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

Dengue, 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 R 0 from epidemic data using different methodologies applied to different epidemic models in order to evaluate the robustness of our estimate.

We 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 R 0 is initially greater than unity leading to an epidemic outbreak. However, control measures implemented several weeks after the initial outbreak successfully reduce R 0 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 R 0, 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.

In conclusion, we have obtained robust estimates for the value of the basic reproduction number R 0 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 R 0 across the different methodologies. Nevertheless, there are also significant differences between the estimates for the post-control value of R 0 across the two different models.