Estimating the basic reproduction number for single-strain dengue fever epidemics

BackgroundDengue, an infectious tropical disease, has recently emerged as one of the most important mosquito-borne viral diseases in the world. We perform a retrospective analysis of the 2011 dengue fever epidemic in Pakistan in order to assess the transmissibility of the disease. We obtain estimates of the basic reproduction number R0 from epidemic data using different methodologies applied to different epidemic models in order to evaluate the robustness of our estimate.ResultsWe first estimate model parameters by fitting a deterministic ODE vector-host model for the transmission dynamics of single-strain dengue to the epidemic data, using both a basic ordinary least squares (OLS) as well as a generalized least squares (GLS) scheme. Moreover, we perform the same analysis for a direct-transmission ODE model, thereby allowing us to compare our results across different models. In addition, we formulate a direct-transmission stochastic model for the transmission dynamics of dengue and obtain parameter estimates for the stochastic model using Markov chain Monte Carlo (MCMC) methods. In each of the cases we have considered, the estimate for the basic reproduction number R0 is initially greater than unity leading to an epidemic outbreak. However, control measures implemented several weeks after the initial outbreak successfully reduce R0 to less than unity, thus resulting in disease elimination. Furthermore, it is observed that there is strong agreement in our estimates for the pre-control value of R0, both across different methodologies as well across different models. However, there are also significant differences between our estimates for the post-control value of the basic reproduction number across the two different models.ConclusionIn conclusion, we have obtained robust estimates for the value of the basic reproduction number R0 associated with the 2011 dengue fever epidemic before the implementation of public health control measures. Furthermore, we have shown that there is close agreement between our estimates for the post-control value of R0 across the different methodologies. Nevertheless, there are also significant differences between the estimates for the post-control value of R0 across the two different models.

[1]  G. Roberts,et al.  Bayesian inference for partially observed stochastic epidemics , 1999 .

[2]  D. Gubler,et al.  Dengue and Dengue Hemorrhagic Fever , 1998, Clinical Microbiology Reviews.

[3]  N. Bailey,et al.  A simple stochastic epidemic. , 1950, Biometrika.

[4]  Duane J. Gubler,et al.  Chapter 72 – Dengue and Dengue Hemorrhagic Fever , 2006 .

[5]  D. Earn,et al.  Cholera Epidemic in Haiti, 2010: Using a Transmission Model to Explain Spatial Spread of Disease and Identify Optimal Control Interventions , 2011, Annals of Internal Medicine.

[6]  Simon E. F. Spencer,et al.  Stochastic epidemic models for emerging diseases , 2008 .

[7]  Abba B. Gumel,et al.  Effect of cross-immunity on the transmission dynamics of two strains of dengue , 2010, Int. J. Comput. Math..

[8]  M. Robinson,et al.  Dengue virus infection: epidemiology, pathogenesis, clinical presentation, diagnosis, and prevention. , 1997, The Journal of pediatrics.

[9]  H. Margolis,et al.  Health Economics of Dengue: A Systematic Literature Review and Expert Panel's Assessment , 2011, The American journal of tropical medicine and hygiene.

[10]  Salisu M. Garba,et al.  Backward bifurcations in dengue transmission dynamics. , 2008, Mathematical biosciences.

[11]  Edward C Holmes,et al.  The origin, emergence and evolutionary genetics of dengue virus. , 2003, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[12]  David A. Flores,et al.  Discrete-time deterministic and stochastic models for the spread of rabies , 2002, Appl. Math. Comput..

[13]  F. Barreto,et al.  Stochastic dynamics of dengue epidemics. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  N. Ferguson,et al.  The effect of antibody-dependent enhancement on the transmission dynamics and persistence of multiple-strain pathogens. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Akira Sasaki,et al.  Why are dengue virus serotypes so distantly related? Enhancement and limiting serotype similarity between dengue virus strains , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[16]  M. Keeling,et al.  On methods for studying stochastic disease dynamics , 2008, Journal of The Royal Society Interface.

[17]  S. Blower,et al.  Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. , 1997, American journal of epidemiology.

[18]  Harvey Thomas Banks,et al.  An Inverse Problem Statistical Methodology Summary , 2007 .

[19]  B. Finkenstädt,et al.  Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention: Ebola as a Case Study , 2006, Biometrics.

[20]  Pejman Rohani,et al.  Ecological and immunological determinants of dengue epidemics. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[21]  L. Allen,et al.  Comparison of deterministic and stochastic SIS and SIR models in discrete time. , 2000, Mathematical biosciences.

[22]  J. Hyman,et al.  Estimation of the reproduction number of dengue fever from spatial epidemic data. , 2007, Mathematical biosciences.

[23]  Luís M A Bettencourt,et al.  The estimation of the effective reproductive number from disease outbreak data. , 2009, Mathematical biosciences and engineering : MBE.

[24]  Lourdes Esteva,et al.  A model for dengue disease with variable human population , 1999, Journal of mathematical biology.

[25]  L. Allen,et al.  Stochastic epidemic models with a backward bifurcation. , 2006, Mathematical biosciences and engineering : MBE.

[26]  Lourdes Esteva,et al.  Coexistence of different serotypes of dengue virus , 2003, Journal of mathematical biology.

[27]  L. Allen.  An introduction to stochastic processes with applications to biology , 2003 .

[28]  Niranjan Kissoon,et al.  Dengue hemorrhagic fever and shock syndromes* , 2011, Pediatric critical care medicine : a journal of the Society of Critical Care Medicine and the World Federation of Pediatric Intensive and Critical Care Societies.

[29]  George H. Weiss,et al.  On the asymptotic behavior of the stochastic and deterministic models of an epidemic , 1971 .

[30]  Chandra Shekhar,et al.  Deadly dengue: new vaccines promise to tackle this escalating global menace. , 2007, Chemistry & biology.

[31]  J. Hyman,et al.  The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. , 2004, Journal of theoretical biology.

[32]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[33]  J A Jacquez,et al.  Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations. , 1991, Mathematical biosciences.

[34]  L. Esteva,et al.  Analysis of a dengue disease transmission model. , 1998, Mathematical biosciences.