In a Model of Epidemics, Let $y ( t )$ , in Thousands, Be the Number of Infected Individuals in

question 93

Essay

In a model of epidemics, let $y ( t )$ , in thousands, be the number of infected individuals in the
population at time $t$ , in days. If we assume that the infection spreads to all those who are
susceptible, one possible solution for $y ( t )$ is given by $\frac { d y } { d t } = k ( p - y ) \cdot y$ where $k$ is a positive
constant which measures the rate of infection and P , in thousands, is the total population in
this situation.(a) Determine the solution of this differential equation if $y ( 0 ) = 1$ .(b) Discuss what $y ( 0 ) = 1$ means.(c) As the time increases without bound, what happens to $y$ ? (That is, what does $\lim _ { t \rightarrow \infty } y$ mean?)
(d) Sketch the solution of the differential equation in part (a).

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Definitions:

Labor Force

The total number of people available to work, including those currently employed and those actively seeking employment, within a particular economy.

Skills Demand

The requirement by employers for specific skills or qualifications from the workforce to fulfill job roles.

Structural Unemployment

A form of unemployment caused by fundamental changes in the economy that reduce the demand for certain skills or labor.

Petroleum Refinery

A processing plant where crude oil is transformed into various usable petroleum products such as gasoline, diesel fuel, asphalt base, heating oil, kerosene, and liquefied petroleum gas.