Question

A population initially consists of 1 million healthy members and 10000 infected members, The rate of infection is 25% and the rate of decease of the infected is also 25%. Assume that those who do not decease will recover, but may become infected again(like a heavy flu epidemic). Apply the mathematical model describing the population distribution to calculate the healthy and infected population distribution after 10 years.

Answer 1

This is a simple problem related to reconciliation of the number of peorple in various catogoies across various time lines.

We are given

Initial population : 1000000

Rate of infection of population in each year : 25 % of healthy population at the start of the year

Rate of demise due to infection in a year : 25 % of infected population at the start of the year

Rate of Recovery from infection : 75 % of infected population at the start of the year.

Now in the question we need to caclulate

the total healthy population, total infected population, total recovered population and total casualty due to infection at the start of each year,

so let us start

At the end of first year/start of 2nd year

Total population of recovered =0.75*10000=7500

This will get added to the total healthy population.

Total deaths =0.25 *10000=2500

Total infected from intial healthy lot

=0.25*1000000

=250000

Total healthly left =total initial healthy population -reduction due to infected population

=1000000-0.25*1000000

=0.75*1000000

Overall healthy left =Total healthy left after infection+total healthy due to recovery over the year

=0.75*1000000+7500

=757500

Thus after end of first year /begininng of second year

Total healthy population =757500

Total infected population =25000

Total recovered =7500

Death =2500

This will form base for the calculation of these parameters for second year end /third year start.

We will continue doing so to get the estimate of these paramenters after each year.

This is shown in the table below.