We then extend the simple model above by introducing an additional parameter to understand to what extent the transmission within species is altered by between species transmission. The parameter r quantifies the degree to which mixing between species is assortative -with r,1 representing assortative mixing and r.1 disassortative mixing. The interaction model still assumes constant parameters with respect to time along the whole observation period T. The mixing matrix defined in equation (2) becomes S c I c rS c I s rS s I c S s I s ð8Þ