A pair formation model with recovery: Application to mpox

The current global outbreaks of mpox is a unique infectious disease in the way it seems to be transmitting: it has been observed to be highly concentrated in communities of men who have sex with men (MSM) through pair formation, and also provides long lasting immunity. This framework of mostly close, prolonged contact spreading a disease that admits immunity after infection is unlike similar infections which either offer little to no immunity post-infection or are lifelong infections. This creates the need for a new model framework that incorporates pair formation structure with recovery. While seemingly a straight forward model, we show how new dynamics arise from the combination of pair formation and recovery that are not present in a standard model with recovery and also not present in a pair formation model without recovery. We see that the combination of these two properties allows for waves of infection that are not seen in a standard SIR model. These dynamics suggest that outbreaks of mpox around the world may require special attention from public health. We also derive a reproduction number for this model and estimate the reproduction number of human mpox to be $\approx 2.3$ using global and Canadian data. The expression derived for $R_0$ can help estimate key parameters for diseases transmission and public health interventions and compare to equivalent models without pair formation.