Minimal model modified of the diabetes to simulate glucose and insulin levels

Debido a la importancia que actualmente tiene la diabetes como enfermedad que se perfila ser una pandemia a nivel mundial, se hace necesario estudiar y comprender, desde diferentes disciplinas, los procesos que se involucran para una mejor identificación y tratamiento de la misma. El presente artículo describe el modelamiento matemático de los niveles de glucosa e insulina presentes en el cuerpo basado en el trabajo de Ackerman realizando una modificación del sistema de ecuaciones diferenciales acopladas (SEDA) en el modelo mínimo incluyendo un aumento gradual exógeno para considerar variaciones exógenas de tales niveles. A partir de la curva experimental se consideraron diferentes casos, de manera que cada familia de curvas correspondiente se analizó en función de la cantidad de glucosa e insulina, respectivamente. La solución aproximada del SEDA se obtuvo usando el método de Runge Kutta de cuarto orden y se comparó con resultados experimentales reportados. Se encontró que pequeños aumentos en la cantidad de Glucosa produce un incremento en la Insulina debido a que el cuerpo aumenta su producción para regularla a niveles normales. Due to the importance that diabetes is nowadays, a disease that is worldwide nominated as a pandemic, it is necessary to study and understand from different disciplines the processes that are involved in a better identification and treatment of it. Thus the mathematical modeling of the glucose and insulin levels present in the body was done making a modification of the minimal model, to consider exogenous variations of the glucose and insulin levels. For that, the study was based on the work done by Ackerman and the minimal model, and the system of differential equations connected (SDEC) was modified in order to include a gradual exogenous increase of the glucose and insulin amount. The approximate solution of the SDEC was obtained using the Runge Kutta method of fourth order and it was compared with the reported experimental results, finding a good behavior. Based on the experimental curve, different cases were modeled where the insulin and glucose amount varies, and for each case, the group of corresponding curves was analyzed according to the insulin and glucose amount respectively. It was found that small increases of the glucose amount causes an increase of the insulin production and this is because the body increases the insulin production to regulate it to the normal levels.