A novel mathematical model of seasonality in Oropouche virus transmission in Amazonas, Brazil

Oropouche virus (OROV) is a vector-borne arbovirus that has caused more than 500,000 infections across South America, Central America, and the Caribbean. Its primary vector, the midge species Culicoides paraensis, acquires the virus from wild reservoir hosts and transmits it to humans during blood feeding. As outbreaks within the Amazon basin continue to occur and confirmed cases steadily increase, a proper understanding of the interplay between climatic variables, vector behavior, and OROV transmission is needed to develop effective public health interventions. In this paper, we develop a novel mathematical model of Oropouche virus spread in Amazonas, Brazil using ordinary differential equations (ODEs). First, we derive the basic reproductive number at baseline to assess the potential for disease persistence. We then incorporate seasonal forcing and fit the model to weekly incidence data from the 2023-2024 outbreak using least squares optimization. With our model structure, we evaluated multiple candidate seasonality functions and implementations, including precipitation-based forcing functions and others intended to model general seasonality or the right-skewed incidence curve. Among these, quantitative results show that the seasonal variation in OROV transmission is best explained (in the sense of minimum $l^2$ error) by an exponentially decaying pulse applied to midge recruitment, which captures the incidence data with a relative $l^2$ error of 11.94%. While moderate levels of observational noise can affect the relative ranking of seasonal mechanisms, the exponential pulse remained the best-performing forcing function to describe the observed incidence data.