Consider a population aggregated by age into M groups ( i = 1,2,,M). The population, within age group i, is comprised of the following classes, susceptible S_i , asymptomatic infectious Ia_i, symptomatic infectious Is_i, and recovered R_i individuals.

The size of the population in age group I is, N_i = S_i + Ia_i + Is_i + R_i. The total population size is:

Let the rate of infection of a susceptible individual in age group i be given by _i(t) which is defined below:

_1(t) = 0.056

_2(t) = 0.072

_3(t) = 0.046

_4(t) = 0.021

We take the age independent recovery rate = 1/5 to be identical for both asymptomatic and symptomatic individuals whose fractions are, respectively, = 1/9 and = 1. Hence the age structured SIR model is governed by the following equations:

Note that S = S_i, Ia = Ia_i, Is = Is_i, R = R_i.

Let M = 4, N_1 = 3900, N_2 = 6000, N_3 = 5600, N_4 = 2500. Assume the following for the initial conditions:

You are to write a code in Python that solves the given system of equations, for all age groups, and plots the number of individuals, from each age group, versus the time, in days, for all classes (Susceptible, Infectious symptomatic, Infectious asymptomatic, Recovered).

M N = : i=1 Si = -lit)Si, in = ali(t) S-710 yl, i =li(t)S-71, R; = (1+1). Age group S_i(0) la_i(0) Is_i(0) R_i(0) 1 3895 3 2 0 2 5990 6 4 0 3 5592 4 4 0 4 2498 1 1 0 M N = : i=1 Si = -lit)Si, in = ali(t) S-710 yl, i =li(t)S-71, R; = (1+1). Age group S_i(0) la_i(0) Is_i(0) R_i(0) 1 3895 3 2 0 2 5990 6 4 0 3 5592 4 4 0 4 2498 1 1 0