Applying a multi-strain dengue model to epidemics data.

Dengue disease transmission is a complex vector-borne disease, mainly due to the co-circulation of four serotypes of the virus. Mathematical models have proved to be a useful tool to understand the complexity of this disease. In this work, we extend the model studied by Esteva et al., 2003, originally proposed for two serotypes, to four circulating serotypes. Using epidemic data of dengue fever in Iquitos (Peru) and San Juan (Puerto Rico), we estimate numerically the co-circulation parameter values for selected outbreaks using a bootstrap method, and we also obtained the Basic Reproduction Number, R, for each serotype, using both analytical calculations and numerical simulations. Our results indicate that the impact of co-circulation of serotypes in population dynamics of dengue infection is such that there is a reduced effect from DENV-3 to DENV-4 in comparison to no-cross effect for epidemics in Iquitos. Concerning San Juan epidemics, also comparing to no-cross effect, we also observed a reduced effect from the predominant serotype DENV-3 to both DENV-2 and DENV-1 epidemics neglecting the very small number of cases of DENV-4.