Harvesting-induced recovery from prey extinction

Consider the predator-prey model given by Equation (HarvestingEqn), and let $q^*$ denote the harvesting threshold appearing in the conjecture. Here $q$ is the predator-harvesting effort, $c_1$ and $c_2$ are positive comparison levels, and the solution to the prey equation describes the prey population. Harvesting-induced recovery conjecture. There exists a harvesting effort satisfying

$$0<c_1<q^*<c_2$$

such that the solution to the prey equation does not go extinct in finite time; in particular, for these levels of predator harvesting, the solution can be driven to a coexistence state if initiated from certain initial conditions. The conjecture proposes that an intermediate range of predator harvesting can prevent finite-time prey extinction and promote coexistence; the supplied text gives no resolution, so it remains open.