Optimal implementation of intervention strategies for elderly people with ludomania.
OBJECTIVE
Now-a-days gambling is growing especially fast among older adults. To control the gratuitous growth of gambling, well-analyzed scientific strategies are necessary. We tried to analyze the adequacy of the health of society mathematically through immediate treatment of patients with early prevention.


METHODS
The model from Lee and Do was modified and control parameters were introduced. Pontryagin's Maximum Principle was used to obtain an optimal control strategy.


RESULTS
Optimal control can be achieved through simultaneous use of the control parameters, though it varies from society to society. The control corresponding to prevention needed to be implemented in full almost all the time for all types of societies. In the case of the other two controls, the scenario was greatly affected depending on the types of societies.


CONCLUSIONS
Prevention and treatment for elderly people with ludomania are the main intervention strategies. We found that optimal timely implementation of the intervention strategies was more effective. The optimal control strategy varied with the initial number of gamblers. However, three intervention strategies were considered, among which, preventing people from engaging in all types of gambling proved to be the most crucial.
Department of Mathematics, Kyungpook National University, Daegu, Korea.
Byul Nim
BN
Kim
Department of Mathematics, Kyungpook National University, Daegu, Korea.
M A
MA
Masud
Department of Mathematics, Kyungpook National University, Daegu, Korea.
Yongkuk
Y
Kim
basic reproduction number; epidemiological model; gambling; maximal principle; optimal control