This study investigated the use of public and private healthcare systems separately and interactively to find solutions to various problems the healthcare sector has faced including waiting time, cost, and quality of service. Patients, private and public healthcare providers, funders, and governments that make rules about healthcare were defined as components of healthcare systems in this study. Mathematical optimization models were developed by deriving scenarios to balance the components of healthcare systems. In addition to derivation of scenarios related to types of healthcare systems and decision variables, including copayment, treatment cost, reimbursement, and premium, numerical studies for the healthcare components were performed to determine which healthcare systems were useful. The minimum fee payable by patients for the easy access to healthcare schemes was calculated. While there was no remarkable change in the waiting time of the patients in the private healthcare system, the waiting time were reduced by 48.70% in the public healthcare system among the findings. The amount of reimbursement decreased significantly as a result of the interaction of healthcare systems. By reducing the amount of co-payment to the amount charged by the public healthcare system, it has been ensured that private healthcare providers treat more patients. Based on computational analyses, because of the agreements provided between the components, we have advocated that public and private healthcare systems must be unified to provide greater benefits for all the components of healthcare.