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Exercise 0.3 Suppose that vaccination strategies are implemented for newborns, so that not all newborns are considered susceptible. If the vaccination rate per capita is p, then a newborn becomes vaccinated with probability p. The modified model now takes the form ds = (1-p)µN - BS- dt - μS - PS N dI = BS- N (μ + y) I (0.3) dt dV = pμN +I+pS - µV dt (a) Find the basic reproduction number Ro by the next generation matrix method. (b) Analyze the stability of the disease-free equilibrium of this model

Exercise 0.3 Suppose that vaccination strategies are implemented for newborns, so that not all newborns are considered susceptible. If the vaccination rate per capita is p, then a newborn becomes vaccinated with probability p. The modified model now takes the form ds = (1-p)µN - BS- dt - μS - PS N dI = BS- N (μ + y) I (0.3) dt dV = pμN +I+pS - µV dt (a) Find the basic reproduction number Ro by the next generation matrix method. (b) Analyze the stability of the disease-free equilibrium of this model

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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Exercise 0.3 Suppose that vaccination strategies are implemented for newborns, so that not all newborns are considered susceptible. If the vaccination rate per capita is p, then a newborn becomes vaccinated with probability p. The modified model now takes the form ds = (1-p)µN - BS- dt S - μS - PS N = BS- N (μ + y) I (0.3) dt dV = pμN+I+pS - µV dt (a) Find the basic reproduction number Ro by the next generation matrix method. (b) Analyze the stability of the disease-free equilibrium of this model Exercise 0.4 Consider the following discrete time epidemic model Sn+1 = (1-p)v + Sn - B- BSn In - µSn N In+1 (0.4) = In + 3√n In - In - μIn N Rn+1 = vp + Rn+In - μRn i. Identify the model and describe the parameters involved in the model. ii. Determine the basic reproduction number Ro using the next generation matrix method. dI [
Transcribed Image Text:Exercise 0.3 Suppose that vaccination strategies are implemented for newborns, so that not all newborns are considered susceptible. If the vaccination rate per capita is p, then a newborn becomes vaccinated with probability p. The modified model now takes the form ds = (1-p)µN - BS- dt S - μS - PS N = BS- N (μ + y) I (0.3) dt dV = pμN+I+pS - µV dt (a) Find the basic reproduction number Ro by the next generation matrix method. (b) Analyze the stability of the disease-free equilibrium of this model Exercise 0.4 Consider the following discrete time epidemic model Sn+1 = (1-p)v + Sn - B- BSn In - µSn N In+1 (0.4) = In + 3√n In - In - μIn N Rn+1 = vp + Rn+In - μRn i. Identify the model and describe the parameters involved in the model. ii. Determine the basic reproduction number Ro using the next generation matrix method. dI [
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