Modeling the diabetic population in Malaysia using a functional rate of unhealthy lifestyle influence

A time-delay model of diabetic population: Dynamics analysis, sensitivity, and optimal control

“…It follows from the discussion in section 3.1 that condition (H2) is satisfied for the parameter set in (21). We can find a positive solution to equation (11) which is z 0 =0.005, and hence ω 0 = 0.0707.…”

“…This shows that periodic solution near E * may occur. Now suppose γ = 0.005 and the rest is as in (21), then E * = (500, 20.6693, 9.8425) is stable independently of τ. By theorem (2), E * is globally asymptotically stable for all τ 0.…”

“…A normalized value is computed to observe the percentage change of the outputs as 1% perturbation is given to the inputs. Using the parameter's value given in (21) along with τ = 5.5, the index sensitivity z S t y , i ( ) for t ä [0, 25] is presented in figures 4 and 5.…”

“…Again, using the value of the parameter given in (21), the index sensitivity E * to each input is given in table 1. In figures 4(C), (D) and 5(G), (H), (M), (N), the state variable D shows no response because the evolution of D does not depends on σ, κ, μ 2 , μ 3 , f 2 , and f 3 .…”

“…In 2021, Avendaño-Valencia et al [13] developed a video-based eye-tracking method with the help of a Heteroscedastic Auto-Regressive with eXogeneous input model for detection of diabetes complications associated with the nervous system. Some of the previous diabetic population models were governed by ordinary differential equations [14][15][16][17][18][19][20][21]. These ordinary differential equations models considered the progression of diabetes instantaneously.…”