A Poisson-multinomial spatial model for simultaneous outbreaks with application to arboviral diseases

Dengue, Zika, and chikungunya are arboviral diseases (AVD) transmitted mainly by Aedes aegypti. Rio de Janeiro city, Brazil, has been endemic for dengue for over 30 years, and experienced the first joint epidemic of the three diseases between 2015-2016. They present similar symptoms and only a small proportion of cases are laboratory-confirmed. These facts lead to potential misdiagnosis and, consequently, uncertainty in the registration of the cases. We have available the number of cases of each disease for the $n=160$ neighborhoods of Rio de Janeiro. We propose a Poisson model for the total number of cases of Aedes-borne diseases and, conditioned on the total, we assume a multinomial model for the allocation of the number of cases of each of the diseases across the neighborhoods. This provides simultaneously the estimation of the associations of the relative risk of the total cases of AVD with environmental and socioeconomic variables; and the estimation of the probability of presence of each disease as a function of available covariates. Our findings suggest that a one standard deviation increase in the social development index decreases the relative risk of the total cases of AVD by 28%. Neighborhoods with smaller proportion of green area had greater odds of having chikungunya in comparison to dengue and Zika. A one standard deviation increase in population density decreases the odds of a neighborhood having Zika instead of dengue by 18% but increases the odds of chikungunya in comparison to dengue by 18% and by 43% in comparison to Zika.