MODELING A REHAB–RECOVERY–RELAPSE CYCLE WITH COMMUNITY DEPENDENCE VIA ODES

In this paper, we introduce a rehab-recovery-relapse cycle model to study the interaction between healthy individuals, individuals that might develop substance use disorders (SUD), which for simplicity here we will call susceptible individuals, individuals with SUD, and individuals recovered in a rehab community. We measure the community's health through a system defined by four non-linear ordinary differential equations in which we include a rehab community. After computing the SUD-free and coexistence equilibrium points, we find the feasibility and stability conditions of an equivalent and reduced system obtained by nondimensionalizing the equations of the original model. We have numerically investigated the importance of the parameter values on the model's outcome via a one- and two-strain parameter analysis. From the numerical results, we observe that an efficient rehab community can be characterized by (i) a high recovery rate (the individuals stay in that community as little time as possible) and (ii) permanent rehabilitation being preferred at the expense of a low recovery rate.