Question 2. (1 point) Find the equilibrium solutions of the SIR Model.
Answers
The SIR model is a mathematical model that is used to study the spread of infectious diseases in a population. It consists of three compartments: susceptible (S), infectious (I), and recovered (R). The equilibrium solutions of the SIR model can be found by setting the derivatives of the three compartments to zero. There are two equilibrium solutions: the disease-free equilibrium, where the number of infectious individuals is zero, and the endemic equilibrium, where the disease is present in the population. The disease-free equilibrium is stable, meaning that if the initial number of infectious individuals is zero, it will remain zero. The endemic equilibrium is unstable, meaning that if the initial number of infectious individuals is not zero, it will eventually converge to the disease-free equilibrium. Therefore, the equilibrium solutions of the SIR model are important in understanding the dynamics of infectious diseases in a population.
To find the equilibrium solutions of the SIR Model, we need to consider the system of equations representing the model:
1. dS/dt = -βSI
2. dI/dt = βSI - γI
3. dR/dt = γI
At equilibrium, the rates of change are zero, so we have:
dS/dt = 0
dI/dt = 0
dR/dt = 0
From these equations, we can find the equilibrium solutions:
1. -βSI = 0
2. βSI - γI = 0
3. γI = 0
From equation 1, either S=0 or I=0. Similarly, from equation 3, either I=0 or R=0. Now, consider equation 2:
- If I=0, then βSI - γI = 0 simplifies to 0, which is an equilibrium solution (no infection).
- If I≠0, we can divide by I and get βS - γ = 0. Solving for S gives S = γ/β. In this case, the equilibrium solution is when the susceptible and infected populations balance, resulting in a constant rate of infection.
In summary, the SIR Model has two equilibrium solutions:
1. I=0 (no infection)
2. S=γ/β (balance between susceptible and infected populations)
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Related Questions
Grandma edith is making apple pies, one for each of her 14 grandchildren. If the recipe calls for 6 apples, 3/4 cup of sugar, 3 tbsp of flour, and 1 tsp of cinnamon for each pie, how many bags of apples does grandma edith need if each bag holds 32 apples?.
Answers
Answer:
3
Step-by-step explanation:
she will need 84 apples total so you do 84/32 and u get aroubd 2.6. You then round up to three because you can't have half a bag
SOLVE PLEASE! (Help)
Answers
Answer:
1. \(\sqrt{218}\)
2. \(\sqrt{89}\)
3. \(2\sqrt{17}\)
Step-by-step explanation:
The formula to find the distance between any two points on a coordinate plane is as follows:
\(D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
Where (\((x_1,y_1)\)) and (\((x_2,y_2)\)) are the two points one is trying to find the distance between. Substitute the points in and solve for the distance between them for each respective problem.
1.
Points: \((-4, 6),\ \ (3, -7)\)
Substitute into the formula,
\(D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
\(D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}\)
Simplify,
\(D=\sqrt{((-4)-(3))^2+((6)-(-7))^2}\)
\(D=\sqrt{(-4-3)^2+(6+7)^2}\)
\(D=\sqrt{(-7)^2+(13)^2}\)
\(D=\sqrt{49+169}\)
\(D=\sqrt{218}\)
2.
Points: \((-6, -5)\ \ (2,0)\)
Substitute into the formula,
\(D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
\(D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}\)
Simplify,
\(D=\sqrt{((-6)-(2))^2+((-5)-(0))^2}\)
\(D=\sqrt{(-6-2)^2+(-5-0)^2}\)
\(D=\sqrt{(-8)^2+(-5)^2}\)
\(D=\sqrt{64+25}\)
\(D=\sqrt{89}\)
3.
Points: \((-1, 4)\ \ (1,-4)\)
Substitute into the formula,
\(D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)
\(D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}\)
Simplify,
\(D=\sqrt{((-1)-(1))^2+((4)-(-4))^2}\)
\(D=\sqrt{(-1-1)^2+(4+4)^2}\)
\(D=\sqrt{(-2)^2+(8)^2}\)
\(D=\sqrt{4+64}\)
\(D=\sqrt{68}\)
\(D=2\sqrt{17}\)
? Work out the surface area of the
cuboid.
10m
5m
2m
Answers
The surface area of the cuboid with the, height of the cuboid being 5m, the width being 2m, and the length being 10m is 160\(m^{2}\)
What is the surface area of the Cuboid ?Add the areas of each of the cuboid's six faces to determine its surface area. Additionally, we can label the prism's length (l), width (w), and height (h), and then calculate its surface area using the formula SA=2lw+2lh+2hw.
As we know:
Height =5m
Width= 2m
Length= 10m
T.S.A=2(LXW) + 2(LXH) + 2(WXH)
=2(10mx2m) + 2(10mx5m) + 2(2mx5m)
=(2x20m²) + (2x50m²) + (2x10m²)
=40m² + 100m² + 20m²
=160m²
Cuboid's surface area, which was determined using the formula 2lw+2lh+2hw, is 160 square meters.
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Can some one help please i just need an correct anwsers
Answers
Answer:
the last one 5/25
Step-by-step explanation:
Julie has 15 nails. she uses 8 to build a birdhouse she subtracts to find the number of nails left. which addition sentence can she use to check her work
Answers
Answer:A
Step-by-step explanation:
.
50 points! Describe the possible values of x in the figure shown. I will mark brainliest
Answers
Answer:
x > 14Step-by-step explanation:
Use the triangle inequality which states that for any triangle, the sum of the lengths of any two sides must be greater than to the length of the remaining side.
FH < FG + GH ⇒ 2x + 31 < 2x + 1 + x + 16 ⇒ x > 14FG < FH + GH ⇒ 2x + 1 < 2x + 31 + x + 16 ⇒ x > - 46GH < FH + FG ⇒ x + 16 < 2x + 31 + 2x + 1 ⇒ x > - 16/3Combine the above three inequalities:
x > 14Answer:
\(x > 14\)
Step-by-step explanation:
By triangle inequality;
\(2x + 1 + x + 16 > 2x + 31 \\ 2x + x - 2x > 31 -17 \\ x > 14\)
The possible values of x is any number above 14, that is, x=[ 15, 16, 17, 18, .....}, if x is integer.
Help asap, need help on this math problem. Solve for x
Answers
Answer:
c. 25
Step-by-step explanation:
According to the intersecting chords theorem, the product of the segments of a chord equals the product of the segments of the other chord it intercepts.
Thus:
3*x = 5*15
3x = 75
x = 75/3
x = 25
Convert the following to a percentage: $0.40 out of $2.50
Answers
Answer:
16%
Step-by-step explanation:
Solution for 0.40 is what percent of 2.50:
0.40:2.50*100 =
(0.40*100):2.50 =
40:2.50 = 16
Answer:
16%planation:
Show the work! Ill mark Brainliest!
2x - 3y = 12
Answers
Answer:
here is explanation by graph
Knob Hill Savings Bank offers a one-year CD at 3.88% interest compounded
daily.
What is the APY for this account? Round to the nearest hundredth of a
percent.
Answers
Answer:
3.95%
Step-by-step explanation:
The computation of the APY is shown below:
As we know that
A = P(1 + rate)^n
where,
A = full and Final amount (Principal + Interest )
r = rate of interest
n = time
Now
Let us assume that P = $100.
Now placing the values,
A = $100 × (1 + (3.88% ÷ 365)^365
= $100 × (1 + 0.000106301 )^365
= $100 × (1.000106301 )^365
= $100 × 1.039560407
= $103.9560407
Now the annual percentage yield is
= Amount - principal
= $103.9560407 - $100
= 3.95%
What is the distance between A and B on the number line below?
On a number line, point A is at 2.15 and point B is at 2.7.
0.55
0.65
2.48
4.85
Answers
Have a nice day bud!
Answer:
A
Step-by-step explanation:
6a+5a=-11 How do I begin to even solve this?
Answers
Answer:
-1 = A
Step-by-step explanation:
First, you add 6+5, which equals 11. Then you have 11a = -11. Since all you have to do is multiply 11 by one and you get 11, add a negative symbol in front of it. 11 x -1 = -11
Hope this helps, it's very simple!
a. Complete the table.
х
f(x) = 2(2)*
=
-2 -1
0
1
2
1
Answers
Answer:
1/2,1,2,4,8 in order
Step-by-step explanation:
Given:
\(\displaystyle \large{f(x)=2(2)^x}\)
The function can be simplified to:
\(\displaystyle \large{f(x)=2^{x+1}}\) via law of exponent.
Recall:
\(\displaystyle \large{a^m\cdot a^n=a^{m+n}}\)
Next, substitute given x-values in:
\(\displaystyle \large{f(-2)=2^{-2+1}=2^{-1}=\dfrac{1}{2}}\\\displaystyle \large{f(-1)=2^{-1+1}=2^0=1}\\\displaystyle \large{f(0)=2^{0+1}=2^1=2}\\\displaystyle \large{f(1)=2^{1+1}=2^2=4}\\\displaystyle \lage{f(2)=2^{2+1}=2^3=8}\)
Therefore, the solution is 1/2,1,2,4,8
What is X?
Please help me
Answers
Answer:29° because the angle in between x and 105 is 54(alternate angles) in theory angles on a straight line add upto 180° so therefore x+105+54=180 thus x+159=180 as a result the remaining angle (x) would be 180-159=29° therefore x=29°
Eight workers took 2 1/4 days to dig half of a tunnel. If only two workers are going to finish the tunnel, how long will it take them?
Answers
Answer:
0.5625
Step-by-step explanation:
what are the portfolio weights for a portfolio that has 135 shares of stock a that sell for $84 per share and 110 shares of stock b that sell for $82 per share? (do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.1616.) portfolio weight stock a % stock b %
Answers
The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.
To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.
The total value of the portfolio can be calculated as follows:
Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)
Total value = (135 × $84) + (110 × $82)
Total value = $11,340 + $9,020
Total value = $20,360
Now, we can calculate the portfolio weights for each stock:
Weight of stock A = (Value of stock A ÷ Total value) × 100%
Weight of stock A = (($84 × 135) ÷ $20,360) × 100%
Weight of stock A = $11,340 ÷ $20,360
Weight of stock A ≈ 0.5569 or 55.69%
Weight of stock B = (Value of stock B ÷ Total value) × 100%
Weight of stock B = (($82 × 110) ÷ $20,360) × 100%
Weight of stock B = $9,020 ÷ $20,360
Weight of stock B ≈ 0.4431 or 44.31%
Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.
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6p = 3p + 2p + p is true for
Answers
Answer:
For any value
Step-by-step explanation:
Answer:
Anything substituted for p should be correct
Step-by-step explanation:
what is a negative multiplied by a negative
Answers
Answer:
\(( - ) \times ( - ) = ( + )\)
Negative × Negative = positive
Example;
\( (- 1) \times (- 1 )=( + 1)\)
I hope I helped you^_^
Absolute value equation with solution -3
Answers
Answer:
m=-3/5
Step-by-step explanation:
Consider the simple majority game with one large party
consisting of 1/3 of the votes and three equal-sized smaller
parties with 2/9 of the votes each. Find the Shapley value of the
large party.
Answers
In the simple majority game with one large party consisting of 1/3 of the votes and three equal-sized smaller parties with 2/9 of the votes each, the Shapley value of the large party can be calculated.
To find the Shapley value of the large party, we consider all possible orderings of the players and calculate the marginal contribution of the large party at each step. The marginal contribution is the difference in the winning probability when the large party joins the coalition compared to when it is not part of the coalition.
In this case, since the large party consists of 1/3 of the votes, it alone can form a majority and win the game. Therefore, its marginal contribution is equal to 1/3.
To calculate the Shapley value, we average the marginal contributions over all possible orderings of the players. Since there are four parties, there are 4! = 24 possible orderings. Therefore, the Shapley value of the large party is (1/3) / 24 = 1/72.
Hence, the Shapley value of the large party is 1/72.
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A football team tries to move the ball forward as many yards as possible on each play, but sometimes they end up behind where they started. The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25. A positive number indicates moving the ball forward, and a negative number indicates moving the ball backward. 1). Which number in the list is the greatest? 2). What is a better question to ask to find out which play went the farthest from where the team started? 3). The coach considers any play that moves the team more than 4 yards from where they started a "big play." Which play(s) are big plays?
Answers
Answer:
Given:
The distances, in yards, that a team moves on its first five plays are 2, 21, 4, 3, and 25.
Solved:
1. The greatest number is 25
2. If the moved distances are square, which one is largest?
3. The move which is greater than 4 is considered "big play"
=> 21 and 25 are big play (21 > 4, 25 > 4)
Hope this helps!
:)
eight-year old susan was tested and found to have an average iq of 100. what would your estimate her mental age (ma) to be?
Answers
Her mental age would be 8 yrs old.
IQ [ Intelligent Quotient ] is a type of standard score that indicates how far above, or how far below, his/her peer group an individual stands in mental ability.
IQ of a person is given by the formula -
IQ = MA/CA * 100
IQ = Mental Age / Chronological Age * 100
According to the question, IQ = 100, CA = 8
⇒ 100 = MA / 8 *100
⇒1 = MA / 8
⇒ MA = 8 Yrs
Hence, the estimated mental age of susan is 8 yrs old.
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Describe the
relationship between two(______)in a graph.
-what’s the missing word?
Answers
Marvin has already walked 11 kilometers this week, plus he plans to walk 1 kilometer during each trip to school. How many trips to school. How many trips will Marvin have to make in all to to walk a total of 40 kilometers
Answers
Marvin has to take 29 trips to the school to make in all to walk a total of 40 kilometers with the help of algebraic equation.
Marvin has already walked 11 kilometers this week, so he needs to walk an additional 29 kilometers (40 - 11) to reach his goal.
If he plans to walk 1 kilometer during each trip to school, we can use algebra to solve for the number of trips he needs to make:
Let's call the number of trips Marvin needs to make "x".
Then, the total distance he walks during these trips is 1 kilometer times "x".
So we can set up the following equation to solve for x:
1x + 11 = 40
Subtracting 11 from both sides:
1x = 29
Dividing both sides by 1:
x = 29
Therefore, Marvin needs to make 29 trips to school to walk a total of 40 kilometers.
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pls give the answers
Answers
Answer:
1/10
Step-by-step explanation:
3/5 + (-1/2) =
= 3/5 - 1/2
= 6/10 - 5/10
= 1/10
Answer:
1/10
Step-by-step explanation:
This is right??
Use the calculator
+) Tickets to the spring festival are being sold online. The ticket price is $8 per person. The
expression 8t + 2 represents the total cost for t tickets, including a $2 service fee.
) What does the term 8t represent?
*) the price of the tickets
) the service fee
) the number of tickets
*) the total cost, including the service fee
Answers
Answer: What does the term 8t represent?
*) the price of the tickets
Step-by-step explanation:
Find the Area of this figure
Answers
Answer:
maybe 144
Step-by-step explanation:
Graph: y - 10 = -2(x – 10) Y χ y 30 20 10 X -10 10 20 -10 Draw Click or tap the graph to plot a point.
Answers
find all natural numbers n such that 1+3+5+7+...+(2n-1) sum is divisible by 4
Answers
n ∈ natural even numbers
Step-by-step explanation:
1 + 3 + 5 + 7 + … + (2n-1)
a = 1b = 2Uₙ = 2n - 1sum of the first n terms :
Sₙ = n/2(a + Uₙ)
Sₙ = n/2(1 + 2n - 1)
Sₙ = n/2(2n)
Sₙ = n²
∴ so, the solution of n is all natural even numbers
Refer to the attachment
y= x+14 , x+ 2y= 36, find x and y and show solution pls
Answers
Answer:
Solve the equation for x.
The simplified system is the arbitrary solution of the original system of equations.
Y=x+14
y=18−x2
Reorder 18
and −x2.
y=−x2+18
Y=x+14
Solve the equation for Y.
Y=−2y+50
x=36−2y
Reorder 36
and −2y.
x=−2y+36
Y=−2y+50
Step-by-step explanation:
Step-by-step explanation:
given
\(y = x + 14 \\ y - x = 14 \\ - x + y = 14\)
as equation 1
and
\(x + 2y = 36\)
as equation 2.
We will now use elimination method to solve simultaneous equations.
We will use equation 1 + equation 2 to eliminate x and solve for y.
\( - x + x + y + 2y = 14 + 36 \\ 0 + 3y = 50 \\ 3y = 50 \\ y = 50 \div 3 \\ = \frac{50}{3} \: or \: 16 \frac{2}{3} \)
Now substitute y into equation 1.
\(y = x + 14 \\ x + 14 = y \\ x = y - 14 \\ x = 16\frac{2}{3} - 14 \\ = 2 \frac{2}{3} \)