Prevention and cure efforts both substitute and complement

Suppose one could expend effort to prevent probabilistic transition to an adverse state, and also effort to expedite probabilistic transition to a beneficial state. Bearing in mind that the efforts occur in different states, should these efforts substitute or complement? Two appealing arguments are in conflict. If cure effort is costly, then the incentive to prevent should be high in order to avoid future cure effort costs, i.e. efforts are gross substitutes in demand. If prevention effort is costly, then the incentive to cure should be low since recidivism is likely, i.e. efforts complement. In a lifetime present value model, we show that both arguments have merit. We also show that the prevalence of the adverse state can rise with a subsidy on cure effort costs.