Phase transitions and hysteresis of cooperative contagion processes

Chen, Li; Ghanbarnejad, Fakhteh; Brockmann, Dirk

We investigate the effects of cooperation between two interacting infectious diseases that spread and stabilize in a host population. We propose a model in which individuals that are infected with one disease are more likely to acquire the second disease, both diseases following the susceptible-infected-susceptible reaction scheme. We analyze cooperative coinfection in stochastic network models as well as the idealized, well-mixed mean field system and show that cooperative mechanisms dramatically change the nature of phase transitions compared to single disease dynamics. We show that, generically, cooperative coinfection exhibits discontinuous transitions from the disease free to high prevalence state when a critical transmission rate is crossed. Furthermore, cooperative coinfection exhibits two distinct critical points, one for outbreaks the second one for eradication that can be substantially lower. This implies that cooperative coinfection exhibits hysteresis in its response to changing effective transmission rates or equivalently the basic reproduction number. We compute these critical parameters as a function of a cooperativity coefficient in the well-mixed mean field system. We finally investigate a spatially extended version of the model and show that cooperative interactions between diseases change the general wave propagation properties of conventional spreading phenomena of single diseases. The presented work may serve as a starting and reference point for a more comprehensive understanding of interacting diseases that spread in populations.