It is often claimed that „flattening the curve“ does not lead to a reduction in the total number of individuals infected during the course of the desease; rather, the infections would only spread over a longer period of time. This is not correct if e. g. the SIR model can be applied to the infection. This is shown using three SIR models (susceptibles: blue; infected: orange; removed/recovered: green) with common initial values S(0)=997,I(0)=3,R(0)=0{\textstyle S(0)=997,I(0)=3,R(0)=0} and constant rate γ=0.04{\textstyle \gamma =0.04} for group R. The models differ from top to bottom as follows:
β=0.0004{\textstyle \beta =0.0004} over a period of time Tmax=200{\textstyle T_{max}=200}: R(200)≈999{\textstyle R(200)\approx 999}, i. e. virtually all individuals were infected.
β=0.0002{\textstyle \beta =0.0002} over a period of time Tmax=250{\textstyle T_{max}=250}: R(250)≈993{\textstyle R(250)\approx 993}, i. e. despite half the infection rate, almost all individuals were still infected.
β=0.0001{\textstyle \beta =0.0001} over a period of time Tmax=400{\textstyle T_{max}=400}: R(400)≈893{\textstyle R(400)\approx 893}, i. e. if the infection rate can be reduced to a quarter, 107 individuals (over 10 %) were not infected.Conclusion: The claim is true with a good approximation as long as the infection rate cannot be reduced to the extreme. However, if it is possible to prevent infections extremely effectively, a significant number of individuals can actually be protected from infection.
This image was created with en:Wolfram Mathematica by computing the numerical solutions of the following system of differential equations:

dSdt=−β⋅S(t)⋅I(t){\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}=-\beta \cdot S(t)\cdot I(t)}
dIdt=β⋅S(t)⋅I(t)−γ⋅I(t){\displaystyle {\frac {\mathrm {d} I}{\mathrm {d} t}}=\beta \cdot S(t)\cdot I(t)-\gamma \cdot I(t)}
dRdt=γ⋅I(t){\displaystyle {\frac {\mathrm {d} R}{\mathrm {d} t}}=\gamma \cdot I(t)}The core part of the construction is as follows:

equationS = s'[t] == -b s[t] i[t]
equationI = i'[t] == b s[t] i[t] - g i[t]
equationR = r'[t] == g i[t]
...
solution = 
  NDSolve[{equationS, equationI, equationR, s[0] == s0, i[0] == i0, 
    r[0] == r0}, {s, r, i}, {t, tmax}];
solutionS = First[s /. solution];
solutionI = First[i /. solution];
solutionR = First[r /. solution];
...
sirPLOT = 
 Plot[{solutionS[t], solutionI[t], solutionR[t]}, {t, 0, tmax}, 
  PlotRange -&gt; {0, 1000}, 
  PlotStyle -&gt; {Blue, Orange, Green}]
Note: Some authors use modified, but equivalent forms of the ODEs. Unfortunately, the same parameters are sometimes used. Example for the first ODE, where the infection rate is named β~{\textstyle {\tilde {\beta }}} for the sake of clarity:

dSdt=−β~N⋅S(t)⋅I(t){\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}=-{\frac {\tilde {\beta }}{N}}\cdot S(t)\cdot I(t)}
By substituting β=β~N{\textstyle \beta ={\frac {\tilde {\beta }}{N}}}, you get the same ODE as above. N{\textstyle N} is a constant value (invariant of the model) and not needed for the ODE; in fact, the implementation didn't even use a variable for N{\textstyle N}.
own image
Phrontis