In Biology, It Is Often Assumed That the Number of People

question 86

Essay

In biology, it is often assumed that the number of people that will contract a certain disease is directly proportional to the product of the number of people $y$ who are currently infected with the disease at a particular time $t$ and the number of people $x$ who, at the same time, are not yet infected but who are susceptible to it. Assume that the total population, $P$ , in the study is a constant.(a) What does $\frac { d y } { d t }$ mean?
(b) Determine a differential equation that $y ( t )$ must satisfy.(c) What happens to $y$ as $t \rightarrow \infty$ ?

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Definitions:

Sensory Input

Information gathered by sensory receptors about internal and external changes or stimuli.

Association Areas

Regions of the cerebral cortex that integrate different types of information from multiple brain areas, involved in complex processes like thinking and planning.

Left Cerebral Hemisphere

The left side of the brain that controls the right side of the body, often associated with logical reasoning, analytical skills, and language functions.

Mathematics

The abstract science of number, quantity, and space, either as abstract concepts (pure mathematics) or as they apply to other disciplines such as physics and engineering (applied mathematics).