Suppose that C = C(t) and D = D(t) represent the numbers of diabetics with and without complications, respectively, and let N = N(t) = C(t) + D(t) denote the size of the population of diabetics at time t (see Nomenclature). Then, as was noted earlier, N(t) ~ 3% of the world population. Let I = I(t) denote the incidence of diabetes mellitus. The model parameters to be incorporated are μ (the natural mortality rate), λ (the probability of a diabetic person developing a complication), γ (the rate at which complications are cured), ν (the rate at which diabetic patients with complications become severely disabled) and δ (the mortality rate due to complications).
Suppose we discover that the C population is at equilibrium
$$ C(t) = 0 $$
When $C(t) = 0$ satisfies the equation with one other known solution, because some number of persons of living with Type 2 Diabetes complications have not yet reported at an initial time 0 to the hospital for an initial history taking and diagnosis in the Emergency Department (E.D.)
Suppose we discover that the D population is at equilibrium
$$ D(t) = 0 $$
When $D(t) = 0$ satisfies the equation with one other known solution, because some number of persons living with Type 2 Diabetes and have non known complications have not yet reported at an initial time 0 to the hospital for an initial history taking and diagnosis in the Emergency Department (E.D.)
Suppose N the total population is at equilibrium
$$ C(t) + D(t) = N(t) = 0 $$
because $C(0) + D(0) = N(0)$ at some initial time 0, neither Population C or Population D have reported to the hospital for an initial history taking and diagnosis in the Emergency Department (E.D.) as a result of no initial Incidence $I$ or $k$
Suppose initial incidence $I$ population that is living with diabetes between 2020 - 2023 had just begun to report to the hospital for an initial history taking and diagnosis for Type 2 Diabetes just a little bit past the initial time $t > 0$ (e.g. $t+1$) , then $k=I \le 1000$.
Suppose $\mu$ comes into the model as a nonzero parameter.
Where $\mu \approx 0.95$ reaches the natural mortality rate, it characterizes the maximum height of the graph of the behavior of both functions $C(t) = C$ and $D(t) = D$ as they individually approach closer to when $N(t) \ge I = k = 1000$, because $C(t) > 0$ and $D(t) > 0$ can naturally occur as an independent event within the same time length, when $t + 1 > 0$. If both of those independent events occur within the same time, that means the total Population N has begun to become unstable.