Epidemic spreading under infection-reduced-recovery

The pandemic transition is a hallmark of current epidemiological models, predicting a continuous shift from a healthy to a pandemic state, whose critical point is driven by the parameters of the disease, e.g., its infection, recovery or mortality rates. These parameters, characterizing the disease cycle, are tuned by the biological characteristics of the pathogen, capturing its natural time-scales, often considered independent of the state of the spread itself. If, however, the disease gains a population-wide impact, its prevalence may exceed the health-care system capacity, resulting in sub-optimal treatment, and hence a potential feedback mechanism, in which the disease cycle is no longer decoupled from the state of the spread. Such dependence was demonstrated during the spread of COVID-19, for instance, where hard-hit places showed elevated mortality rates, likely due to an over-stressed health-care system. We therefore introduce an infection-reduced recovery mechanism, linking an individual's rate of recovery to the prevalence of the disease. The outcome, we show, may have dramatic consequences on the observed patterns of spread. For instance, under rather broad conditions, the pandemic transition becomes discontinuous, exhibiting an abrupt shift from a healthy to a pandemic state. In some cases the disease reaches population-wide coverage even below the classically predicted critical transition point. We also observe a potential multi-stability and hysteresis, capturing an irreversible pandemic transition, in which overcoming the disease requires us to quench infection rates significantly below the critical threshold. These findings not only provide hints on the current difficulties to contain COVID-19, but more broadly, they set the bar for sustaining a stably functioning treatment capacity in the face of population-wide demand.