(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[SUB]0[/SUB] 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[SUB]0[/SUB] is R(0).

The equation R[SUB]0[/SUB] = 0 simply says that no people have died, yet, at the very beginning (when t = 0).

The inequality I[SUB]0[/SUB] << 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[SUB]0[/SUB] ≈ 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).