In recent years measles has been one of the most critical public health problem in Bangladesh. Although the Ministry of Health in Bangladesh employs a broad extension of measles control policies, logistical challenges exist, and there is significant doubt regarding the disease burden. Mathematical modelling of measles is considered one of the most effective ways to understand infection transmission and estimate parameters in different countries, such as Bangladesh. In this study, a mathematical modelling framework is presented to explore the dynamics of measles in Bangladesh. We calibrated the model using cumulative measles incidence data from 2000 to 2019. Also, we performed a sensitivity analysis of the model parameters and found that the contact rate had the most significant influence on the basic reproduction number R0. Four hypothetical intervention scenarios were developed and simulated for the period from 2020 to 2035. The results show that the scenario which combines enhanced treatment for exposed and infected population, first and second doses of vaccine is the most effective at rapidly reducing the total number of measles incidence and mortality in Bangladesh. Our findings also suggest that strategies that focus on a single interventions do not dramatically affect the decline in measles incidence cases; instead, those that combine two or more interventions simultaneously are the most effective in decreasing the burden of measles incidence and mortality. In addition, we also evaluated the cost-effectiveness of varying combinations of three basic control strategies including distancing, vaccination and treatment, all within the optimal control framework. Our finding suggested that combines distancing, vaccination and treatment control strategy is the most cost-effective for reducing the burden of measles in Bangladesh. Other strategies can be comprised to measles depending on the availability of funds and policymakers' choices.