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Abstract A dramatic increase in the number of outbreaks of dengue has recently been reported, and climate change is likely to extend the geographical spread of the disease. In this context, this paper shows how a neural network approach can incorporate dengue and COVID-19 data as well as external factors (such as social behaviour or climate variables), to develop predictive models that could improve our knowledge and provide useful tools for health policy makers. Through the use of neural networks with different social and natural parameters, in this paper we define a Correlation Model through which we show that the number of cases of COVID-19 and dengue have very similar trends. We then illustrate the relevance of our model by extending it to a Long short-term memory model (LSTM) that incorporates both diseases, and using this to estimate dengue infections via COVID-19 data in countries that lack sufficient dengue data. 

Through the action of an anti-holomorphic involution $$\sigma$$ (a real structure) on a Riemann surface $$X$$, we consider the induced actions on $${\rm SL}(r,\mathbb{C})$$-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of $${\rm SL}(r,\mathbb{C})$$-opers, we are able to give a natural parametrization of the fixed point locus via differentials on the Riemann surface, which in turn allows us to study their geometric properties.