Regrding https://twitter.com/Birdyword/status/1468087528087502854

hospitalization_rate.py

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

plt.rcParams["figure.dpi"] = 250

delta_r0 = 1.2
omicron_r0 = 1.35
hosp_fraction = 0.05
icu_fraction = 0.30
icu_shift = 5
hosp_shift = 4
df = pd.DataFrame({"days": list(range(30))}).set_index("days")
# Same formula for ICU fraction for both
hosp = lambda x: x.shift(hosp_shift) * hosp_fraction
icu = lambda x: x.shift(icu_shift) * icu_fraction


def add_columns(df, vr, r0):
    df[f"Cases {vr}"] = np.power(r0, df.index)
    df[f"Hosp {vr}"] = hosp(df[f"Cases {vr}"])
    df[f"ICU {vr}"] = icu(df[f"Hosp {vr}"])

    def frac(c1, c2, cum_sum):
        if cum_sum:
            df[f"{c1} / {c2} {vr}"] = df[f"{c1} {vr}"] / df[f"{c2} {vr}"].cumsum()
        else:
            df[f"{c1} / {c2} {vr}"] = df[f"{c1} {vr}"] / df[f"{c2} {vr}"]

    frac("Hosp", "Cases", True)
    frac("ICU", "Hosp", False)


for vr in [("Delta", delta_r0), ("Omicron", omicron_r0)]:
    add_columns(df, *vr)

fig, ax = plt.subplots(3, figsize=(7, 9))
df[["Cases Delta", "Cases Omicron"]].plot(ax=ax[0])
df[["ICU Delta", "ICU Omicron"]].plot(ax=ax[0])
df[["Hosp / Cases Delta", "Hosp / Cases Omicron"]].plot(ax=ax[1])
df[["ICU / Hosp Delta", "ICU / Hosp Omicron"]].plot(ax=ax[2])
for a in ax:
    a.set_xlabel("Days")
ax[0].set_title(
    f"Growth Delta (${delta_r0}^t$) vs Omicron (${omicron_r0}^t$), 5% hosp, 1.5% ICU"
)
ax[1].set_ylim(bottom=0)
ax[2].set_ylim(bottom=0)