9]  Cláudia Torres Codeço,et al.  Spatial Evaluation and Modeling of Dengue Seroprevalence and Vector Density in Rio de Janeiro, Brazil , 2009, PLoS neglected tropical diseases.

[10]  M. Gomes,et al.  On the Final Size of Epidemics with Seasonality , 2009, Bulletin of mathematical biology.

[11]  D. Higdon,et al.  Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self-Adaptive Randomized Subspace Sampling , 2009 .

[12]  H. Schatzmayr,et al.  Dengue in the State of Rio de Janeiro, Brazil, 1986-1998. , 1999, Memorias do Instituto Oswaldo Cruz.

[13]  Jinn-Guey Lay,et al.  Higher temperature and urbanization affect the spatial patterns of dengue fever transmission in subtropical Taiwan. , 2009, The Science of the total environment.

[14]  Pejman Rohani,et al.  Interactions between serotypes of dengue highlight epidemiological impact of cross-immunity , 2013, Journal of The Royal Society Interface.

[15]  A. Mira.  On Metropolis-Hastings algorithms with delayed rejection , 2001 .

[16]  E. S. Pearson,et al.  THE USE OF CONFIDENCE OR FIDUCIAL LIMITS ILLUSTRATED IN THE CASE OF THE BINOMIAL , 1934 .

[17]  C. Codeço,et al.  Temporal Distribution of Aedes aegypti in Different Districts of Rio De Janeiro, Brazil, Measured by Two Types of Traps , 2009, Journal of medical entomology.

[18]  Tom Starzl,et al.  THE LANCET , 1992, The Lancet.

[19]  M. Gabriela M. Gomes,et al.  A Bayesian Framework for Parameter Estimation in Dynamical Models , 2011, PloS one.

[20]  Heloísa Helena Pelluci Duarte,et al.  [Data quality of dengue epidemiological surveillance in Belo Horizonte, Southeastern Brazil]. , 2006, Revista de saude publica.

[21]  A. Galvani,et al.  Disability adjusted life years lost to dengue in Brazil , 2009, Tropical medicine & international health : TM & IH.

[22]  Rosanna W. Peeling,et al.  Dengue: a continuing global threat , 2010, Nature Reviews Microbiology.

[23]  H. Schatzmayr,et al.  Virological surveillance for early warning of dengue epidemics in the State of Rio de Janeiro, Brazil. , 2013, Transactions of the Royal Society of Tropical Medicine and Hygiene.

[24]  Attack rates of seasonal epidemics. , 2012, Mathematical biosciences.

[25]  E. B. Wilson.  Probable Inference, the Law of Succession, and Statistical Inference , 1927 .

[26]  M. Kretzschmar,et al.  Reconstruction of measles dynamics in a vaccinated population. , 2003, Vaccine.

[27]  J. Wallinga,et al.  The ideal reporting interval for an epidemic to objectively interpret the epidemiological time course , 2010, Journal of The Royal Society Interface.

[28]  Derek A T Cummings,et al.  Revealing the microscale spatial signature of dengue transmission and immunity in an urban population , 2012, Proceedings of the National Academy of Sciences.