Diabetes and sarcopenia both affect seriously the quality of life of elderly men and women. The present mathematical model describes and analyses the flow in and out of three compartments representing healthy adult people (H), diabetics (D) and sarcopenics (S). The mathematical model proposed has a unique positive solution and a locally asymptotically stable equilibrium. Sensitivity analysis is conducted to show how decision makers can adopt an optimal strategy to reduce at the same time the prevalence of sarcopenia and that of type 2 diabetes. Finally, numerical simulations are carried out with varying model parameters to illustrate results yielded by different scenarios. As a conclusion, the incidence and prevalence of sarcopenia and type 2 diabetes can be reduced by adopting preventive strategies based mainly on healthy lifestyle, physical activity and weight control.