Modeling and Analysis of Unemployment Problem in Bangladesh using Optimal Control Technique

Unemployment problem has become most immense concerns all over the world. Unemployment can be defined as a state of workless for a person fit and willing to work. It is observed that the main reason for socio-economic damage, deletion of morality and social values is unemployment. With the increasing of unemployed population, other factors are significantly affected, such that the income per person, health costs, quality of health-care and poverty. But, according to the World Employment Social Outlook of ILO in 2017, Global unemployment levels and rates were predicted to remain high in the short term, as the global labour force continues to grow. In particular, the global unemployment rate was predicted to rise modestly in 2017 to 5.8 per cent (from 5.7 per cent in 2016) representing 3.4 million more unemployed people globally (bringing total unemployment to just over 201 million

in 2017). So unemployment is one of the most serious issues for every country, specially in a densely populated developing country. Unemployment issue is significantly an alarming concern in Bangladesh as well. A large portions of young energetic people in Bangladesh are unemployed which may cause main obstacle in achieving a sustainable economic growth. Although, unemployment rate in Bangladesh has decreased to 4.20 percent in 2019 from 4.30 percent in 2018 (source: World Bank), it is still crucial to reduce the unemployment rate in a significant fashion for a stable and strong economy of the country to meet the challenge of Sustainable Development Goals (SDGs). 

In recent years, mathematical models have become very important tools in analyzing the changing phenomena of economic fluctuations due to unemployment. The real situation of unemployment problems can be described by dynamic model to find out a suitable reduction intervention. This project deals with a nonlinear mathematical model of unemployment which describes the situation of unemployment, employment and vacancies. The system of nonlinear differential equations has been developed and analyzed by introducing two control policies of the government. In this study, we have first verified the model both  analytically and numerically by checking the stability of equilibrium points of the model. We also discuss the characteristics of states at equilibrium point for various parameters. Secondly, we have established an optimal control model to obtain better control strategies for reducing the unemployment rate. Specially, we have proposed a five years plan to reduce the unemployment problems. The optimal control analysis for the unemployment model has been  performed by applying Pontryagin's Maximum Principle. Our findings show that for a successful  implementation of the policies of the government, the number of new vacancies and skilled persons will be increased while reducing the unemployed persons. The research predicts the new vacancies (12 lac per year) and providing skilled persons (10 lac per year) for five years to decrease the unemployed persons of Bangladesh. This study establishes the two control strategies so that the number of employed persons at end of implemented policies of the government is maximized while minimizing the cost of policy making. So, the numerically analyzed control strategies of our proposed model can effectively reduce the unemployed population in our country.

• Research Project