Substance abuse impedes the productivity of the labour force and reduces economic growth. Efficient management of an organization’s workforce must involve eradicating drug use. In this paper, we formulate a mathematical productivity epidemiological model for the substance abuse transmission dynamics that includes intervention strategies. In particular, we investigate the productivity of organizational labour force with enlightenment/monitoring, preventive and treatment measures in enhancing workforce output in the presence of substance abuse. We use the model to estimate the cost of the non-productive individuals to organizations as well as project the benefits when the employees have access to interventions. We calculate the basic reproduction number and investigate the existence and stability of equilibria. We also investigate the sensitivity of the basic reproductive number to the model’s parameters and use Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Numerical simulations are performed to illustrate the analytical results. Finally, we use incremental cost effectiveness ratios to identify the optimal combination.

substance abuse; reproduction number; optimal control; numerical simulation; cost effectiveness