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Epidemic model: The spread of an infectious disease, such as influenza, is often modelled using the following autonomous differential equation: dI = BI(N – I) – µI dt where I is the number of infected people, N is the total size of the population being modelled, B is a constant determining the rate of transmission, and µ is the rate at which people recover from infection. The parameters B, N,µ are positive constants. (a) Find all equilibria and their stability. (b) We define the basic reproductive number Ro as BN Ro := Show that for Ro > 1 the zero solution is unstable. (c) For the values B = 0.01, N = 1000, µ = 20 compute Ro and explain if in this situation an epidemic would break out or not.

Epidemic model: The spread of an infectious disease, such as influenza, is often modelled using the following autonomous differential equation: dI = BI(N – I) – µI dt where I is the number of infected people, N is the total size of the population being modelled, B is a constant determining the rate of transmission, and µ is the rate at which people recover from infection. The parameters B, N,µ are positive constants. (a) Find all equilibria and their stability. (b) We define the basic reproductive number Ro as BN Ro := Show that for Ro > 1 the zero solution is unstable. (c) For the values B = 0.01, N = 1000, µ = 20 compute Ro and explain if in this situation an epidemic would break out or not.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Epidemic model: The spread of an infectious disease, such as influenza, is often modelled using the following autonomous differential equation: dI = BI(N – I) – µI dt where I is the number of infected people, N is the total size of the population being modelled, B is a constant determining the rate of transmission, and u is the rate at which people recover from infection. The parameters B, N,µ are positive constants. (a) Find all equilibria and their stability. (b) We define the basic reproductive number Ro as BN Ro Show that for Ro >1 the zero solution is unstable. (c) For the values B = 0.01, N = 1000, µ = 20 compute Ro and explain if in this situation an epidemic would break out or not.
Transcribed Image Text:Epidemic model: The spread of an infectious disease, such as influenza, is often modelled using the following autonomous differential equation: dI = BI(N – I) – µI dt where I is the number of infected people, N is the total size of the population being modelled, B is a constant determining the rate of transmission, and u is the rate at which people recover from infection. The parameters B, N,µ are positive constants. (a) Find all equilibria and their stability. (b) We define the basic reproductive number Ro as BN Ro Show that for Ro >1 the zero solution is unstable. (c) For the values B = 0.01, N = 1000, µ = 20 compute Ro and explain if in this situation an epidemic would break out or not.
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