  In this paper, we introduce a general framework for co-infection as
cooperative SIR dynamics. We first solve analytically CGCG model [1] and then
the generalized model in symmetric scenarios. We calculate transition points,
order parameter, i.e. total number of infected hosts. Also we show analytically
there is a saddle-node bifurcation for two cooperative SIR dynamics and the
transition is hybrid. Moreover, we investigate where symmetric solution is
stable for initial fluctuations. Then we study asymmetric cases of parameters.
The more asymmetry, for the primary and secondary infection rates of one
pathogen in comparison to the other pathogen, can lead to the less infected
hosts, the higher epidemic threshold and continuous transitions. Our model and
results for co-infection in combination with super-infection [2] can open a
road to model disease ecology.
