(4) N = S(L) + I(t) + R(t) That ought to be S(t)
i appreciate if any can explain me this form
S(t) represents the output of a function (i.e., the result from using a formula). This notation is generally taught after beginning algebra.
From what I can tell, t represents elapsed time since an epidemic started. S(t) represents the number of uninfected (susceptible) people in a population.
For example, if 3,500,000 people were susceptible 20 weeks after the epidemic started, then we could write:
S(20) = 3 500 000
where t is measured in weeks.
I(t) represents the number of infected people, at time t.
R(t) represents the number of people who have died, at time t.
N represents the total population. It is a constant.
N = S(t) + I(t) + R(t)
The symbol R
0 is read as "R sub zero", and it represents the initial value of R (i.e., the number of people who have died at the beginning of the epidemic). In other words, R
0 is R(0).
The equation R
0 = 0 simply says that no people have died, yet, at the very beginning (when t = 0).
The inequality I
0 << N says that the initial value of I(t) is very small compared to the total population. In other words, relatively few people in the population were infected, at the beginning.
S
0 ≈ N says that the initial number of uninfected people was approximately the same as N (the total population).
The rest of the image deals with how fast S, I, and R are changing over time. dS/dt represents such a rate. This is a calculus topic, and equations that contain these rates are called differential equations (studied after calculus). :cool: