### Abrupt Epidemic Spreading

#### Speaker : Professor
Hans J. Herrmann

##### ETH Zurich, Switzerlandâ€‹

*Chair : Asst Professor Saskia E. Werners*

**Abstract : **

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill.Here a simple generalized Susceptible-Infected-Susceptible (SIS) model is used to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. The epidemics can spiral out of control into explosive spread, if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. Analytical expressions can be given for the critical cost and the size of the explosive jump in infection levels in terms the parameters that characterize the spreading process. The model and its results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process. The spread of an infection is also investigated when a system component can recover only if it remains reachable from a functioning central component. More precisely, infection spreads from infected to healthy nodes, with the constraint that infected nodes only recover, if they remain connected to a pre-defined central node, through a path that contains only healthy nodes.In this case, clusters of infected nodes will absorb their non-infected interior, because then no path exists between the central node and encapsulated nodes. This gives rise to the simultaneous infection of multiple nodes. Interestingly, the system converges to only one of two stationary states: either the whole population is healthy or it becomes completely infected. This simultaneous cluster infection can give rise to discontinuous jumps of different sizes in the number of failed nodes. Larger jumps emerge at lower infection rates. The network topology has an important effect on the nature of the transition: hysteresis appears for networks with dominating local interactions. The model shows how local spread can abruptly turn uncontrollable, when it disrupts connectivity at a larger spatial scale.
http://www.hans-herrmann.ethz.ch/