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kirza4 [7]
3 years ago
14

Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit the disease but who exhibit n

o overt symptoms. Let x and y denote the proportions of susceptibles and carriers, respectively, in the population. Suppose that carriers are identified and removed from the population at a rate β, so dy/dt = −βy. Suppose also that the disease spreads at a rate proportional to the product of x and y; thus dx/dt = −αxy. a) Determine y at tany time t by solving eq(i) subject to the initial condition y(0)=y0
b) Use the result of part (a) to find x at any time t by solving Eq.(ii) subject to the initial condition x(0)=x0
c) Find the proportion of the population that escapes the epidemic by finding the limiting value of x as t approaches infinity

Mathematics
1 answer:
Margaret [11]3 years ago
6 0

Answer:

The detailed derivation is shown in the attachment

Step-by-step explanation:

The step by step explanation is as shown in the attachment.

Basically, what was applied is the knowledge of differentiation and integration.

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Which steps should be taken to solve the equation
Leviafan [203]

Answer:

Remove 1 x-tile from both sides.

Remove 3 unit tiles from both sides.

Step-by-step explanation:

2x + 3 = x + 5

First we want all the variables on one side

Subtract x from each side so Remove 1 x-tile from both sides.

x+3 = 5

Now we need to get all the constants on the same side

Subtract 3 from each side so Remove 3 unit tiles from both sides.

x = 5-3

x=2

7 0
3 years ago
Read 2 more answers
CD has endpoints C(-3, 4) and D(1, -2). Find the coordinates<br> of its midpoint.
Natalija [7]

Answer:

Midpoint (-1 , 1)

Step-by-step explanation:

Formula: (midpoint)

Let the point A(x , y) be the midpoint of CD.

x=\frac{x_c+x_D}{2} =\frac{-3+1}{2} =\frac{-2}{2} =-1

y=\frac{x_C + y_D}{2} =\frac{4+(-2)}{2} =\frac{2}{2} =1

Then

A(-1 , 1)

4 0
2 years ago
Read 2 more answers
K(a)= 4a-4, Find k(-9)
FromTheMoon [43]

We simply replace a with -9

k(-9) = 4 * -9 - 4

k(-9) = -40

:)

5 0
3 years ago
Find K such that the points (-2, 5), (2, 8) and (6, K) are collinear.
damaskus [11]

Answer:

k = 11

Step-by-step explanation:

let the points be A(-2,5), B(2,8), C(6,K).

for the points to be collinear slope of line AB maust be equal to line BC.

slope of line AB = \frac{8-5}{2+2}=\frac{3}{4}

slope of line BC = \frac{k-8}{6-2}=\frac{k-8}{4}

therefore \frac{k-8}{4}= \frac{3}{4}

therefore k = 8 + 3

k = 11

8 0
3 years ago
Maria has already written  of her 1,000 word essay. If she continues writing at the same pace of 6 words per minute, which expre
neonofarm [45]
The first thing we must do in this case is to define variables:
 t = time to write the words
 v = write speed.
 w = number of words.
 The correct expression is:
 t = w / v
 By substituting we have:
 t = 1000/6
 t = 166.6666667
 Rounding:
 t = 167 minutes
 Answer:
 
The correct expression is:
 
t = w / v
 The time is:
 t = 167 minutes
8 0
3 years ago
Read 2 more answers
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