5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN 0.25N(10 – N), N(0) = 2 %3D dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. a. Since this is an autonomous differential equation, perform a qualitative graphical analysis as discussed in Section 11.4. (i) Plot dN/dt versus N. Find and label all rest points (equilibrium points). (ii) Estimate the value where the rate of change of the disease is the fastest. Justify your answer. (iii) Plot N versus t for each of the following initial conditions: N (0) = 2, N(0) = 7, and N(0) 14. %3D

5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN 0.25N(10 – N), N(0) = 2 %3D dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. a. Since this is an autonomous differential equation, perform a qualitative graphical analysis as discussed in Section 11.4. (i) Plot dN/dt versus N. Find and label all rest points (equilibrium points). (ii) Estimate the value where the rate of change of the disease is the fastest. Justify your answer. (iii) Plot N versus t for each of the following initial conditions: N (0) = 2, N(0) = 7, and N(0) 14. %3D

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days. If the…

A: Given initial population = 120 So, for t=0, P=120 Using that we get: Quadruples in size every 1.5…

Q: Let S represent sales of a new product (in thousands of units), let L represent the maximum level of…

A: Introduction : Sales in math deals with rough estimating at times and it gives that big picture view…

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

Q: Is the following a homogenous differential equation? dy/dx = (x2y-y2x)/(x3-y3)

A: Let's find

Q: The population of a given city is governed by the law, dx/dt +5 = (0.02) x - (0.0001) x² where time…

Q: Five years ago a family was in debt $9.000. They are now in debt $10,000. Assuming their…

A: Given that indebtedness of the family is changing at a rate proportional to their indebtedness. Five…

Q: Consider the family of curves y = kx2, where k is a constant. (a) Show that the differential…

A: According to the given information, Consider a family curve:

Q: For non-negative PP, look at the differential equation: dP/dt=-0.1P(1-P/200) What are the…

Q: Most savings banks advertise that they compound interest continuously, meaning that the amount S(t)…

Q: An infectious disease is spreading at rate proportional to the number of people with the disease, or…

A: Given C= initial value= 118 For t=8, P=358 We have to find k

Q: in differentials of functions, if x change by a small amount dx then, what will happen to y?

A: Let a function be y=fx then here y is the dependent variable and x is the independent variable. The…

Q: A population N(t) is controlled by the ordinary differential equation (ODE) dN dt with values A =2,…

Q: The total number of reported cases of an illness in a large city tt days after the start of an…

A: Given the logistic differential equation is: y'=15600y1400-y…1 The standard form of a logistic…

Q: A polluted pool has an initial concentration of bacteria of 10* part/m³, while the a) acceptable…

A: Given first order differential equation is dCdt +0.05C=0 with C0=104 Here, t is time (in weeks) and…

Q: ccording to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is…

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: HU reports Covid-19 statistics daily for each US state as a function of time t, in days. These…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Suppose a population function P(t) the following differential equation. P is measured in millions…

A: Given dPdt = P(P-10) The slope field is plotted in Desmos slope field generator

Q: (d) Determine the (i) critical points of Eq. (3). (ii) limiting and threshold solutions from Eq.…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Von Bertalanffy's equation states that the rate of growth in length of an individual fish is…

Q: 1. A population grows continuously at the rate of 8% per year. How long does it take for the…

Q: dP dt =rP-ap² Think of a small population of fish growing in a public pond-P measures the number of…

A: The logistic model is a mathematical model that describes the growth of a population over time. It…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
dN
0.25N(10 – N), N (0) = 2
(a)
dt
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
a. Since this is an autonomous differential equation, perform a qualitative graphical
analysis as discussed in Section 11.4.
(i) Plot dN/dt versus N. Find and label all rest points (equilibrium points).
(ii) Estimate the value where the rate of change of the disease is the fastest. Justify
your answer.
(iii) Plot N versus t for each of the following initial conditions:
N(0) = 2, N(0) = 7, and N(0) = 14.
%3D
(iv) Describe the stability of each rest point (equilibrium point).

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Given the equation y=2x^2+2x, determine the differential dy for x=3 and dx=0.4. Round your answer to four decimal places if necessary.
Please help for c and d.
please show work
a continuing increase of the population on Earth eventually encourages settlement of the moon and mars. After colonization of the moon and mars, births rates continue to exceed death rates on earth, but life is hard away from earth so that the opposite is true elsewhere in the solar system. Nonetheles, the rising earth population constantly relocates the moon and Mars depending on the relative differences in population sizes. You have modelled the population dynamics via the following differential equations, where X1(t) is the Earth population at time t, X2(t) is the moon population, a and X3(t) is the population on mars. x`1 = -3/2 (x1-x2) - (x1-x3) + 3/2 x1 x`2 = -1/2 (x2 -x1) - 1/2(x2 -x3) - x2 x`3 = -1/2 (x3 -x1) - 1/2 (x3 -x2) - 1/2x1 a) if at time t=0 there are five bilion people on earth , and no one on moon and mars, Whats the population distribution far in the future? b) suppose instead that at a time t=0, 5/3 bilion people were on the moon, leaving 10/3 bilion on earth,…
This is Differential Equation, "Applications of FOODE"
2. (10%) Consider a tank filled with water with a draining tap at the bottom. The water level in the tank is a function of the time, h(t). It has been observed that the rate of change of h with respect to time is proportional to the square root of the water level h at a given time. Write the differential equation for the water level h(t) at a given time t. h(t) Тар exit