Diversity of hysteresis in a fully cooperative coinfection model

We propose a fully cooperative coinfection model in which singly infected individuals are more likely to acquire a second disease than susceptible ones and doubly infected individuals are also assumed to be more contagious than singly infected ones. The dynamics of such a fully cooperative coinfection model is investigated through the well-mixed approach. In particular, discontinuous outbreak transitions from the disease free state or the low prevalence state to the high prevalence state can be separately observed as a disease transmission rate crosses a threshold α_o from the below when the epidemic is still in the early stages. Moreover, discontinuous eradications from the high prevalence state to the low prevalence or disease free state are also separately seen as the transmission rate reaches a threshold α_e(<α_o) from the above when the outbreak occurs. Such phenomena constitute three types of hysteresis, where only one type has been identified before. Complete characterization of these three types of hysteresis in terms of parameters measuring the uniformity of the model is both analytically and numerically provided.