A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and noninfected persons, who are assumed to move freely among each other. Set up the model. Find the equilibrium solutions and indicate their stability or instability. Solve the ODE. Find the limit of the proportion of infected persons as time approaches infinity and explain what it means

A model for the spread of contagious diseases is obtained by assuming that the rate of spread is proportional to the number of contacts between infected and noninfected persons, who are assumed to move freely among each other. Set up the model. Find the equilibrium solutions and indicate their stability or instability. Solve the ODE. Find the limit of the proportion of infected persons as time approaches infinity and explain what it means

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

Similar questions

b. Find the equilibrium quantity.
Population equilibria can be stable or unstable. If, when a population deviates a bit from the equilibrium value (as populations inevitably do), it tends to return to it, this is a stable equilibrium; if, however, when the population deviates from the equilibrium it tends to diverge from it even further, this is an unstable equilibrium. Think of a ball in the pocket of a snooker table versus a ball balanced on a snooker cue. Unstable equilibria are a feature of Allee effect models such as the following. dN Use a phase portrait of the autonomous equation above to determine whether the nonzero equilibria that you found in question (2) are stable or unstable. (Hint: See Section 2.1 of the text. List the equilibria according to their stability. Enter your answers as comma-separated lists. If there are no equilibria in a certain category, enter NONE.) stable N = unstable N =
D. Only OLS assumption #2 is satisfied. The estimated regression is Y = 39+0.45X; Compute the estimated regression's prediction for the average score of students given 99, 129, or 155 minutes to complete the exam. Given 99 minutes, the estimated regression's prediction for the average score of students is Given 129 minutes, the estimated regression's prediction for the average score of students is Given 155 minutes, the estimated regression's prediction for the average score of students is (Round your responses to two decimal places.) Compute the estimated gain in score for a student who is given an additional 19 minutes on the exam. The estimated gain in score for a student who is given an additional 19 minutes on the exam is (Round your response to two decimal places.) Click to select your answer(s). W (DELL] o search PROU II
Find the linearization L(x) of the function at a. f(x) = x2/3, a = 64 %3! L(x) =
A linear regression line y = 80 + 0.2x is computed to predict the final exam score y on the basis of the first score x on the first test. Suppose Maria scores a 95 on the first test. What would be the predicted value of her score on the final exam? STEP 1: Substitute the value of the first test into the equation of the linear regression line. y = 80 + 0.2 STEP 2: Solve the equation of the linear regression line.y =
Exercise 4 In this regression we presented the results of the consumption fitted to the income in the period 1980-2005. We divide the data in two periods as 1980-1992 and 1993-2005. Decide if there is a structural change in the consumption-income regression in the two periods. The results for all data are as follows cons = 179 + 0.85 Income RSSfull = 265277 The results for 1980-1992(1) and 1993-2005 (2) are as follows 143 - 0.85 Income RSSfull = 13310 (1) cons = cons = 110 + 0.18 Income RSSfui = 163505 (2) fll
For Shock G: Suppose the economy starts in the long run equilibrium. Illustrate changes that the shock will cause in the short run (using AD-SRAS). Explain why each curve shifts. Determine how the price level and output will be affected in the short run. Mark the output gap on the diagram. Is the output gap positive or negative? Is the economy is booming, or is it in a recession? On the same diagram illustrate how the economy will adjust to the shock in the long run and explain the mechanism. Determine how the price level and output will be affected in the long run. G. The government increases its spending on national defense As a result of this shock, in the short run the (SRAS Curve/AD Curve) will shift? In consequence, in the short run prices and output will? In the short run, there will be a ? (negative/postive) output gap,which means there will be a ? (boom/recession) As time passes, because of high unemployment the wages in the economy will? (decrease/increase) As a…
Q13) assume the final regression equation from the stepwise regression analysis of the dependent variable cost (C) and the 10 potential independent variables is as follows: C = -5000 + 75 D + 0.4 S - 130 PT + 100 NE Given that the final model is valid, interpret the coefficient of S: On average, with each additional MWe of net capacity, the construction cost _____ while keeping other variables constant. A) decreases by $0.4 B) increases by $400,000 C) increases by $0.4 D) decreases by $400,000