Optimization of medication distribution in Mexico through a mathematical model incorporating mortality, incidence and prevalence

Abstract

Objective: To develop a mathematical model that incorporates the mortality, incidence and prevalence of Mexico’s most common diseases—ulcer, hypertension, type 2 diabetes mellitus and obesity—in order to improve the accuracy of future medication demand predictions. The model utilizes Markov chains, Monte Carlo simulations, econometric methods and financial projections. Materials and methods: A research design was employed using a predictive mathematical model based on econometric and f inancial approaches, such as Markov chains and Monte Carlo simulations. A simulated population of 20,000 individuals was analyzed over 10 simulation cycles in Excel, where individuals transitioned between the healthy, sick and deceased states. The model included previously researched rates of mortality, incidence and prevalence. Results: Transition tables with probabilities, based on Mexico's most common diseases, were generated in Excel. The considered states included “healthy-deceased,” “healthy-sick” and “healthy-healthy.” The “sick-deceased” transition was calculated using both disease-specific and overall mortality rates. In the second disease cycle, the annual treatment costs were as follows: 285,120 pesos for ulcer, gastritis and duodenitis; 3,525,120 pesos for hypertension; 35,490 pesos for type 2 diabetes; and 752,000 pesos for obesity. An increase in the required budget for each disease was observed since no new healthy population was added during these transitions. Conclusions: Applying a mathematical model based on epidemiological data, combined with the historical method, could improve the accuracy of pharmaceutical budget allocation. Countries such as Spain, Panama and Peru use methods that combine historical adjustments with morbidity data. More accurate, up-to-date and reliable statistics are needed to optimize the government’s financial resources for health.