Diabetes is a disease which caused by socio-environmental and / or genetic factors. The negative effect of socio-environmental or lifestyle leads a susceptible individual to become a diabetic. On the one hand, social interaction wields a great deal of influence over lifestyle. On the other hand, genetic factors are the main cause of the birth diabetes genetic disorder. Considering these above mentioned factors. In the present paper, we study a discrete age continuous mathematical model that describes the dynamics of diabetics. We highlight the negative impact of socio-environmental on diabetic patients according to age groups. We also suggest an optimal strategy to implement the best campaigns of rising awareness that aims at protecting diabetic patients from the negative impact of a lifestyle that leads them to complications. In addition to psychological treatment and follow-up of diabetic patients with complications, an awareness campaign will also be carried out for people with potential diabetes that aims at educating them about the dangerous of diabetes and its complications. Pontryagin’s maximum principle is used to characterize the optimal controls and the optimality system is solved by an iterative method. The numerical simulation is carried out using MATLAB.

糖尿病是一种由社会环境和/或遗传因素引起的疾病。社会环境或生活方式的负面影响导致易感个体成为糖尿病患者。一方面，社交互动对生活方式有很大影响。另一方面，遗传因素是导致出生糖尿病遗传病的主要原因。考虑到上述这些因素。在本文中，我们研究了描述糖尿病患者动态的离散年龄连续数学模型。我们根据年龄组强调社会环境对糖尿病患者的负面影响。我们还提出了一个最佳策略，以实施旨在保护糖尿病患者免受导致他们并发症的生活方式的负面影响的最佳宣传活动。除了对患有并发症的糖尿病患者进行心理治疗和随访外，还将针对潜在糖尿病患者开展宣传活动，旨在教育他们了解糖尿病及其并发症的危险性。采用庞特里亚金极大值原理表征最优控制，通过迭代法求解最优系统。数值模拟使用MATLAB进行。