Plasmodium vivax (P. vivax) malaria is a major public health problem worldwide, including in the high endemic Chittagong district of Bangladesh. Here, we used mathematical modelling to explore the dynamics of P. vivax at Chittagong district in Bangladesh, including reported and unreported cases with and without importation. Our model was calibrated using actual P. vivax incidence data. A sensitivity analysis of the model parameters showed that the P. vivax transmission rate had the greatest effect on the basic reproduction number\(\:\:\left({\text{R}}_{\text{c}}\right)\). We used the model to estimate the impacts of various intervention policies on reducing P. vivax disease burden (measured by the number of reported and unreported cases per 1,000 population). Of the individual intervention policies, increased vector control was the most effective at reducing the reported and unreported cases of P. vivax in the Chittagong district of Bangladesh, while enhanced treatment for the liver-stage infections was the second most effective for reducing reported and unreported cases of P. vivax. Our findings also suggest that combining interventions leads to greater success in reducing cases of P. vivax. We estimate this approach could substantially reduce cases for a modest investment, whereas eliminating P. vivax in the Chittagong district of Bangladesh would require a much greater investment. We also evaluated cost-effectiveness of single and combination of three control strategies including treatment for blood-stage infection, liver-stage infection, and vector control. Our finding suggested that vector control, either alone or in combination with blood-stage and liver-stage treatment represents the most cost-effective and sustainable strategy for P. vivax control in the Chittagong district of Bangladesh.