Question

The Kermack-Mckendrick model for infectious disease transmission can be used to predict the population size P as a function of the disease's virulence (that is, the extent to which the disease kills people). The population size P is large when virulence is low and it is also large when virulence is high because the disease kills people so fast that very few people get infected. For a specific choice of parameter values, the population size is v)=10+v+ Find the largest population size and the virulence values v for which it occurs. (Round your answer for P to the nearest person. Round your answer for v to two decimal places. If needed, enter your answers as comma-separated lists. If arn answer does not exist, enter DNE. people Find the smallest population size and the virulence values v for which it occurs. people

Answer 1

The Kermack Mckendrick model for infectious diseases.

The population size function is

P(v) = (10 + v + v_{​​​​​​}^{​​​​​​2} ) / ( 1 + v )

v --> virulence value

P(v) --> population size

For maximum and minimum of any function the slope must be zero

v = 2.162 and - 4.162

TO 2 2

Since 9 > v > 0

So v = 2.162

So we will check for boundary condition and 2.162

at v = 2.162

fov maximum , do dUf く。 ナV o check ho valu-e less than o 2

d^{​​​​​​2} P(v) / dv = 35.89

It is not less than 0 , so no Maxima at this point

Rather at positive value it is minimum condition

At v = 2.162

P(v) = 5.32 ~ 5

Checking boundary condition

At v = 0

P(v) = 10

At v = 9

P(v) = 10

Maximum : P(v) .= 10 at v = 0 or 9

Minimum P(v) = 5 at v = 5.16