Modeling seasonality of the Babesia canis infection using SEIRS model with periodic contact rate

Babesia canis is a canine tick-borne protozoan that can cause acute illness in dogs. Seasonal meteorological factors affect the tick vector activity, thus drive the infection, while climate change reshapes the global map of the tick habitat and the disease prevalence. Clinical characteristics of the infection have been investigated, but the existing body of knowledge has not yet been synthesized in a mathematical model. We here develop a SEIRS-type model to describe the annual prevalence and bi-annual seasonality of the B. canis infection. Specifically, we introduce a time-dependent, periodic rate for conversion of the susceptible dogs into the dogs exposed to the infection, which reproduces two seasonal maxima in the number of infected dogs. The height and timing of the seasonal peaks are modulated by a periodic annual term in the rate function. Varying other model parameters further shows that the length of the mean immunity period is inversely proportional to the number of infected dogs outside the peak seasons, the mean incubation period weakly affects the height of the seasonal peaks and only slightly changes their timing, and the mean infection period governs the ratio of the newly infected dogs and currently infected dogs. Our model reproduces well the temporal evolution seen in the published canine babesiosis data. Further, fitting the model to a selected B. canis data set yields temporal characteristics of the B. canis infection comparable to those reported in the literature, allowing for a future investigation into the underlying physical factors that govern the contact rate.