Optimal curing rate allocation in the SIS epidemic model

We consider a susceptible-infected-susceptible (SIS) epidemic model on an undirected graph, with a homogeneous infection rate and heterogeneous curing rates. We set an overall network curing rate, $\Delta$, and study optimal allocation of curing rates to nodes, in terms of the expected time to the extinction of the epidemic. As other parameters are fixed, we study these allocations as the infection rate tends to 0 and $\infty$ in both regular and non-regular graphs. We further illustrate this optimisation with some numerical examples. Our findings demonstrate that, while the uniform split of $\Delta$ is optimal in some situations, it is typically not optimal, even for regular graphs.