Modelling disease spread using a logistic model in Python

Simplified epidemic model of COVID 19

The infections on day n+1 are calculated as

N_d is the current infected population, pop is the total susceptible population, E is the Number of people exposed to an infected person per day and p
is the probablity that an exposed person catches on the disease.

The (1-N_d/pop) factor indicates that as a larger and larger fraction is exposed, the probability that the new person being exposed is “not infected” goes down.

Assuming the following:

# Number people exposed to an infected person (E)
E = 1
# Probablity that an exposed person catches on the disease
p = 0.05
# Total population Size (set at 100 million)
pop = 1e8
#Total Infections by day (starts by 1 person getting infected)

Plotting the impact of Exposure

These are for various values of the “number of people exposed, E”. Each line is for a certain value of E, the left most is for 20 people exposed to each other every day, the right most is 1 person exposed every day. Huge difference.

E = 1
for j in range(20):
    for i in range(1,300): #100 days
        N_d[i] = (1+ E*p*(1-N_d[i-1]/pop))*N_d[i-1]
    E= E+1
    plt.plot(N_d, label= E-1)
#plt.yscale('log')
plt.legend()
plt.show()

The number of new cases Every Day

This can be modelled as the gradient of the curves above. This what is meant by “flattening the curve”. Compare E =1 (right most) with E = 20 (left most)

E = 1
del_d = np.zeros(300)
for j in range(20):
    for i in range(1,300): #100 days
        N_d[i] = (1+ E*p*(1-N_d[i-1]/pop))*N_d[i-1]
        del_d[i] = N_d[i] - N_d[i-1]
    E= E+1
    plt.plot(del_d, label= E-1)
#plt.yscale('log')
plt.legend()
plt.show()

Modelling with Recovery @ 1% of the population

This models recovery as well (1% of the infected populace recovers/dies every day, and hence is no longer infected). Letgamma be the recovery rate.

R = 0.01
E = 1
p = 0.05
for j in range(10):
    for i in range(1,300): #100 days
        N_d[i] = (1+ E*p*(1-N_d[i-1]/pop))*N_d[i-1] - R*N_d[i-1]
    E= E+2
    plt.plot(N_d, label= "E=" + str(E-1)+" with recovery="+str(100*R) +"%")
#plt.yscale('log')

R = 0.01
E = 1
p = 0.05
for j in range(10):
    for i in range(1,300): #100 days
        N_d[i] = (1+ E*p*(1-N_d[i-1]/pop))*N_d[i-1] #- R*N_d[i-1]
    E= E+2
    plt.plot(N_d, label= "E=" + str(E-1)+" (model without recovery)")

plt.legend()
plt.show()

Stay safe everyone. Keep E low, that’s the only variable you can control.