An approach for modeling cross-immunity of two strains, with application to variants of Bartonella in terms of genetic similarity

• Proposed is a two-strain SIR model for cross-immunity with proportions.
• The proposed model accounts for seasonality in the birth rate.
• We found partial cross-immunity between some Bartonella variants.

We developed a two-strain susceptible-infected-recovered (SIR) model that provides a framework for inferring the cross-immunity between two strains of a bacterial species in the host population with discretely sampled co-infection time-series data. Moreover, the model accounts for seasonality in host reproduction. We illustrate an approach using a dataset describing co-infections by several strains of bacteria circulating within a population of cotton rats (Sigmodon hispidus). Bartonella strains were clustered into three genetically close groups, between which the divergence is correspondent to the accepted level of separate bacterial species. The proposed approach revealed no cross-immunity between genetic clusters while limited cross-immunity might exist between subgroups within the clusters.