This article investigates the dynamics of measles spread using the  model and inverse problem-solving methods. The mathematical modeling was based on epidemiological data, monitoring results and analytical calculations. A genetic algorithm was employed as the optimization method. As part of the study, a quantitative analysis of the dynamics of the spread of infection in Bangladesh from 2000 to 2020 was conducted. Using the model, the main parameters influencing the spread of infection were reconstructed, including the rate of spread of the virus, the effectiveness of the first and second doses of vaccination, and the mortality rate from the disease. The proposed mathematical model can be adapted to different regions and utilized to assess the effectiveness of epidemic containment strategies.