Co-circulation of Dengue and Zika viruses: A modelling approach applied to epidemics data

Since the 1980s, the prevalence of diseases caused by arboviruses, in particular, those transmitted by Aedes Aegypti mosquitoes have increased in the Americas. The diseases transmitted by this mosquito include Dengue, Zika, and Chikungunya, which are endemic diseases in the region between the tropics. It is relevant to investigate the effect of virus co-circulation in the transmission of these diseases because there are evidences of both cross-protection and cross-enhancement among the viruses causing Zika and Dengue. In order to understand that effect, in this work we formulate an stochastic model, based on a previous deterministic model for co-circulation of Dengue serotypes. We applied both the deterministic and stochastic versions of the model to epidemics data of Dengue and Zika in Brazilian cities during 2015–2016. We use the deterministic model to calculate the basic reproductive number associated to the co-circulation of both diseases, and we show a non-trivial epidemic behavior associated to the entrance of Zika disease in 2015 in Brazil. Based on the stochastic model we evaluated the importance of the population size and the initial number of cases for the subsequent development of both diseases. Using actual data of simultaneous epidemics of dengue and Zika from Brazilian cities, we mainly find regions of the parameters compatible to cross protection of the population against the infections.