title: Optimal Implementation of Intervention to Control the Self-harm Epidemic.
abstract: OBJECTIVE
  Deliberate self-harm (DSH) of a young person has been a matter of growing concern to parents and policymakers. Prevention and early eradication are the main interventional techniques among which prevention through reducing peer pressure has a major role in reducing the DSH epidemic. Our aim is to develop an optimal control strategy for minimizing the DSH epidemic and to assess the efficacy of the controls.
  
  
  METHODS
  We considered a deterministic compartmental model of the DSH epidemic and two interventional techniques as the control measures. Pontryagin's Maximum Principle was used to mathematically derive the optimal controls. We also simulated the model using the forward-backward sweep method.
  
  
  RESULTS
  Simulation results showed that the controls needed to be used simultaneously to reduce DSH successfully. An optimal control strategy should be adopted, depending on implementation costs for the controls.
  
  
  CONCLUSIONS
  The long-term success of the optimum control depends on the implementation cost. If the cost is very high, the control could be used for a short term, even though it fails in the long run. The control strategy, most importantly, should be implemented as early as possible to attack a comparatively fewer number of addicted individuals.
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu, Korea.
authors.forename: Byul Nim
authors.initials: BN
authors.lastname: Kim
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu, Korea.
authors.forename: M A
authors.initials: MA
authors.lastname: Masud
authors.affiliation: Department of Mathematics, Kyungpook National University, Daegu, Korea.
authors.forename: Yongkuk
authors.initials: Y
authors.lastname: Kim
keywords: Pontryagin's Maximal Principle; contagious social issue; deliberate self-harm; epidemiological model; optimal control